# Datasets: yuntian-deng /im2latex-100k-raw

Dataset Preview
formula (string)filename (string)image (image)preprocessing (string)
"L_{E-H}=\epsilon _{abcd}R^{ab}e^{c}e^{d}+dB, \label{EH}"
"3c8a88ae01.png"
"none"
"- { \textstyle \frac { 1 } { 2 } } \omega ^ { + a b } _ { \hat { 0 } } \sigma _ { a b } \epsilon _ { I } = \gamma ^ { i } ( - { \textstyle \frac { i } { 4 } } e ^ { 3 \phi } \partial _ { \hat { \imath } } \overline { \lambda } \gamma ^ { 0 } \epsilon _ { I } ) \, ."
"15c867a6fd.png"
"tokenized"
"- \kappa ^ { 2 } g ^ { 2 } \alpha ^ { \prime } \left( \frac { 7 1 1 6 8 } { 5 9 0 4 9 } \right) ( A ^ { \mu } A _ { \mu } ) ^ { 2 } ."
"730c5a7d8e.png"
"normalized"
"\Phi _ A ^ { a b c } = 2 \varepsilon ^ { a \underline { b } } \rho _ A ^ { \underline { c } }"
"77698e6a46.png"
"tokenized"
"\int _ { C } T _ { \mu \nu } k ^ { \mu } k ^ { \nu } d \lambda \ge 0"
"689c90715b.png"
"normalized"
"{\cal W}_{\rm PM}(\phi ) =\frac{m^2}{4\lambda}\,\phi-\frac{\lambda}{3}\,\phi^3\,,\label{PS}"
"3261c47dbf.png"
"none"
"{ \frac { 2 m } { N } } - 2 m _ { 1 } = r - \ell \; ."
"f999974fcf.png"
"normalized"
"p(\beta,L)=\rho(\beta,L)= \frac{1}{L^{2}}f'\left(\frac{\beta}{L}\right)\;."
"490579c383.png"
"none"
"\tilde { S } _ { 0 } ^ { L } \left [ A _ { \mu } ^ { a } , B _ { a } ^ { \mu \nu } \right ] = \frac { 1 } { 2 }"
"622144b02c.png"
"tokenized"
"d s ^ { 2 } = h ( l ) d t ^ { 2 } - \frac { d l ^ { 2 } } { h ( l ) } - d y ^ { 2 } - d z ^ { 2 }"
"4f28beb022.png"
"normalized"
"(\stackrel{(0)}{S},\stackrel{(0)}{S})=0\longrightarrow(S,S)=0 \label{fullmasterequation}."
"8dde546d93.png"
"none"
"c=\frac{1}{1-\hat{u}}~~, \hspace{1cm}b=64 e^{2 \pi i\tau}.\label{15}"
"29bd63f199.png"
"none"
"A _ { l } = \sum _ { k } \alpha _ { l k } ^ { * } a _ { k } - \beta _ { l k } ^ { * } a _ { k } ^ { \dagger } \; ."
"62eba0fb07.png"
"normalized"
"\varphi(n)=\frac{\sin\vartheta n}{\sin\vartheta} \ \ ."
"64496dd5d8.png"
"none"
"U^{\dagger}(\Lambda)\vec{\jmath}\,(P)U(\Lambda)={\cal R}_W(\Lambda,P)\vec{\jmath}."
"755a918771.png"
"none"
"\delta \left( Z _ { \; \; b _ { 1 } } ^ { a _ { 0 } } { \cal P } _ { a _ { 0 } } \right) = - D _ { \; \; b _ { 1 } } ^ { a _ { 1 } } \pi _ { a _ { 1 } } ."
"65563600ef.png"
"normalized"
"0 = \int _ { K 3 } \eta _ { I J } F ^ { I } \wedge F ^ { J } = m ^ { A I } m ^ { B J } \rho _ { A B } \, \eta _ { I J } \ ,"
"154c1f75c2.png"
"normalized"
"n ( x ) = \Psi ^ { \dagger } ( x ) \Psi ( x ) ,"
"20cbba4e5a.png"
"tokenized"
"S _ { \mathrm { t o t a l } } = S + S _ { \mathrm { s o u r c e } } ~ ,"
"6495600e1f.png"
"normalized"
"\hat { \hat { \epsilon } } ^ { \hat { \hat { \mu } } _ { 0 } \ldots \hat { \hat { \mu } } _ { 1 0 } } = 1 ."
