image
imagewidth (px) 4
512
| latex
stringlengths 1
188
| sample_id
stringlengths 16
16
| split_tag
stringclasses 1
value | data_type
stringclasses 1
value |
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4^{\sqrt{8}}+10-\frac{10}{9}-8
|
9790d7b3eab07bcc
|
train
|
human
|
|
(\begin{matrix}4\\ 2\end{matrix})
|
ff5f3b793bb2203b
|
train
|
human
|
|
(\begin{matrix}11\\ 4\end{matrix})
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9b80da473e90dda8
|
train
|
human
|
|
(\frac{n0-n1}{n0+n1})^{2}
|
fe69f75f269e9831
|
train
|
human
|
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\tilde{L}
|
c1f6af2d09493891
|
train
|
human
|
|
\frac{N_{G}}{N}
|
6a10cc9f34bd1494
|
train
|
human
|
|
\alpha_{1}=\frac{3-k}{4}
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1a878045bff0df2a
|
train
|
human
|
|
\frac{\partial F}{\partial y}=J
|
37483b1cacba9e73
|
train
|
human
|
|
AG(p)
|
66f5aa1cb2206692
|
train
|
human
|
|
X_{0}=x
|
3b74e884ea56b647
|
train
|
human
|
|
A^{\prime}[\vec{v}]_{B^{\prime}}=[T(\vec{v})]_{B^{\prime}}
|
8fe0da049234e267
|
train
|
human
|
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r=\frac{r_{a}r_{b}}{r_{c}}
|
81c116ac2971d233
|
train
|
human
|
|
y^{2}=\frac{1}{1+c\times e^{2x}}
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e187b54c58cb2fa1
|
train
|
human
|
|
\sqrt{nc}
|
ebb1cc625f73f668
|
train
|
human
|
|
\hat{y}_{t}
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2fe27c8432727274
|
train
|
human
|
|
n^{\underline{k}}
|
8ee6b1b885c92808
|
train
|
human
|
|
\frac{\pi}{3\sqrt{3}}\simeq0.6046
|
e3dec4b77aea373d
|
train
|
human
|
|
H^{i}(X,L^{-1})=0
|
80da3f702f8280b3
|
train
|
human
|
|
|f_{n}(x)|\le\frac{1}{2n}
|
30696f1bad274ade
|
train
|
human
|
|
e^{\cdot\frac{(F\cdot M)^{0}}{0{(s_{F})}^{0}}}
|
066bb817712233dd
|
train
|
human
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|
(\begin{matrix}n\\ q\end{matrix})
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a70b8481e15d7d28
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train
|
human
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\frac{(A\times B)\cdot(A\times N)}{||A\times B||||A\times N||}
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8627e0506e6ebc55
|
train
|
human
|
|
B(p,q)=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}
|
fcc27906178371e0
|
train
|
human
|
|
\frac{449}{7}+9^{\sqrt{106}}
|
ef91a0d39b92af02
|
train
|
human
|
|
||\vec{E}||=||\vec{N}||=1
|
364f54f61f400c60
|
train
|
human
|
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\frac{E_{c,t_{0}}}{p_{c,t_{0}}}=q_{c,t_{0}}
|
f2ff1d5f6991b31d
|
train
|
human
|
