image
imagewidth (px) 4
512
| latex
stringlengths 1
188
| sample_id
stringlengths 16
16
| split_tag
stringclasses 1
value | data_type
stringclasses 1
value |
|---|---|---|---|---|
\langle\rho\rangle\frac{\partial\tilde{u}}{\partial t}=-\nabla\tilde{p} | be181baba010f266 | train | human |
|
n=513 | 5c118286f7e908f8 | train | human |
|
e^{xlog4}=x\cdot x\cdot x\cdot x | cee4b544b76b13f2 | train | human |
|
Z_{(a_{\delta})} | 259e41ff804e9256 | train | human |
|
\int_{a}^{b}f(x)dv(x) | 0ba8fe1e97486b62 | train | human |
|
\frac{\Delta Q}{\Delta t}=-kA\frac{\Delta T}{\Delta x} | dd97a4cf426764e9 | train | human |
|
y(x)=(\begin{matrix}y_{1}(x)\\ y_{2}(x)\end{matrix}) | cacb666b79b957e6 | train | human |
|
\frac{\partial}{\partial g_{i}}(g_{j})=\delta_{ij} | 67970a4f1559bb82 | train | human |
|
\tilde{O}(log^{3}n)) | d25e44fa4f57f119 | train | human |
|
\frac{d\psi}{dt} | 3782010d106c4c3e | train | human |
|
(\begin{matrix}0&-1\\ 1&0\end{matrix}) | 9db60ccdb3074d8b | train | human |
|
d\vec{B}=\frac{\mu_{0}}{4\pi}\frac{Id\vec{l}\times\vec{r}}{r^{2}} | 48e3602cb3ff2a06 | train | human |
|
O(\frac{1}{\sqrt{N}}) | 8e64903b8c6bbe14 | train | human |
|
STUVWXYZ | ad4e2a43436c3a85 | train | human |
|
D\overline{D} | 00a0fbd63ee9d87a | train | human |
|
\frac{(\frac{7}{362}+8)}{\sqrt{3}^{3}} | 95de408af24d9244 | train | human |
|
PQ | b8b3d437a5167c16 | train | human |
|
q=\sqrt{y_{c}^{3}g} | 9f3cd34de66193bd | train | human |
|
\underline{x}\in\mathbb{R}^{n} | 7ddb5cd77c204d2b | train | human |
|
\frac{\partial J}{\partial x}=\frac{\partial R}{\partial x}\psi | c1c5ee1004817ac0 | train | human |
|
\nabla_{X}g=0 | 7c81c668960134be | train | human |
|
x=50\frac{1}{2}-49\frac{1}{2}=1 | 9be1bcf92f6b2c99 | train | human |
|
\mu=arcsin(\frac{1}{M}) | 61a8e5494eb0abee | train | human |
|
\frac{1}{|a|}\cdot tri(\frac{\nu}{2\pi a}) | 685308837be1e1b7 | train | human |
|
a\notin A | 833d19cb6c12361f | train | human |
|
/R | 7709bad0ae560243 | train | human |
|
Y=\frac{X}{1-e^{X}} | a742c10f388a8028 | train | human |
|
v\notin C | 6582b0d654148bb9 | train | human |
|
(\begin{matrix}n\\ t\end{matrix}) | f643b1e0b270565f | train | human |
|
\partial_{y}=\frac{\partial}{\partial y} | e1ccf5a96e9e40df | train | human |
|
\int_{0}^{1}2x^{3}+3dx | e880e8b446f6d724 | train | human |
|
[G]_{o}>>>[H]_{o} | cef183286d7a26ef | train | human |
|
\frac{k(k+1)}{2}+(k+1) | bbe863ee93feee12 | train | human |
|
\int xsinx^{2}dx | 07e03ef698cb02c5 | train | human |
|
\hat{A}_{2}=\frac{1}{N}\sum_{n=0}^{N-1}x[n] | 99698ba982c3c41c | train | human |
|
y=\sqrt{b^{2}-\frac{b^{2}x^{2}}{a^{2}}} | c9ce312e6f646838 | train | human |
|
\sum_{n=1}^{\infty}(\zeta(2n)-1)=\frac{3}{4} | 83d26f8a2eecbe79 | train | human |
|
\frac{1}{2}\mu v_{(}rel)^{2}=\Delta | 663fc762e35f0a62 | train | human |
|
\frac{n_{1}}{n_{2}}sin(\theta_{I}) | c46cb1c1ef552c99 | train | human |
|
S_{11}=S_{22}=1 | 24786af5b356c2b2 | train | human |
|
[\begin{matrix}4\\ 1\\ 8\end{matrix}] | 299fe110a393e760 | train | human |
|
f:R^{k}\rightarrow R | 88a94bb6f5d1cd48 | train | human |
|
A_{i,j,k} | af8407942f841046 | train | human |
|
\frac{2^{b-a}}{10^{b}p^{k}q^{l}\cdot\cdot\cdot} | f18f8d376a711a19 | train | human |
|
x_{0}=1 | 4683388cc36a8e23 | train | human |
|
\frac{(380^{9}+\sqrt{10})}{\frac{9}{7}} | 302a8e15c1b61004 | train | human |
|
4^{4^{+^{+^{+^{n}}}}} | 9a24bc710585a371 | train | human |
|
\frac{{409^{7}}^{142}}{{7^{276}}^{62}} | a74681dcdc259bea | train | human |
|
