image
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512
latex
stringlengths
1
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sample_id
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16
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g=\frac{g_{0}}{({1+\frac{v^{6}}{c^{6}})}^{9/6}}
641253913424c350
train
human
\sqrt{-i}
a6fe3be99d25ec6f
train
human
k_{B}T=\frac{m\overline{v^{2}}}{3}
151569a1568b9d7c
train
human
\hat{A}_{n,\alpha}^{\dagger}
8e69c7909cbc0cdd
train
human
{d^{\chi}}^{m}
29b9a9f32e660595
train
human
\neg\psi\vee\neg\varphi
3554385faafc0725
train
human
nDCG_{p}=\frac{DCG_{p}}{IDCGp}
a1c698e65fb9d28c
train
human
\overline{1^{1/N}}=1^{-1/N}
8380afe6ac62c3eb
train
human
\overline{X_{j}}
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train
human
y=f(x)=\frac{a+bx}{c+dx}
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train
human
D(n)=\sum_{k=0}^{n}(\begin{matrix}n\\ k\end{matrix})^{2}2^{k}
fbd7fc1d92f768b9
train
human
(y^{\prime}(0),y(0))=(1,0)
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train
human
\hat{z}(t)
dd90d388cdd4d995
train
human
\sqrt{nN}
b0c1fd90271e6a13
train
human
lim_{n\rightarrow\infty}\frac{N(A,n)}{n}
52d21367cf412ae8
train
human
\sqrt{2}
58c2bfc5c52ca071
train
human
\prod_{p\le X}\frac{N_{p}}{p}
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train
human
\frac{5^{500}}{7}+(5\cdot8)/\sqrt{170}
317cc88cd6f45ea9
train
human
V_{s}\sqrt{n}
417914ca643c0921
train
human
\frac{sin\alpha}{\sqrt{2-sin^{2}\alpha}}
d467f1a135d8b6f7
train
human
x^{x^{x^{+^{+^{+}}}}}
8cd0c97d9f8e2175
train
human
\Delta_{P2}
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train
human
K=\frac{L_{H}-L_{L}}{L_{H}}
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train
human
\forall p\forall x(x\notin p)
206a0f94e047fc00
train
human
p=\prod_{i=1}^{n}p_{i}
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train
human
q=[\begin{matrix}u\\ d\end{matrix}]
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train
human
E=\frac{1}{4\pi\epsilon_{0}}\frac{q}{r^{2}}\hat{r}
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train
human
\int dx=x+C
636daa83082519ac
train
human
e=\frac{1}{1+\delta}
b08653b68adf3277
train
human
H_{0}(x)=\frac{e^{-x^{2}/2}}{\sqrt{2\pi}}
ea77559fe85c1ad2
train
human
\hat{v}_{k}
412fd4ce943eb0f8
train
human
\frac{\frac{99}{6}}{\frac{147}{4}-94}
806ba936abccbcf4
train
human
\beta=\frac{0}{\sqrt{\sum_{\upsilon=0}^{s}\frac{j^{2}}{v_{\upsilon}^{2}}}}
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train
human
\tilde{P}_{*}
8e256840cca52e5b
train
human
\frac{q^{2}}{4}+\frac{p^{3}}{27}<0
c36b9618581f0ef5
train
human
M[\cdot]:=D(F\circ G)[\cdot]
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train
human
\frac{1}{\sqrt{1-\delta}}
3d4df931c2a0fd68
train
human
c=\sqrt{n}
210fdbf631e8aff6
train
human
\zeta(-3)=\frac{1}{120}
5e204ab7492190ea
train
human
\hat{\eta}
531a628526164261
train
human
\frac{\partial u_{i}}{\partial x_{i}}=0
cd941aae3bf35840
train
human
\frac{|F_{m}|}{L}=\frac{\mu_{0}}{2\pi}\frac{|I|^{2}}{|r|}
8aa02fe9d15899fc
train
human
\overline{X}_{0}
cff2e78e61bcdaf0
train
human
\gamma=\frac{5}{3}\approx1.67
fd31bf0834785cdb
train
human
j^{l}=N_{L/K}(A)O_{K}
1a7808a01e74d27b
train
human
a_{c}^{3}=\frac{9R^{2}\gamma\pi}{4E^{*}}
59b2ccbc825c23b4
train
human
|(-x)^{-x}|=\frac{1}{|x^{x}|}
8b5fe44f5c5d5197
train
human