"5defd0d234.png"
"normalized"
"{ \cal N } _ { A B } = \frac { \partial } { \partial \bar X ^ A } \frac { \partial } { \partial \bar X ^ B } \bar F \ ."
"4382c7358f.png"
"tokenized"
"n_{i}\longrightarrow n_{i}+q_{i}m,\;\;m\in{\bf Z}\label{3.210}"
"495140179c.png"
"none"
"m _ t / v \sim m _ b / w \sim ( 1 8 0 G e V / 2 4 6 G e V ) ."
"52b4e85f58.png"
"tokenized"
"\bar { K } ( z ; i _ { s } ) \bar { Z } ( z ) G ( i _ { s } ) = Z ( z ^ { \prime } ) ^ { t } \, ,"
"18a0b011ab.png"
"tokenized"
"( { \bf u } _ { I } , [ D _ { a } , \Delta _ { f } ] { \bf u } _ { J } ) = 4 C _ { ( I J ) a }"
"705378be90.png"
"normalized"
"\{ Q ^ a _ \alpha , Q ^ b _ \beta \} = 2 \omega ^ { a b } \gamma _ { \alpha \beta } ^ \mu P _ \mu + \gamma _ { \alpha \beta } ^ \mu Z ^ { a b } _ \mu"
"7d13cc7b51.png"
"tokenized"
"m_l/M={\rm Log} \left( \frac {F_l}{F_0}\right) .\label{mass}"
"25a3d6b46b.png"
"none"
"T^{(1,\dots ,N)}_{k}\left( \theta _{1},\dots ,\theta _{N}\right)"
"2a1d9ee0c1.png"
"none"
"{\Pi}^{(-N)}=p^{(-N)} [ {\bf 1} - {\pi}^{(j^{(-N)})}],"
"12d7c2d6c5.png"
"none"
"[ D, Q_{+{1\over 2}} ] = {1\over 2} Q_{+{1\over 2}} \ , \qquad [ D,S_{-{1\over 2}} ] = -{1\over 2} S_{-{1\over 2}} \ ."
"4b452efb15.png"
"none"
"\label{n5.9}c_0=\int_{\bar{B}}{\bar h}^{1/2} d^2x=\mbox{Vol}~\bar{\cal B},"
"5d0d6d68cc.png"
"none"
"w = \underbrace { r _ { \epsilon } \cdots r _ { 0 } r _ { 1 } } _ { l } ,"
"772bdb8815.png"
"tokenized"
"r(n;s)=\int_s^\infty (x-s) \psi(q_0,\cdots,q_n)\, dx\label{r_integral}"
"5161b969da.png"
"none"
"\eta _{2}\,=\,\frac{1\,-\,{\frac{\partial _{+}\,\hat{\varphi}}{\partial_{-}\,\hat{\varphi}}}}{1\,+\,{\frac{\partial _{+}\,\hat{\varphi}}{\partial_{-}\,\hat{\varphi}}}}\;\;."
"21461a3038.png"
"none"
"\label{symm:metr1} ds^2 = dy^A dy^B \eta_{AB}"
"none"
"M _ { \psi } ^ { 2 } = { \frac { d ^ { 2 } } { ( \pi \alpha ^ { \prime } ) ^ { 2 } } } \ ,"
"5b097371e7.png"
"normalized"
"\hat X_{i} \equiv\sqrt{ X_{i}^{2}+r_{0}^{2}}, \ \ \ X_{i}=(X,Y,P)."
"18723c2065.png"
"none"
"\left( b + a \nabla ^ { 2 } \right) \nabla ^ { 2 } G ( \bar { x } , \bar { y } ) \, = \, \delta ^ { 2 } ("
"3a1b30f7bd.png"
"normalized"
"N t _ { 1 1 } \equiv k \ { \rm m o d } \ N \, ."
"5b5eb83840.png"
"tokenized"
"\label{breflect} \eta\sim \lambda_1\, e^{-i\omega t}\left(e^{ikx}+K_B\, e^{-ikx}\right) ,"
"d698e7cd31.png"
"none"
"\label{cyl3} \lambda_i(\tau,x+2\pi) = \lambda_{Q(i)}(\tau,x)~."
