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\min\sum_{\mu=1}^{C}s|x^{\mu}\cdot w|^{2}+\eta g(w). |
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\|w\|_{2}=1 |
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\displaystyle V_{1}(x-x_{0}) |
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\displaystyle\delta^{\mu}_{\nu}=e^{\mu}_{a}E^{a}_{\nu}+\frac{\varepsilon}{N}t^{\mu}n_{\nu}\,. |
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\displaystyle-\frac{2}{T}x_{n}(\lambda) |
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\displaystyle V^{GG}(x,y) |
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\displaystyle\Delta V^{qq}(x,y) |
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\displaystyle\Delta V^{qG}(x,y) |
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\displaystyle-2N_{f}T_{R}\frac{x}{y^{2}} |
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\displaystyle\Delta V^{Gq}(x,y) |
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\displaystyle C_{F}\left[\frac{x^{2}}{y}\right] |
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\displaystyle\Delta V^{GG}(x,y) |
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\displaystyle f^{q}(z,\mu) |
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\displaystyle zf^{G}(z,\mu) |
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\displaystyle(2x-1)V_{ext}^{Gq}(x,y) |
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\displaystyle\log(f(\epsilon^{\prime}_{\lambda n}(\lambda))) |
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\displaystyle\Gamma_{n}^{qq}(z,z^{\prime}) |
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\displaystyle\Gamma_{n}^{qG}(z,z^{\prime}) |
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\displaystyle\Gamma_{n}^{Gq}(z,z^{\prime}) |
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\displaystyle\Gamma_{n}^{GG}(z,z^{\prime}) |
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\displaystyle+\beta_{0}\delta(z-z^{\prime}). |
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\displaystyle\Delta\Gamma_{n}^{qq}(z,z^{\prime}) |
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\displaystyle\Delta\Gamma_{n}^{qG}(z,z^{\prime}) |
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\displaystyle+\Theta(z^{\prime}-z)[(\frac{1+z}{1+z^{\prime}})^{n}\frac{1}{n}]\}, |
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\displaystyle\Delta\Gamma_{n}^{Gq}(z,z^{\prime}) |
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\displaystyle\Delta\Gamma_{n}^{GG}(z,z^{\prime}) |
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\displaystyle\rho_{p/h}(q) |
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\displaystyle(1-z^{\prime 2})^{n}\Gamma_{n}^{i,j}(z,z^{\prime}) |
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\displaystyle\Gamma_{n}^{i,j}(z^{\prime},z)(1-z^{2})^{n}, |
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\displaystyle(1-z^{\prime 2})^{n}\Delta\Gamma_{n}^{i,j}(z,z^{\prime}) |
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\displaystyle\Delta\Gamma_{n}^{i,j}(z^{\prime},z)(1-z^{2})^{n}~{}. |
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\displaystyle\Gamma_{n}^{i,j}(z,z^{\prime}) |
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\displaystyle\Delta\Gamma_{n}^{i,j}(z,z^{\prime}) |
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\displaystyle\sigma_{p/hn}(\lambda) |
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E/K\colon y^{2}=x(x-(2\alpha^{2}+7\alpha+19))(x-(18\alpha^{2}+7\alpha+3)). |
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E_{b,c}/K\colon y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)). |
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E/K\colon y^{2}=x(x+(10\beta^{2}-3))(x-(\beta+4)) |
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E/K\colon y^{2}+xy+\beta y=x^{3}-8x^{2}-6x-1 |
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E/K:y^{2}=x(x-(2\alpha^{2}+7\alpha+19))(x-(18\alpha^{2}+7\alpha+3)). |
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\displaystyle=361\alpha^{2}-22\alpha-83 |
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\displaystyle=-2112\alpha^{2}-2048\alpha-640 |
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\displaystyle=-372\alpha^{2}+1976\alpha+1552. |
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\displaystyle\sigma(\lambda)f(\pm\epsilon_{\lambda n}(\lambda)); |
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E_{b,c}/K:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)). |
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E/K:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)) |
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y^{2}+\alpha^{2}xy=x^{3}+\frac{-A-B+\alpha(\alpha+1)}{4}x^{2}-\frac{AB}{16}x. |
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E/K\colon y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)), |
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K(E[4])=K(x_{1},x_{2},x_{3},\sqrt[4]{\Delta}) |
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\displaystyle-16(b+c)\alpha^{2}-16(c-2)\alpha-16(c-b-1) |
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\displaystyle-32(\alpha^{2}+\alpha+1)x+16((b+c)\alpha^{2}+(c-2)\alpha+(c-b+1)) |