n_{1},n_{2},n_{3}
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train
human
\frac{(4+285-95)}{\frac{\frac{360}{500}}{41}}
f910659390d8eba2
train
human
ye^{2\pi ix/10}
6de84bf8dcc23c7a
train
human
\frac{\frac{268+7}{236}}{88^{\sqrt{347}}}
ff0cd9577dd89425
train
human
{{7^{5}}^{4}}^{(\frac{6}{101})^{6}}
6ec1e54cd667899e
train
human
\tilde{B}_{6}
504f2c45b5b9d3bd
train
human
(\begin{matrix}r1\end{matrix})(\begin{matrix}r-11\end{matrix})
d7e562ea81ac45a7
train
human
2Y\dot{\varphi}_{r}
adabb3dfd9a670fe
train
human
(A+B\sqrt{C})^{n}
fba524c486089ff8
train
human
\overline{x}=\sigma_{\overline{x}}^{2}\sum_{i=1}^{n}x_{i}/\sigma_{i}^{2}
07f6ab1d6929f881
train
human
a\odot b=\frac{a}{b}+\frac{b}{a}
b428006b606c67b9
train
human
Q=\int j_{0}a^{3}d^{3}x
b9e5951e10bcd8ac
train
human
\sum_{i,j}a_{ij}x^{i}y^{j}
345e371b1e70fc75
train
human
\tilde{d}=\frac{gcs}{\sqrt{\frac{g_{7}g_{2}}{g_{7}\cdot g_{2}}}}
909e712d4fade984
train
human
A\underline{\delta}B
aef0251929e8b3c8
train
human
\frac{2rect(\frac{\nu}{2})}{\sqrt{1-\nu^{2}}}
42c079d4931eefef
train
human
x<\frac{1}{3}log(\frac{4}{3D})
492a886114eba46e
train
human
\int_{0}^{1}n(x)dx
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train
human
h\le(\begin{matrix}k+l\\ k\end{matrix})
afed1e6792575024
train
human
\prod_{i=1}^{n}a_{i,\sigma_{i}}
c4b2e1ac71cb261b
train
human
T\Delta S_{int}-Q\ge0
21ec2853a2326fbd
train
human
\sigma=\int\rho ds
2b2b5068a926ba1f
train
human
\frac{\sqrt{157}}{394}\cdot(90\cdot1)
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train
human
B=[\begin{matrix}1&0\\ 0&0.6\\ 0&0.8\end{matrix}]
a694396596760a86
train
human
\frac{e^{\cdot\frac{x^{8}}{8\sigma^{8}}}}{\sqrt{8\vartheta}\sigma}
7108a4630cd79081
train
human
d=r_{1}+r_{2}
22dbf134127b7e57
train
human
\tilde{N}
38470bb62b16de82
train
human
0=MU_{x}+MU_{y}\frac{dy}{dx}
3c9bc7b4884ac348
train
human
\prod_{j=1}^{s}[\frac{a_{j}}{b^{d_{j}}},\frac{a_{j}+1}{b^{d_{j}}}]
55afcdd95d012335
train
human
\tilde{u}
ff0450ad5310e297
train
human
R^{2^{n}-1}
cc7857615ff2c20f
train
human
\int_{Q}r^{2}dm
2b76a6869090fe60
train
human
\hat{r}_{j}
f0d746d47f3632f1
train
human
\sqrt{17}
ae647011f48b4dac
train
human
R_{E}=c/\sqrt{4\pi G\rho}
e7ab385e6aa70946
train
human
v=\frac{|a-b|}{2}
8ce90c2a46c45d2a
train
human
t^{\prime}=t-\frac{|r-r^{\prime}|}{c}
a71618ea9589f40d
train
human
U=\int f(v)E(v)dv
fffe3427cfe7a245
train
human
\frac{a_{i}}{a_{j}}
4e40ef6762e53c24
train
human
\tilde{C}_{7}
b4ab238b5f63411f
train
human
n\le\frac{N-1}{2}
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train
human
\infty\notin A
ed89243d680430a0
train
human
\sqrt{2/(N-1)}
aa7bc9304e7fb839
train
human
m\frac{d^{2}x}{dt^{2}}+kx=0
86c9d839249ce7bd
train
human
\epsilon=\cdot\frac{log\frac{\tau_{\lambda_{1}}}{\tau_{\lambda_{9}}}}{log\frac{\lambda_{1}}{\lambda_{9}}}
419b34f8f9f5e039
train
human
M_{i}(n)=\prod_{j=1}^{n}\mu_{i}(j)
b68dc060f01b2f5a
train
human
T_{L}=\frac{T_{N}}{cos(\theta)}
0475485f18919d3f
train
human
\sqrt{390}^{\sqrt{7}}+\frac{6}{\sqrt{10}}
1d581145a563067f
train
human
\gamma=2+\frac{k_{0}+a}{m}
2fb9a4d9a34963db
train
human
\sqrt{\langle x,x\rangle}=||x||_{p}
f2a591a2ddc0aa24
train
human
\tilde{C_{n}^{m}}=-\frac{C_{n}^{m}}{\mu R^{n}}
c0f21ea9026c3012
train
human
r=a\frac{sin(-\theta+\theta_{0})}{sin(-2\theta+\theta_{0})}
648a823dc6117269
train
human
k=\Omega(\sqrt{nlogn})
e7b9fa2486d9cc01
train
human