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f^{*}=min_{x\in R^{n}}\{f(x)\}
|
000000200
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
[x,x+\sqrt{2x}],x\ge2
|
000000201
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\sqrt{n_{1}n_{2}/(n_{1}+n_{2})}g
|
000000202
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\{0,9\}^{7^{7^{\aleph_{0}}}}
|
000000203
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
l_{4}^{l_{2}^{l_{3}^{-^{-^{-}}}}}
|
000000204
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
f,g\in\pi_{n}(X,x_{0})
|
000000205
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
n^{\underline{k}}
|
000000206
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
cov(X,Y)=\frac{1}{2}+\frac{1}{\pi}
|
000000207
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\eta_{mean}=\frac{\sum_{i}p_{i}t_{i}\eta_{i}}{\sum_{i}p_{i}t_{i}}
|
000000208
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
0\le\underline{d}(\vec{X})\le\overline{d}(\vec{X})\le n
|
000000209
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
V=f(t)=V_{0}e^{-\frac{t}{\tau}}
|
000000210
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(\frac{N-1}{N})
|
000000211
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
41-164^{{3^{300}}^{6}}
|
000000212
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
a=\frac{\sqrt{3}}{3}
|
000000213
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
distance=\frac{c\delta t}{2}
|
000000214
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\beta(g)=\lambda\frac{\partial g}{\partial\lambda}
|
000000215
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
c_{\epsilon}^{\rho}
|
000000216
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
2y\frac{dy}{dx}=3x^{2}-1
|
000000217
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\tilde{Y}
|
000000218
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(\begin{matrix}k\\ 2\end{matrix})=\frac{k(k-1)}{2}
|
000000219
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\int_{0}^{x}f(t)dt
|
000000220
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
[F^{[l]},F^{[l^{\prime}]}]=0
|
000000221
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{u}
|
000000222
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
||p_{\sigma}||\in[0,\alpha\sqrt{n}]
|
000000223
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
b=a\sqrt{1-\epsilon^{2}}
|
000000224
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
R=(0,w)\times(0,h)
|
000000225
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\overline{V^{\prime}L}
|
000000226
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(1-\frac{1}{e})
|
000000227
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(\frac{96}{387})^{\frac{10}{2}}
|
000000228
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
n\hat{F}_{n}(t)
|
000000229
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{48}{2(9+3)}
|
000000230
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(\begin{matrix}50\\ 3\end{matrix})=19,600
|
000000231
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
dS=\frac{dQ}{T}
|
000000232
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{w}_{2}
|
000000233
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
OB
|
000000234
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
A_{p}(\kappa)=\frac{I_{p/2}(\kappa)}{I_{p/2-1}(\kappa)}
|
000000235
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
P=-(\frac{\partial F}{\partial V})_{T}
|
000000236
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
q(x,t)=\delta(\underline{x},t)-r(\underline{x},t)
|
000000237
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
N=m_{w}g+T
|
000000238
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{df}{dz}=f
|
000000239
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
p(0)=\sqrt{2\hbar\rho}
|
000000240
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\iint f(x,y)dxdy
|
000000241
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\Phi=\int E(\hat{e}_{\angle}\cdot dA)
|
000000242
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
||
|
000000243
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
g(x)=min(\frac{x}{\alpha},1)
|
000000244
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{1}{1},\frac{4}{2},\frac{10}{3},\frac{20}{4},...
|
000000245
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{D}=D
|
000000246
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\lambda_{0}=\frac{h}{m_{0}c}-
|
000000247
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
|\psi^{\prime}\rangle=U_{\alpha}|\psi\rangle
|
000000248
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
[\begin{matrix}x^{\prime}\\ y^{\prime}\end{matrix}]
|
000000249
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
|\Omega\rangle
|
000000250
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\tilde{\omega}
|
000000251
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{1}{\sqrt{1-x^{2}}}
|
000000252
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{dy}{dx}
|
000000253
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
J=[\begin{matrix}0&I\\ -I&0\end{matrix}]
|
000000254
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
[\begin{matrix}-1\\ 1\end{matrix}]
|
000000255
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
x^{\frac{n+1}{2}}\notin Z/nZ
|
000000256
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
K_{\lambda g}=\frac{1}{\lambda}K_{g}
|
000000257
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{1}{4n}p^{2}\cdot cot(\pi/n)
|
000000258
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
q=\frac{1}{\sqrt{1\cdot\frac{v^{5}}{c^{5}}}}\xi
|
000000259
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{log_{e}(x)-log_{e}(a)}{log_{e}(b)-log_{e}(a)}
|
000000260
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\int\frac{1}{u}du
|
000000261
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
(\begin{matrix}u&&-v\\ v&&u\end{matrix})
|
000000262
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
V=x^{2}+y^{2}+z^{2}
|
000000263
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
C
|
000000264
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\varphi=\frac{3}{2}\eta
|
000000265
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
u_{12}=\frac{z_{1}-z_{2}}{\sqrt{2}}
|
000000266
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
S_{ab}=(\psi_{a}^{-},\psi_{b}^{+})
|
000000267
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
e=\sqrt{1-(b/a)^{2}}
|
000000268
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
x_{min}
|
000000269
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
s\{\begin{matrix}5\\ 4\end{matrix}\}
|
000000270
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
f(x)=\int_{a}^{x}g(t)dt
|
000000271
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\forall\epsilon_{1}>0\exists k_{1}
|
000000272
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
[\frac{2n\pi}{3};\frac{2(n+1)\pi}{3}]
|
000000273
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\{1,2,6,12\}
|
000000274
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
x^{-}=\frac{t-x}{\sqrt{2}}
|
000000275
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\overline{(\frac{\alpha}{\pi})_{3}}=(\frac{\overline{\alpha}}{\overline{\pi}})_{3}
|
000000276
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
W^{\mathbb{C}}\cong W\oplus\overline{W}
|
000000277
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
S_{22}=\frac{-T_{21}}{T_{22}}
|
000000278
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{g}
|
000000279
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\tilde{y}=\tilde{w}=h(\tilde{X})-\tilde{Y}
|
000000280
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{x}_{1}
|
000000281
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
E^{g}[X|F_{t}]:=Y_{t}
|
000000282
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
S^{+}=T^{+}
|
000000283
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{d^{2}y}{dt^{2}}
|
000000284
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\tilde{T}_{i}:G/G^{\prime}\rightarrow H_{i}/H_{i}^{\prime}
|
000000285
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}\sqrt{\gamma_{2}}
|
000000286
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{\partial p}{\partial z}+\rho g=0
|
000000287
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\sqrt{p}=\frac{b}{\sqrt{a}}
|
000000288
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\mathbb{Q}
|
000000289
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{dB}{dG}
|
000000290
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho\vec{v})=0
|
000000291
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
x+1\notin J
|
000000292
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
P_{L}=I_{R}^{2}\cdot ESR
|
000000293
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
m\ge(\begin{matrix}k\\ 2\end{matrix})
|
000000294
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
y_{t}=y_{t-1}+c+e_{t}
|
000000295
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\hat{w}(f)
|
000000296
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\prod_{i=1}^{n}
|
000000297
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
r<m<n
|
000000298
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
|
\frac{df}{d\tau}=\frac{1}{2\pi i}f^{\prime}(\tau)
|
000000299
|
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|
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