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\displaystyle=2^{6}((b+c)\alpha^{2}+(c-2)\alpha+(c-b-1)) |
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K(E[4])=K(\sqrt{d_{1}},\sqrt{d_{2}},\sqrt{d_{3}},\sqrt{d_{4}}). |
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\displaystyle\sigma^{\prime}_{p/hn}(\lambda) |
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E:y^{2}=x(x-(\alpha^{2}+b\alpha+c))(x-16(\alpha^{2}+\alpha+1)), |
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\displaystyle d_{4}=-64(\alpha^{2}+\alpha+1)d_{3}. |
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y^{2}=(x-a)(x-b)(x-c) |
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T^{2}-\frac{a_{p}-2}{\ell}T+\frac{1+p-a_{p}}{\ell^{2}}. |
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T^{2}-a_{p}T+p, |
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\displaystyle e^{i\delta_{e}(E)} |
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s\circ t=st\mbox{ providing $R(s)=D(t)$,} |
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a=\{(w,x),(x,w)\},\ g=\{(w.w),(x,x)\},\ e=\{(w.w),(x,x),(y,y)\}, |
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st=(sD(t))(R(sD(t))t)=(sD(R(s)t))(R(s)t). |
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st=s|D(t)\circ R(s|D(t))|t=s|D(R(s)|t)\circ R(s)|t. |
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D(R(es)t)=D(R(esR(s))t)=D(R(esD(t))t)=R(esD(t))=R(esR(s))=R(es). |
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D(xy)=D(xD(R(x)y)))=D(xD(D(y)y)))=D(xD(y))=D(xR(x))=D(x). |
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\displaystyle R(st) |
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\displaystyle R(stR(t)) |
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\displaystyle R(stD(R(t))) |
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\displaystyle D(R(stD(R(t)))R(t))\mbox{ by the left match-up condition} |
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\displaystyle{\cal R}(E)+{\cal T}(E); |
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\displaystyle D(R(stR(t))R(t)) |
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\displaystyle D(R(st)R(t)). |
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\displaystyle R(sD(t)) |
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\displaystyle D(R(sD(t))R(D(t)))\mbox{ by the first additional law} |
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\displaystyle D(R(sD(t))D(t)) |
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\displaystyle D(R(sD(t))t)\mbox{ by the left congruence condition.} |
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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)). |
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st=s|D(t)\circ R(s|D(t))|t=s|D(R(s)|t)\circ R(s)|t\mbox{ in }{\mathcal{C}}(S). |
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D(ef)=D(eef)D(ef)=D(eD(ef))D(ef)=R(eD(ef))D(ef) |
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=R(eD(D(ef)))D(ef)=R(e)D(ef)=eD(ef)=eD(R(e)f)=eD(f)=ef, |
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\displaystyle 1={\cal R}(E)-{\cal T}(E). |
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D(R(sD(t))t)=D(R(sD(t))D(t))=D(R(sD(t)))=R(sD(t)), |
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R(sD(t))tR(st)=R(sD(t))D(tR(st))t=R(sD(t))t, |
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\displaystyle R(xy) |
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\displaystyle R((xy)R(y)) |
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\displaystyle R(R(xyD(R(y)))R(y))\mbox{ by the right weak congruence condition} |
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\displaystyle R(R(xy)R(y))R(y)) |
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\displaystyle R(R(xy)R(y)) |
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\displaystyle R(xy)R(y)\mbox{ since $D(S)$ is a band,} |
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s\otimes_{l}t=s|D(t)\circ R(s|D(t))|t, |
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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). |
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p=p^{\rm bulk}+p^{\rm imp}/L=p^{\rm bulk}+\delta_{e}(E)/L. |
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(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). |
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x|e=(x\circ R(x))|e=x|D(R(x)|e)\circ R(x|D(R(x)|e))|(R(x)|e), |
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\displaystyle(A|e)|e |
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\displaystyle((R(s)|R(x))|e)|e |
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\displaystyle(R(s)|(R(x)|e))|e |
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\displaystyle R(s)|((R(x)|e)|e) |
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\displaystyle R(s)|(R(x)|(e|e)) |
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\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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Latex
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Dataset({
features: ['image', 'text'],
num_rows: 1586584
})
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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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