"340f3b32e3.png"
"none"
"X _ \tau = F _ 1 X _ \sigma - F _ 2 X _ \sigma - F _ 3 X _ \tau ,"
"7236c5e44b.png"
"tokenized"
"\label{density_HO}\rho(q)=1,\;\; \rho(Q,t)={1\over 2\pi \sin t}."
"10a2d8959a.png"
"none"
"F _ { i } = F _ { i } ( \phi ) \ ; \ G _ { i } = G _ { i } ( \phi ) \ ; \ D _ { i } = D _ { i } ( \phi )"
"13e0a96d36.png"
"normalized"
"( d s ) ^ { 2 } = - [ d \tau ^ { 2 } - ( M \tau ) ^ { 2 } d x ^ { 2 } ] ; \hspace { 0 . 3 c m } 0 \le \tau < \infty"
"5707afe575.png"
"normalized"
"\sum _ { i } { \cal C } _ { i } N _ { i } ^ { 2 } = \sum _ { i \neq j } { \cal L } _ { i j } | N _ { i } N _ { j } | + \sum _ { i } { \cal K } _ { i } N _ { i } ^ { 2 } ."
"4c5f67d242.png"
"normalized"
"{\tilde D}_{m}= D_{m}-\frac{1}{2}m\Gamma_{m}"
"cd3df81d00.png"
"none"
"D = - ( \partial _ \mu + i A _ \mu ) ( \partial _ \mu + i A _ \mu ) + \sigma ."
"4131a87e8b.png"
"tokenized"
"\Delta \sigma ( A ) = \Delta \sigma \left( 1 + A ^ { 2 } / 4 m ^ { 4 } ( \Delta \sigma ) ^ { 4 } \right) ^ { 1 / 2 } \ ."
"1d84bfb0a6.png"
"normalized"
"{ Q } ( \iota _ * { F } ) = { Q } ( \iota _ * { E } ) + { Q } ( \iota _ * { G } ) \, ."
"2d402da897.png"
"tokenized"
"G _ F = M _ { \rm W } ^ { - 2 } \sim 1 0 ^ { - 5 } \ \ \mbox { G e V } ^ { - 2 }"
"7afe963f09.png"
"tokenized"
"U_{4\pi} = 4(\delta_{ij} \delta_{kl}+ cyclic) f^{\prime\prime}(v^2)"
"468de1bc01.png"
"none"
"E ^ \prime = - B G ^ { - 1 } B - B = { B _ { 1 2 } ^ 2 \over \det ( G ) } ~ G - B ~ ."
"41bb18acbf.png"
"tokenized"
"\phi _ i = x _ i / l _ s ^ 2 ~ , ~ \phi ^ 8 = x _ { 1 1 } / l _ s ^ 2 ~ , ~ u = v / l _ s ^ 2 ,"
"4b4fcc7892.png"
"tokenized"
"{ \cal P } _ { a } = p _ { a } \qquad { \cal J } _ { a } = \epsilon _ { a b c } x ^ { b } p ^ { c } + J _ { a } \, ,"
"4b14213a34.png"
"normalized"
"r _ { - } = - q _ { - } \circ \left( q _ { - } - \bar { M } \circ q _ { + } \right) ^ { - 1 } ."
"4fda75d93a.png"
"normalized"
"\hat { c } _ { - \alpha } = e ^ { - i q \alpha } \sum _ { \beta \in \Lambda _ { R } } | \beta + \bar { p } > < \beta + \bar { p } |"
"3a523a6698.png"
"tokenized"
"W _ { \perp } = e x p \{ \frac { i } { 2 } \operatorname { t a n } ^ { - 1 } \frac { p _ { \perp } } { m } \mathrm { \boldmath ~ \gamma ~ } _ { \perp } \cdot { \bf p } _ { \perp } \}"
"27d084c7f2.png"
"normalized"
"[ { \cal E } ^ \alpha _ i ( x ) , A ^ \beta _ j ( x ' ) ] = i \delta ^ { \alpha \beta } \delta _ { i j } \delta ( x - x ' ) ,"
"5620a21fd2.png"
"tokenized"
"E _ c = - 2 \frac { n l r _ + ^ { n - 1 } V o l ( \Sigma _ n ) } { 1 6 \pi G R } ."