cf(\prod A/D)<\lambda | 279c2a727647e931 | train | human |
|
\epsilon:=\frac{1}{n}tr | 8a9bc184f244b600 | train | human |
|
\frac{\sqrt{x+2}}{x^{2}-3} | 9ca71d93a87a2c90 | train | human |
|
\overline{hu^{2}}+\frac{1}{2}k_{ap}g_{z}h^{2} | 140882c74928a6aa | train | human |
|
cos\theta=\frac{d_{2}\cdot q}{|d_{2}||q|} | 66accc6dbeb15f69 | train | human |
|
(\frac{7}{2}+201)^{4-9} | e53455f220d3fbda | train | human |
|
xsin(\frac{1}{x}) | 6b9c8359f0074a93 | train | human |
|
V(\tilde{\beta}) | bcab004893afd737 | train | human |
|
M=[\begin{matrix}0&1\\ -1&0\end{matrix}] | 41f3fa4878b63e03 | train | human |
|
4.\overline{2} | 02b4ff904a174d59 | train | human |
|
t_{c}=\sqrt{\frac{m}{k}} | e53e20aead2577ed | train | human |
|
ab\le\frac{a^{p}}{p}+\frac{b^{q}}{q} | fed2a68e2680ab05 | train | human |
|
\nu_{f}^{\sigma_{j}} | 595598255131d91d | train | human |
|
\int_{0}^{1}n(x)dx | d2c352bd95d5151b | train | human |
|
\sum_{j,k=1}^{3}\epsilon_{jkl}=0 | 5ef2fb1fb1f17fa8 | train | human |
|
\rho\in H_{A}\otimes H_{B} | b4460988485edd78 | train | human |
|
1/\sqrt{2} | fd014e5396056d0f | train | human |
|
Z_{0}=\sqrt{L/C} | 97d89c443eb59225 | train | human |
|
liminf\frac{\varphi(n)}{n}=0 | 2ab3b4c68303d3f1 | train | human |
|
\tilde{B}_{3} | 50f37f7f2fde6849 | train | human |
|
q=\frac{\partial\psi}{\partial n} | 4dff17e4fb65591d | train | human |
|
\frac{r^{\prime}}{\sqrt{5-\frac{r^{8}}{6}}}\ge5 | c973571452547e2e | train | human |
|
|\alpha-\frac{p}{q}|>\frac{C(\alpha,\epsilon)}{q^{2+\epsilon}} | bc053d40872a56de | train | human |
|
\frac{2}{a+b} | 24f4b0c907a59f5e | train | human |
|
c^{\prime}=\sqrt{c} | e323fb5c84f1b751 | train | human |
|
440Hz\cdot(\sqrt[12]{2})^{-10}\approx | 09f19bbddb927882 | train | human |
|
x_{ij}=\frac{S_{i}-S_{j}}{\sigma} | 4369648574b3a3d6 | train | human |
|
n_{pas} | af828f2e009de940 | train | human |
|
||e_{i}||=||e_{i}^{*}||=1 | 83166716037c475d | train | human |
|
P_{2}=(0,\sqrt{3}) | 48f5e56b995c3b2c | train | human |
|
\overline{w_{i}} | cf6b21c59d3b6f10 | train | human |
|
\int_{x}^{x}f(t)dt=0 | 287a60731c83fb61 | train | human |
|
(-b-\sqrt{b^{2}-4c})/2 | fea96365ba29a8c3 | train | human |
|
\frac{\delta(k_{1}+k_{2})}{k_{1}^{2}} | 6fd720b920ab9e92 | train | human |
|
\frac{\partial x}{\partial r}=cos\phi | 302f4f1aa2b97ec3 | train | human |
|
M^{\beta}=(X^{T}WX)^{-1} | a34db0384f077d91 | train | human |
|
X=t^{t^{t^{...^{t^{i}}}}} | 38960ace079eaac1 | train | human |
|
[\frac{\pi}{\theta}]=-[\frac{\theta}{\pi}] | 222551f5e888bccb | train | human |
|
\frac{dt}{ds}=1 | a93fac978ea7b2d5 | train | human |
|
(y,g(y)+K) | 5cc45d6747d26470 | train | human |
|
\frac{\frac{4-5}{341}}{\frac{\frac{62}{5}}{4}} | cc726f24c2a16659 | train | human |
|
\sqrt{S} | a8ea97d224c709be | train | human |
|
T_{\alpha\beta} | b30d34b781bc0d76 | train | human |
|
\frac{1}{\sqrt{(1-\beta^{2})}} | 0b9aa673a612716b | train | human |
|
B_{1}=\{|a_{i}\rangle_{i=1}^{d}\} | cbe50a27303719e5 | train | human |
|
V=\frac{E*G*U}{O*R} | 0020f62a652b7ade | train | human |
|
V_{h^{\beta}} | dd5e4ae68082ce04 | train | human |
|
A_{i}A_{j}\subseteq A_{i\cdot j} | a296cf49570c9ceb | train | human |
|
\frac{(50\cdot48)}{370^{311}} | 3dd58d4d833479bd | train | human |
|
\Delta f=\frac{f_{0}}{kA^{2}}\langle F_{ts}q^{\prime}\rangle | 798d806de87c62f7 | train | human |
|
\sum_{i=1}^{m}w(P_{i})\ge w(C) | d1a848eb4d21d722 | train | human |
|
U=\sum_{i=1}^{n}\frac{C_{i}}{T_{i}}\le1 | 463d396a0688f2cc | train | human |
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