image
image
| text
string
|
|---|---|
 | "5^{\prime}" |
 | "<8000" |
 | "\sim 5^{\prime}" |
 | "{}^{\dagger}" |
 | "W_{N}" |
 | "G(q;x,\sigma)" |
 | "\omega_{z}(k)=\omega_{0}" |
 | "\mathscr{L}_{X_{0}}=\mu_{\infty}" |
 | "b(\cdot,\mu_{\infty})" |
 | "K=-(K_{2}-K_{1}),\lambda_{t}^{2}=\lambda" |
 | "\delta_{t}=\|\sigma\|_{\infty}." |
 | "\mu_{\infty}(f^{2})\leq 1" |
 | "\|\sigma\|_{\infty}<\infty" |
 | "k\in(0,K_{2})" |
 | "2\varepsilon\|\sigma\|_{\infty}^{2}<K_{2}" |
 | "c_{1}(\varepsilon),c_{2}(\varepsilon)>0" |
 | "\bar{X}_{0}=0" |
 | "Q=(\pi,\pi,\pi)" |
 | "\|(\sigma\sigma^{*})^{-1}\|_{\infty}<\infty" |
 | " and noting that " |
 | "K_{0}\in\mathbb{R}" |
 | "f\in W^{1,2}(\mu)" |
 | "\mathscr{E}(f,f)=0" |
 | "(X_{t},Y_{t})\in\mathbb{R}^{d_{1}}\times\mathbb{R}^{d_{2}}:" |
 | "d_{1}\times d_{1}" |
 | "d_{2}\times d_{2}" |
 | "\mu:=\mathscr{L}_{(X_{0},Y_{0})}\in\mathscr{P}_{2}(\mathbb{R}^{d_{1}+d_{2}})." |
 | "P^{*}_{t}\mu:=\mathscr{L}_{(X_{t},Y_{t})}" |
 | "\Delta^{x}" |
 | "\mathscr{L}_{(X_{t},Y_{t})}=P_{t}^{*}\mu." |
 | "(\bar{X}_{0},\bar{Y}_{0})" |
 | "Y_{T}=\bar{Y}_{T}" |
 | "\mathbb{Q}:=R\mathbb{P}" |
 | "\mathscr{L}_{(\bar{X}_{0},\bar{Y}_{0})}=\nu" |
 | "\mathscr{L}_{(\bar{X}_{t},\bar{Y}_{t})|\mathbb{Q}}=P_{t}^{*}\nu" |
 | "f\in\mathscr{B}_{b}^{+}(\mathbb{R}^{d_{1}+d_{2}})" |
 | "\tilde{W}_{t}" |
 | "\mathbb{Q}|_{\mathscr{F}_{0}}=\mathbb{P}|_{\mathscr{F}_{0}}" |
 | "\mu_{\infty}\in\mathscr{P}_{2}(\mathbb{R}^{d_{1}+d_{2}})" |
 | "\Delta^{y}" |
 | "(x,y),(\bar{x},\bar{y})\in\mathbb{R}^{d_{1}+d_{2}}." |
 | "(\bar{X}_{t},\bar{Y}_{t})" |
 | "\mathscr{L}_{(X_{0},Y_{0})}=\mu,\mathscr{L}_{(\bar{X}_{0},\bar{Y}_{0})}=\nu" |
 | "\Theta(M)dM=(M/M^{*})^{-\alpha}\exp{-(M/M^{*})}d(M/M^{*})" |
 | "V_{c}=V_{200}f_{V}" |
 | "V_{200}=0.017(MH(z)h)^{1/3}" |
 | "R_{d}=R_{d}^{iso}f_{c}^{-0.5}f_{R}" |
 | "R_{d}^{iso}=0.7(H(z)h)^{-1.0}\lambda V_{200}(j_{d}/m_{d})" |
 | "\Sigma_{0}=\frac{2.0\times 10^{13}m_{d}M}{R_{d}^{2}}" |
 | "e=\frac{1}{2^{1/4}}(\lambda^{\prime}/m_{d})^{0.5}f_{c}^{-1/4}f_{R}^{1/2}f_{V}" |
 | "(J/t=(J/t)_{c},T=0)" |
 | "Vol\propto A(\sigma_{rms}\delta V)^{-3/2}" |
 | "\sigma_{rms}" |
 | "M^{*}=10^{12}" |
 | "<\lambda>=0.05" |
 | "\sigma_{\lambda}=0.5" |
 | "H(z)=1.0" |
 | "H_{o}=72" |
 | "e>1.0" |
 | "\lambda^{\prime}=\lambda j_{d}/m_{d}" |
 | "m_{d}M" |
 | "\Delta/J" |
 | "\Sigma_{Crit}\approx 5\times 10^{20}" |
 | "\Sigma_{0}>5\times 10^{20}" |
 | "\Sigma_{0}<5\times 10^{20}" |
 | "\Omega_{Baryon}/\Omega_{M}" |
 | "m_{d}\approx 0.15" |
 | "m_{d}=0.004" |
 | "m_{d}=0.05" |
 | "m_{d}<0.05" |
 | "\Delta V=2V_{c}" |
 | "(1+\frac{1}{M_{HI}/L_{B}})" |
 | "t/J" |
 | "M_{HI}/L_{B}\approx 0.1" |
 | "\approx 2.5\sigma_{rms}" |
 | "2.5\times\delta V" |
 | "S_{Int}\approx S_{p}W" |
 | "W=\Delta V\sin{i}" |
 | "W^{Min}=10" |
 | "M_{HI}/L_{B}" |
 | "M_{HI}/L_{B}=1.5" |
 | "S_{p}>2.5\sigma_{rms}" |
 | "\sigma_{rms}=13" |
 | "J/t" |
 | "W>2.5\delta V" |
 | "\delta V=13" |
 | "V_{Hubble}" |
 | "(W)" |
 | "S_{Int}" |
 | "V_{Hubble}<1000" |
 | "M_{B}=-12.5" |
 | "m_{B}=18" |
 | "10^{5.1}" |
 | "V^{Max}" |
 | "(1d)" |
 | "M_{HI}" |
 | "(\sigma_{rms}\delta V)^{-1/2}" |
 | "t_{exp}^{1/2}" |
 | "t_{exp}" |
 | "At_{exp}^{3/4}" |
Dataset Card for Dataset Name
Dataset Summary
This dataset is a set of pairs: an image and its corresponding latex code for expression. This set of pairs was generated by analyzing more than 50,000 articles on natural sciences and mathematics and further generating a corresponding set of latex expressions. The set has been cleared of duplicates. There are more than 1600000 images in the set.
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Languages
Latex
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Source Data
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