"1a18ff0317.png"
"tokenized"
"\operatorname { l n } \, [ \alpha _ { a ( M _ { T } ) } / \alpha _ { a ( M _ { Z } ) } ] , \, \, \operatorname { l n } \, [ \alpha _ { a ( M _ { X } } ) / \alpha _ { a ( M _ { T } ) } ]"
"6f23402f3b.png"
"normalized"
"| \Phi \rangle = | \Phi ^ { ( 0 ) } \rangle + a _ { _ U } | \Phi ^ { ( 1 ) } \rangle \, ,"
"4afee14dde.png"
"tokenized"
"u_a v^a = 0, \hspace{1.5em} v_a v^a = -2.%\label{U_VNorm}"
"664e7c7be4.png"
"none"
"\lambda\equiv\tau_2/\tau_1=\theta g_{\rm YM}^2/8\pi^2~."
"1b1bea9d9a.png"
"none"
"\left| \left. b,\frac{1}{2},a,\frac{1}{2}\right| l,k-l,n\right\rangle \: ."
"22659be215.png"
"none"
"x_d^{(1/2)}(u,\xi)={x(u,\xi)\,x(u+\omega_{1},\xi)\over x(\omega_{1},\xi)}."
"3b7c6d1cf7.png"
"none"
"G \left( \xi \right) = \frac { 3 } { 8 } \xi ^ { - 4 } - \frac { 7 } { 8 } \, \frac { 1 } { 1 2 0 } + O \left( \xi ^ { 2 } \right) ,"
"6c8f12167c.png"
"normalized"
"S _ { \mathrm { H } } ^ { 2 } - S _ { \mathrm { \Lambda } } ^ { 2 } = S _ { \mathrm { B H } } ( 2 S _ { \mathrm { B V } } - S _ { \mathrm { B H } } ) ."
"3c05985550.png"
"normalized"
"a _ { q } = a f ( \hat { n } ) , ~ ~ ~ a _ { q } ^ { \dag } = f ( \hat { n } ) a ^ { \dag }"
"4640fe556f.png"
"normalized"
"\Pi^{(2)}_{PV}(k^2,m)=\Pi^{(1)}(k^2,m)-\frac{g^2}{4\pi} sgn(M)\ .\label{2.9}"
"7e92ebb935.png"
"none"
"[ e _ { a } , A _ { b } ^ { i } ( \vec { x } ) ] _ { D } = g c _ { a b c } A _ { c } ^ { i } ( \vec { x } )"
"3d77393477.png"
"normalized"
"\widehat { \cal M } _ { i } = K _ { i j } ( \widehat { \Delta } ) s \widehat { \Delta } _ { j } \ \ ."
"4068bb05c2.png"
"tokenized"
"W _ { t r e e } = \lambda \Phi Q { \widetilde Q } ~ ,"
"104056c5f8.png"
"normalized"
"t=\int_0^\tau d\tau'\,e(\tau'),\quad T=\int_0^1 d\tau\,e(\tau)"
"23e7a0604e.png"
"none"
"g = e ^ { \frac { i } { 2 } \theta _ { \mathrm { L } } \sigma _ { 2 } } e ^ { \frac { 1 } { 2 } r \sigma _ { 1 } } e ^ { \frac { i } { 2 } \theta _ { \mathrm { R } } \sigma _ { 2 } } ,"
"761e65e445.png"
"normalized"
"\eta \cdot k = - i k ^ { 2 } \pm i \sqrt { { \frac { ( k ^ { 2 } + \eta ^ { 2 } ) ( k ^ { 2 } + i \epsilon ) } { 1 - \lambda } } } ."
"56dccf2265.png"
"normalized"
"\label{sequestered}K\ =\ -3\log \left[\, -\frac{1}{3} Q^+ Q \ +\ f(H^+, H)\,\right]\ .\label{K_RS}"
"3506377aa4.png"
"none"
"\vec {k}_1^{ex}= (0,0,0,1):\,\,\,\,\,|C_4|=4,"
"7a6324e979.png"
"none"
"\label{dm}\frac{d G(\rho_2)}{d \rho_2} = - \frac{g_2^2}{8 \pi^2} \rho_2 G(\rho_2)~."
"46a1c22be4.png"
"none"
"\Omega = D A + A \wedge A \doteq D X ^ { M } \wedge D X ^ { N } \Omega _ { M N } ."
"971339cd43.png"
"normalized"
"K^m_A \frac{\partial}{\partial z_m} = \frac{\partial}{\partial \xi_A} ."
