image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1
value | data_type stringclasses 1
value |
|---|---|---|---|---|
(\begin{matrix}a&b\\ b&1-a\end{matrix}) | 4d0542cc564a1443 | train | human | |
\frac{\sum_{k=1}^{n}\delta_{x_{k}}}{n}\Rightarrow\mu | 8c54efc509cc8656 | train | human | |
\phi_{e}\notin F | 9c2ee2d88eba73ea | train | human | |
d_{1}=d_{2} | 23c2ee286726fa77 | train | human | |
{7^{398}}^{\frac{(4-2)}{10}} | c4393eed093e2ce4 | train | human | |
|A+A|\ge2|A|-1 | 7ab06fb59618e337 | train | human | |
v=\frac{dr}{dt} | b9890b74e37b218b | train | human | |
PQ+r=PQ^{\prime}+r^{\prime} | f41ce5e6873b43c3 | train | human | |
E=v^{2}/2-GM/r | 7048c512af73786b | train | human | |
8\cdot9+(5-6-8) | c22b320737ac417b | train | human | |
(\iota x.\phi) | 99cd6a769c6a804e | train | human | |
f^{\prime}\rightarrow1 | bb0c267bcd0f0a28 | train | human | |
\int(\int f(r)dv)dr | ad0d5625c75550d3 | train | human | |
\rho=\frac{\partial V}{\partial r} | 5edfec6d54cbcf49 | train | human | |
w_{u}^{h} | 7dff9035528deb76 | train | human | |
|AB|=\frac{|AC||FE|}{|FC|} | 8edc625a8e2d84f5 | train | human | |
Y_{j}=y_{j} | 3c723cba27ed2d6c | train | human | |
\tilde{\varphi}:\mathbb{S}^{\lambda}E\rightarrow M | 189f84d274d6171c | train | human | |
7^{7^{\cdot^{\cdot^{\cdot^{u}}}}} | cb98009c621f6874 | train | human | |
\hat{f}_{i} | d8131f5a033644be | train | human | |
\sum_{i=0}^{4}(\begin{matrix}8\\ 2i\end{matrix})(\begin{matrix}28\\ 16-i\end{matrix}) | 7c9e60465dd43077 | train | human | |
\frac{\partial u}{\partial t}=\Delta u+F(u) | d243bebcf3a1e5bf | train | human | |
m_{zal}=\frac{m_{5}}{\sqrt{1-\frac{p^{6}}{c^{6}}}} | 9bcfd322e00439b6 | train | human | |
G=K_{III}^{2}(\frac{1}{2\mu}) | bffc7894488ebb65 | train | human | |
\delta(y)=\frac{e^{-\frac{y^{7}}{7}}}{\sqrt{7\pi}} | 5e615d0163dfe926 | train | human | |
\frac{\dot{Q}}{T} | 893ff88ccd879172 | train | human | |
\frac{\frac{c_{n-1}b_{n}}{c_{n}}+\frac{c_{n+1}}{c_{n}b_{n}}}{2} | 4f30f3bd115cb4cb | train | human | |
P=\frac{dy}{dx} | d25e5d4fa1f7db49 | train | human | |
u_{s}=dx_{s}(t)/dt | e6ded50ff3cf1302 | train | human | |
\sqrt{\frac{2Gm}{r}} | 9d81a1751cd653ec | train | human | |
\mu_{e}=\frac{C_{1}}{\Sigma\frac{l}{\mu A}} | 633b610810a31201 | train | human | |
\frac{P_{1}}{P_{2}} | eab7225ce4e0f7d3 | train | human | |
B^{\prime}=B\cdot\sqrt{4\pi/\mu_{0}} | b95af5d122820a7b | train | human | |
\hat{\Pi}_{\rho_{X^{n}(m-1)},\delta} | 733bbd7ad3c3fb02 | train | human | |
Z_{0}=\sqrt{\frac{L}{C}} | 3aed366e08603ba2 | train | human | |
e^{\int f(x)dx} | 126ef9a6ec6cd210 | train | human | |
H=\int\rho hdV | 10a3ee929a871a1a | train | human | |
P(G-uv,k) | 649ca5af16ccbaf1 | train | human | |
(\begin{matrix}n\\ i\end{matrix})2^{-n} | bcfcf273a8c5401e | train | human | |
N\approx\frac{v_{N}-v_{F}}{2c} | 562679e5b3cb579b | train | human | |
p=\frac{m+u}{\sqrt{6-\frac{u^{2}}{c^{2}}}} | 17ed8b86250c3b60 | train | human | |
\tilde{n}=n+z^{2} | 497080fd824b79b1 | train | human | |
\frac{\partial u}{\partial x} | bdbe7a5715246185 | train | human | |
Z=\frac{y\cdot c^{6}}{\sqrt{3-\frac{|v|^{6}}{c^{6}}}} | 802dfc7225e9dcf0 | train | human | |
ntan\frac{\pi}{n} | d09391492d895ab7 | train | human | |
\mathbb{Z}[\alpha] | 760deb5cac2ab667 | train | human | |
N\ge(\begin{matrix}n\\ i\end{matrix}) | ddab92f0efec07ca | train | human | |
|H(s)|^{2}=H(s)\overline{H(s)} | 376dfac6d8d4ec21 | train | human | |
Z=[\begin{matrix}X_{i}&Y_{-i}\end{matrix}] | 6dce19a02351f792 | train | human | |