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W_{i+1}=exp(\frac{...}{...})
|
85df626724695e74
|
train
|
human
|
|
\sqrt{390}^{\sqrt{7}}+\frac{6}{\sqrt{10}}
|
f575b44e2e20d769
|
train
|
human
|
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\frac{da}{dN}=C(\Delta K)^{m}
|
27cec1a9aaee6111
|
train
|
human
|
|
\frac{ml}{min}
|
95ad8070aa5e62bf
|
train
|
human
|
|
((387+\sqrt{261})+\frac{\frac{8}{7}}{\sqrt{8}})
|
97fa4b68d39905f4
|
train
|
human
|
|
\frac{1}{2}+\frac{1}{6}+\frac{1}{21}
|
99468169d1d568b3
|
train
|
human
|
|
[x,x+\sqrt{2x}],x\ge2
|
a3ad55520d3626b3
|
train
|
human
|
|
\phi(x)=\frac{e^{-x^{2}}}{\sqrt{\pi}}
|
886b847befc6d000
|
train
|
human
|
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\frac{\partial\psi}{\partial t}=P\psi
|
3ace43c017b71cdd
|
train
|
human
|
|
|a|<1
|
fa86a12a3610392b
|
train
|
human
|
|
\frac{1\pi}{\sqrt{\frac{Gz_{lbn}}{y^{3}}}}
|
25cc0d28ceb7dc3b
|
train
|
human
|
|
n_{i}=\frac{g_{i}}{e^{\alpha+\beta\epsilon_{i}}+1}
|
88ce27253581a20c
|
train
|
human
|
|
[\begin{matrix}1&0\\ G&1\end{matrix}]
|
66e81460b3b57a67
|
train
|
human
|
|
\int_{X}\int_{Y}\int_{Z}
|
4e78fd418450f93d
|
train
|
human
|
|
\sqrt{!}
|
3f180073864006b7
|
train
|
human
|
|
\tilde{\sigma}(xG^{\prime})=\sigma(x)G^{\prime}
|
ab8d3c36953eabc1
|
train
|
human
|
|
(\frac{7}{2}+201)^{4-9}
|
931a028bf02732b4
|
train
|
human
|
|
\frac{dh}{dr}=\frac{\Omega^{2}r}{g}
|
33b0a95c04cd8fed
|
train
|
human
|
|
\rho(u)=\frac{1}{\sqrt{1-\frac{u^{4}}{r^{4}}}}
|
7a494e47d0430946
|
train
|
human
|
|
\sigma=\frac{My}{I}=Ey\frac{\partial^{2}u}{\partial x^{2}}
|
6f7ac2227171fe98
|
train
|
human
|
|
{\sum_{n=1}^{\infty}}^{\prime}\frac{1}{n}
|
66e4718d268a450e
|
train
|
human
|
|
g\otimes C[t,t^{-1}]
|
7260fab864c63bf3
|
train
|
human
|
|
\frac{Dv}{Dt}+u\beta y=-\frac{\partial\phi}{\partial y}
|
e52a7595407bdc4f
|
train
|
human
|
|
A=G\frac{\lambda^{2}}{4\pi}
|
6dccc253ee77ad54
|
train
|
human
|
|
=120\pi
|
ec51a752a792f680
|
train
|
human
|
|
\hat{A}
|
fa053d4ce8f021ca
|
train
|
human
|
|
\sqrt{y}
|
ec3e871506623550
|
train
|
human
|
|
[\begin{matrix}3&0\\ 0&-2\end{matrix}]
|
e043274b6313aacd
|
train
|
human
|
|
\sqrt{12\times RV}
|
60e71bfb446f0cef
|
train
|
human
|
|
\mu_{T}=(\pi_{ST})_{*}(\mu_{S})
|
4c0da555835a33e0
|
train
|
human
|
|
D_{j}=-i\frac{\partial}{\partial x_{j}}
|
d1596731b6d8fe68
|
train
|
human
|
|
\overline{\phi}
|
6ded0aab3ed1f60b
|
train
|
human
|
|
\frac{d\phi}{dx}
|
eecd6210e39591a5
|
train
|
human
|
|
MPK=\frac{\partial F}{\partial K}
|
77c8cf93eaf713eb
|
train
|
human
|
|
I_{2}=\int f(\theta)d^{3}x
|
2b09c51899522363
|
train
|
human
|
|
\frac{ISO_{B}\Delta t_{B}}{ISO_{N}\Delta t_{N}}
