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\min\sum_{\mu=1}^{C}s|x^{\mu}\cdot w|^{2}+\eta g(w).
\|w\|_{2}=1
\displaystyle V_{1}(x-x_{0})
\displaystyle\delta^{\mu}_{\nu}=e^{\mu}_{a}E^{a}_{\nu}+\frac{\varepsilon}{N}t^{\mu}n_{\nu}\,.
\displaystyle-\frac{2}{T}x_{n}(\lambda)
\displaystyle V^{GG}(x,y)
\displaystyle\Delta V^{qq}(x,y)
\displaystyle\Delta V^{qG}(x,y)
\displaystyle-2N_{f}T_{R}\frac{x}{y^{2}}
\displaystyle\Delta V^{Gq}(x,y)
\displaystyle C_{F}\left[\frac{x^{2}}{y}\right]
\displaystyle\Delta V^{GG}(x,y)
\displaystyle f^{q}(z,\mu)
\displaystyle zf^{G}(z,\mu)
\displaystyle(2x-1)V_{ext}^{Gq}(x,y)
\displaystyle\log(f(\epsilon^{\prime}_{\lambda n}(\lambda)))
\displaystyle\Gamma_{n}^{qq}(z,z^{\prime})
\displaystyle\Gamma_{n}^{qG}(z,z^{\prime})
\displaystyle\Gamma_{n}^{Gq}(z,z^{\prime})
\displaystyle\Gamma_{n}^{GG}(z,z^{\prime})
\displaystyle+\beta_{0}\delta(z-z^{\prime}).
\displaystyle\Delta\Gamma_{n}^{qq}(z,z^{\prime})
\displaystyle\Delta\Gamma_{n}^{qG}(z,z^{\prime})
\displaystyle+\Theta(z^{\prime}-z)[(\frac{1+z}{1+z^{\prime}})^{n}\frac{1}{n}]\},
\displaystyle\Delta\Gamma_{n}^{Gq}(z,z^{\prime})
\displaystyle\Delta\Gamma_{n}^{GG}(z,z^{\prime})
\displaystyle\rho_{p/h}(q)
\displaystyle(1-z^{\prime 2})^{n}\Gamma_{n}^{i,j}(z,z^{\prime})
\displaystyle\Gamma_{n}^{i,j}(z^{\prime},z)(1-z^{2})^{n},
\displaystyle(1-z^{\prime 2})^{n}\Delta\Gamma_{n}^{i,j}(z,z^{\prime})
\displaystyle\Delta\Gamma_{n}^{i,j}(z^{\prime},z)(1-z^{2})^{n}~{}.
\displaystyle\Gamma_{n}^{i,j}(z,z^{\prime})
\displaystyle\Delta\Gamma_{n}^{i,j}(z,z^{\prime})
\displaystyle\sigma_{p/hn}(\lambda)
E/K\colon y^{2}=x(x-(2\alpha^{2}+7\alpha+19))(x-(18\alpha^{2}+7\alpha+3)).
E_{b,c}/K\colon y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)).
E/K\colon y^{2}=x(x+(10\beta^{2}-3))(x-(\beta+4))
E/K\colon y^{2}+xy+\beta y=x^{3}-8x^{2}-6x-1
E/K:y^{2}=x(x-(2\alpha^{2}+7\alpha+19))(x-(18\alpha^{2}+7\alpha+3)).
\displaystyle=361\alpha^{2}-22\alpha-83
\displaystyle=-2112\alpha^{2}-2048\alpha-640
\displaystyle=-372\alpha^{2}+1976\alpha+1552.
\displaystyle\sigma(\lambda)f(\pm\epsilon_{\lambda n}(\lambda));
E_{b,c}/K:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)).
E/K:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1))
y^{2}+\alpha^{2}xy=x^{3}+\frac{-A-B+\alpha(\alpha+1)}{4}x^{2}-\frac{AB}{16}x.
E/K\colon y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)),
K(E[4])=K(x_{1},x_{2},x_{3},\sqrt[4]{\Delta})
\displaystyle-16(b+c)\alpha^{2}-16(c-2)\alpha-16(c-b-1)
\displaystyle-32(\alpha^{2}+\alpha+1)x+16((b+c)\alpha^{2}+(c-2)\alpha+(c-b+1))
\displaystyle=2^{6}((b+c)\alpha^{2}+(c-2)\alpha+(c-b-1))
K(E[4])=K(\sqrt{d_{1}},\sqrt{d_{2}},\sqrt{d_{3}},\sqrt{d_{4}}).
\displaystyle\sigma^{\prime}_{p/hn}(\lambda)
E:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)),
\displaystyle d_{4}=-64(\alpha^{2}+\alpha+1)d_{3}.
y^{2}=(x-a)(x-b)(x-c)
T^{2}-\frac{a_{p}-2}{\ell}T+\frac{1+p-a_{p}}{\ell^{2}}.