s\{\begin{matrix}4\\ 4\end{matrix}\} | 6b34e4ec2cfa9171 | train | human | |
2(\sqrt{2}-1)\approx0.828 | 6484a87f36bf95bf | train | human | |
\theta_{OW} | 7691bbc97a305691 | train | human | |
\prod_{i=1}^{m}K[x]/p_{i}(x) | 38ec8eabe8d79a02 | train | human | |
\frac{\frac{10^{10}}{113}}{\frac{4}{6}} | 123e820414ac395e | train | human | |
b=\frac{ac}{d}-c | d5506c6ecc6029bd | train | human | |
\hat{A}_{i} | a809176ec5fac18c | train | human | |
\frac{\partial^{2}z}{\partial x\partial y} | c866c8f4d30f3411 | train | human | |
T=\frac{\partial U}{\partial S} | 3c3ab134681f6953 | train | human | |
G=\int_{0}^{T}S(t)x(t)dt | 46c5d6a66abec8e0 | train | human | |
\frac{\partial x}{\partial u} | 6edd7d23636f7f88 | train | human | |
\sqrt[\infty]{\infty!} | a67262df161fae5d | train | human | |
\int_{K}f(gk\cdot y)dk | f20f20ba07119555 | train | human | |
Z_{01}=\frac{V_{1}}{I_{1}} | 31e03b31b1cebf85 | train | human | |
\{\begin{matrix}6\\ 6\end{matrix}\} | dbcaf869bdd6f0da | train | human | |
\frac{(287\cdot\sqrt{207})^{8}}{(122+155)} | 812accb1dc9c3897 | train | human | |
\lfloor\sigma(G)\rfloor | 1181bc683a3ecba8 | train | human | |
377^{2}-\frac{\sqrt{356}^{499}}{59} | 17dc1b06d67df98a | train | human | |
X_{i(K+1)}=1 | 40ca0b699d5ceca2 | train | human | |
(1-\gamma)n | 0ffa26bb179fa935 | train | human | |
H_{n,m}=\sum_{k=1}^{n}\frac{1}{k^{m}} | e936c8e10cd6d989 | train | human | |
(\frac{96}{387})^{\frac{10}{2}} | c0404b4e44fa75e5 | train | human | |
(\frac{315+194}{8})^{303/47+5} | ebd866c9b4e38ae3 | train | human | |
r_{isco}=\frac{6GM}{c^{2}} | 84160ab3bfe75eab | train | human | |
A=( | 0353cae0d9b6afb7 | train | human | |
S_{+}|-\rangle=\hbar|+\rangle | 65fcc78a45ac97c2 | train | human | |
\hat{Y}_{j} | 4798b4d72a41dd99 | train | human | |
h(a)_{n}=n\cdot a_{n} | 90542411d873c884 | train | human | |
X^{\prime}=\partial X/\partial s | dd06102132c81d09 | train | human | |
\Rightarrow m_{1,2}=\pm\sqrt{\frac{n}{2}} | bf04908eb3308222 | train | human | |
lim_{\Delta x\rightarrow0}sin\frac{1}{\Delta x} | 38601e9538d269b1 | train | human | |
\beta=\frac{Cov(r_{a},r_{b})}{Var(r_{b})} | f12fe79760d2b013 | train | human | |
\mu(x)=\frac{F_{X}^{\prime}(x)}{1-F_{X}(x)} | c98cc6dd5de670a7 | train | human | |
\frac{dQ_{T}}{dQ_{*}} | 50abefb794a93535 | train | human | |
F[t_{1},t_{2},...,t_{n}] | a6de456e552d6412 | train | human | |
F(x)=\int ln(f(x))dx | 3b8ea0dfe2644ac3 | train | human | |
\int_{0}^{T}wx(t)dt | a67adcdd61c124b6 | train | human | |
184+414+408^{163} | d02069613ea7d07b | train | human | |
a_{j}-\sum k_{i}b_{i} | de5bd347a0b71a89 | train | human | |
a(x)+x^{b}b(x)=0 | eaafc74e55c0dfa2 | train | human | |
y=\int sin\psi ds | 12f3e106212e9dda | train | human | |
\frac{\sqrt{2}}{12} | 9a0a940239df154e | train | human | |
\omega+2 | ddb67ad3a2c20130 | train | human | |
123\cdot8-7^{\frac{\frac{164}{313}}{10}} | 0fdf66fe79f00ac6 | train | human | |
\tau_{N}=\tau_{0}e^{\frac{KV}{k_{B}T}} | c77ff4c5dcdcebe9 | train | human | |
{(\nu^{\phi})}^{\alpha} | b7f470069d3a6245 | train | human | |
\frac{1}{\tau_{U}}=2\gamma^{2}\frac{k_{B}T}{\mu V_{0}}\frac{\omega^{2}}{\omega_{D}} | 616301d9a40e7e7d | train | human | |
\hat{\rho} | a770100130f43d6e | train | human | |
\tilde{W}_{t} | b5b081039b3290b4 | train | human | |
|V_{o}|=\frac{V_{o}}{V_{i}} | fe1dd1d898c3aba0 | train | human | |
\frac{1}{1\cdot h^{\frac{U\times(1\cdot U)}{5^{N+1}}}} | 1dad8527708d124a | train | human |
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