|
9c95433bd3077de4
|
train
|
human
|
|
\prod_{i=1}^{m}Q(\beta_{i}z)
|
dd3370198ce0632c
|
train
|
human
|
|
W(z)=\prod_{j\ge1}(1-z/2^{j})
|
9859dba6e4c11486
|
train
|
human
|
|
\int_{L}f(z)dz
|
f03f0dfc78f5cee8
|
train
|
human
|
|
\langle\psi|A|\psi\rangle
|
ebc106e4746b1b9f
|
train
|
human
|
|
Q=ubh
|
35986e7c33151445
|
train
|
human
|
|
Im(\frac{tanh(x+iy)}{x+iy})
|
3d7127e1f4ff4561
|
train
|
human
|
|
\sqrt{\frac{1}{126}}
|
1906d1b0edc4cfa8
|
train
|
human
|
|
w=19.5
|
2b41fb007d8c6f0d
|
train
|
human
|
|
\sum k(\begin{matrix}n\\ k\end{matrix})
|
a396c75be4b410ac
|
train
|
human
|
|
\frac{1}{\sqrt{1-x^{2}}}
|
bbea576b91eccb0c
|
train
|
human
|
|
(-\Delta)^{\frac{1}{2}}u=f
|
eaa8071f1836a0f7
|
train
|
human
|
|
b=\frac{D}{e^{\int_{s_{4}}^{x}P(s)ws}}
|
a6a6102f0c81d69d
|
train
|
human
|
|
(\frac{\sqrt{332}}{7}-\sqrt{81}+6)
|
3b71abf55ba715c6
|
train
|
human
|
|
x_{0}\in R^{n}
|
00d7dbaaebc93c25
|
train
|
human
|
|
s\{\begin{matrix}2\\ 2\end{matrix}\}
|
9e03643014163106
|
train
|
human
|
|
c=(1,2)
|
a1e421d14c491bcd
|
train
|
human
|
|
d_{\hat{K}}
|
dbe6b586a8d5efa6
|
train
|
human
|
|
\hat{p}=1
|
3fe106672705f520
|
train
|
human
|
|
\frac{e^{\cdot\frac{x^{8}}{8\sigma^{8}}}}{\sqrt{8\vartheta}\sigma}
|
078fc55a49e1975f
|
train
|
human
|
|
W_{0}^{1,p}(X)\subseteq L^{\varphi}(X)
|
14bcba1b720e75f9
|
train
|
human
|
|
z=\frac{R(t_{0})}{R(t_{e})}-1
|
257d1657890fbf08
|
train
|
human
|
|
B=\int_{0}^{1}L(X)dX
|
e706e1c75effb7a2
|
train
|
human
|
|
\frac{x^{2}-x+1}{5x^{2}+3}
|
1da63938d195cd37
|
train
|
human
|
|
K_{Ic}=\sqrt{E^{*}J_{Ic}}
|
32495d86de0bd027
|
train
|
human
|
|
2^{7/12}=\sqrt[12]{128}
|
355faef7aa129fb3
|
train
|
human
|
|
\frac{\sqrt{\frac{(d_{1}u)^{d_{1}}d_{5}^{d_{5}}}{(d_{1}u+d_{5})^{d_{1}+d_{5}}}}}{uC(\frac{d_{1}}{5},\frac{d_{5}}{5})}
|
515e1ad65cf1dadb
|
train
|
human
|
|
273^{4}+26+403
|
8592d2f66d8df573
|
train
|
human
|
|
\frac{9}{4}-218+1^{7}
|
14205dace4b332c3
|
train
|
human
|
|
\sqrt{\mu}
|
9f8e0b6a661528b1
|
train
|
human
|
|
A^{T}=A
|
85580480e8fddec0
|
train
|
human
|
|
2am(\frac{t}{2}|4)
|
ca01ebdcd35f9e8b
|
train
|
human
|
|
\hat{6}
|
699d63d380847aba
|
train
|
human
|
|
(\frac{\frac{297}{265}}{419})^{5^{7}}
|
71c9f8296a8504bb
|
train
|
human
|
|
C_{x}(t_{1}-t_{2},0)
|
5bb76f8c3560eada
|
train
|
human
|
|
{177^{323}}^{\sqrt{6}\cdot219}
|
6886bfc3d39926d5
|
train
|
human
|
|
\frac{dS}{dt}-\frac{\dot{Q}}{T}\ge0
|
bade0d9356ca5243
|
train
|
human
|
|
\beta=\frac{\partial f}{\partial y}
|
b78bb9a8151eeaa0
|
train
|
human
|
|
f^{(3)}(x)=120x^{3}
|
43fa40c0d6267cc6
|
train
|
human
|
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