Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity argument revisited: geometry of root clustering via symmetric
  products   We study the spaces of polynomials stratified into the sets of polynomial
with fixed number of roots inside certain semialgebraic region $\Omega$, on its
border, and at the complement to its closure. Presented approach is a
generalisation, unification and development of several classical approaches to
stability problems in control theory: root clustering ($D$-stability) developed
by R.E. Kalman, B.R. Barmish, S. Gutman et al., $D$-decomposition(Yu.I.
Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A.
Fam, J. Meditch, J.Ackermann).
  Our approach is based on the interpretation of correspondence between roots
and coefficients of a polynomial as a symmetric product morphism.
  We describe the topology of strata up to homotopy equivalence and, for many
important cases, up to homeomorphism. Adjacencies between strata are also
described. Moreover, we provide an explanation for the special position of
classical stability problems: Hurwitz stability, Schur stability,
hyperbolicity.

31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an