T^{2}-a_{p}T+p,
\displaystyle e^{i\delta_{e}(E)}
s\circ t=st\mbox{ providing $R(s)=D(t)$,}
a=\{(w,x),(x,w)\},\ g=\{(w.w),(x,x)\},\ e=\{(w.w),(x,x),(y,y)\},
st=(sD(t))(R(sD(t))t)=(sD(R(s)t))(R(s)t).
st=s|D(t)\circ R(s|D(t))|t=s|D(R(s)|t)\circ R(s)|t.
D(R(es)t)=D(R(esR(s))t)=D(R(esD(t))t)=R(esD(t))=R(esR(s))=R(es).
D(xy)=D(xD(R(x)y)))=D(xD(D(y)y)))=D(xD(y))=D(xR(x))=D(x).
\displaystyle R(st)
\displaystyle R(stR(t))
\displaystyle R(stD(R(t)))
\displaystyle D(R(stD(R(t)))R(t))\mbox{ by the left match-up condition}
\displaystyle{\cal R}(E)+{\cal T}(E);
\displaystyle D(R(stR(t))R(t))
\displaystyle D(R(st)R(t)).
\displaystyle R(sD(t))
\displaystyle D(R(sD(t))R(D(t)))\mbox{ by the first additional law}
\displaystyle D(R(sD(t))D(t))
\displaystyle D(R(sD(t))t)\mbox{ by the left congruence condition.}
D(R(xD(y))y)=D(R(xD(y))D(y))=D(R(xD(y))R(D(y)))=D(R(xD(y)))=R(xD(y)).
st=s|D(t)\circ R(s|D(t))|t=s|D(R(s)|t)\circ R(s)|t\mbox{ in }{\mathcal{C}}(S).
D(ef)=D(eef)D(ef)=D(eD(ef))D(ef)=R(eD(ef))D(ef)
=R(eD(D(ef)))D(ef)=R(e)D(ef)=eD(ef)=eD(R(e)f)=eD(f)=ef,
\displaystyle 1={\cal R}(E)-{\cal T}(E).
D(R(sD(t))t)=D(R(sD(t))D(t))=D(R(sD(t)))=R(sD(t)),
R(sD(t))tR(st)=R(sD(t))D(tR(st))t=R(sD(t))t,
\displaystyle R(xy)
\displaystyle R((xy)R(y))
\displaystyle R(R(xyD(R(y)))R(y))\mbox{ by the right weak congruence condition}
\displaystyle R(R(xy)R(y))R(y))
\displaystyle R(R(xy)R(y))
\displaystyle R(xy)R(y)\mbox{ since $D(S)$ is a band,}
s\otimes_{l}t=s|D(t)\circ R(s|D(t))|t,
R(a|D(R(a)|(b|e)))=D(R(a)|(b|e))=D(D(b)|(b|e))=D((D(b)|b)|e)=D(b|e).
p=p^{\rm bulk}+p^{\rm imp}/L=p^{\rm bulk}+\delta_{e}(E)/L.
(a\circ b)|e=a|D(b|e)\circ b|e=a|D(b|e)\circ R(a|D(R(a)|(b|e))|(b|e).
x|e=(x\circ R(x))|e=x|D(R(x)|e)\circ R(x|D(R(x)|e))|(R(x)|e),
\displaystyle(A|e)|e
\displaystyle((R(s)|R(x))|e)|e
\displaystyle(R(s)|(R(x)|e))|e
\displaystyle R(s)|((R(x)|e)|e)
\displaystyle R(s)|(R(x)|(e|e))
\displaystyle R(s)|(R(x)|e)

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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 100,000 articles on natural sciences and mathematics and further generating a corresponding set of latex expressions. The set has been cleared of duplicates. There are about 1 500 000 images in the set.

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Languages

Latex

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Data Fields

Dataset({
    features: ['image', 'text'],
    num_rows: 1586584
})

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Source Data

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Citation Information

@misc{alexfrauch_VSU_2023, title = {Recognition of mathematical formulas in the Latex: Image-Text Pair Dataset}, author = {Aleksandr Frauch (Proshunin)}, year = {2023}, howpublished = {\url{https://huggingface.co/datasets/AlFrauch/im2latex}}, }

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