"24bea46896.png"
"none"
"\frac { d ^ { 2 } \xi ^ { \mu } } { d t ^ { 2 } } = - R _ { 0 k 0 } ^ { \mu } \xi ^ { k } - \frac { 1 } { 2 } ["
"d754c9bd4a.png"
"tokenized"
"S_iW_\alpha\bar W_{\dot \alpha},\bar S_iW_\alpha\bar W_{\dot \alpha}"
"2378b01281.png"
"none"
"{ \partial L \over \partial t } = \{ B _ 1 , L \}"
"4e70ffd19c.png"
"tokenized"
"{\cal F}_2 %= - \frac{{\rm ln}Z_2}{\beta V}= \frac{g_r^2M_rT^2}{(4\pi)^2}\left(\frac{1}{x^2}[g_2(x,-r)-g_2(x,r)]^2+[x-h_2(x,-r)-h_2(x,r)]^2\right)\;.\label{F2}"
"20c4c431a7.png"
"none"
"- \partial ^ 2 _ { \rho } \chi + \frac { 2 } { \rho ^ 2 } \chi - \frac { \Lambda ^ 2 } { k ^ 2 } ( 1 - \frac { l ( l + 1 ) k ^ 2 } { E ^ 2 } ) \chi = 0"
"639e7f6e5f.png"
"tokenized"
"\tilde G ^ { - 1 } ( k ) = \sum _ { s } c ( s ) e ^ { - i k s }"
"a2f01db623.png"
"tokenized"
"\label{18}\gamma = \mp f_{\infty} \left( f_{\infty} + {v_0 ^2 \over 2 f_0} \right)"
"16ba257815.png"
"none"
"c _ { 0 j } ^ { N } \ = \ \operatorname { e x p } \left[ \frac { 1 } { 2 } \sum _ { n = 1 } ^ { j } \operatorname { l n } \frac { 1 - n / ( N + 1 ) } { 1 + n / ( N + 1 ) } \right] \ = \"
"4d220a28ce.png"
"normalized"
"\xi_j = \sqrt{\kappa} z_j\ , \label{wkba}"
"425cfe4777.png"
"none"
"\varepsilon_0 = \langle 0| {\cal H} |0 \rangle = - \sum_{{\bf {p}}, \sigma} \epsilon_{{\bf {p}} \sigma}^{(-)},"
"4990db8e1d.png"
"none"
"\psi _ { n } ( x ) = x B _ { n - 1 } ( { 1 + \eta \over \sqrt { 1 + 2 \eta } } - x ^ { 2 } )"
"1fbe0941c5.png"
"tokenized"
"p _ \Lambda = \sum _ { \ell = 1 } ^ { n } c _ { \Lambda \Lambda ^ { ( \ell ) } } \, s _ { \Lambda ^ { ( \ell ) } } ,"
"5f18fee927.png"
"tokenized"
"\chi ( T M ) = \chi ( M ) \equiv \sum _ { k } ( - 1 ) ^ { k } b _ { k } ( M ) ,"
"10e8ca5fd0.png"
"normalized"
"\Delta _ F ( x , x ' ) = \int \, { d ^ 4 k \over ( 2 \pi ) ^ 4 } { e ^ { i k x } \over k ^ 2 + m ^ 2 - i \epsilon } \, ,"
"6e9797a29f.png"
"tokenized"
"\triangle = { \frac { 1 } { \sqrt { g } } } \sum _ { j j ^ { \prime } } { \frac { \partial } { \partial t _ { j } } } \; \left( \, \sqrt { g } \, g ^ { j j ^ { \prime } } \, { \frac { \partial } { \partial t _ { j ^ { \prime } } } } \, \right)"
"3d5d30549d.png"
"normalized"
"\Gamma = A _ { h } \frac { 1 } { ( e ^ { \frac { \omega } { T _ { H } } } - 1 ) } \frac { d ^ 3 k } { ( 2 \pi ) ^ 3 } ,"
"5050998e2a.png"
"tokenized"
"{ \cal R } = { \cal R } _ { r } \operatorname { s i n } \eta , ~ ~ ~ \tau = { \cal R } _ { r } ( 1 - \operatorname { c o s } \eta ) ."
"1e1bbaef2b.png"
"normalized"
"{ \widehat M } _ { P } ^ { 2 } \sim { \frac { r ^ { 2 } } { ( \alpha ^ { \prime } ) ^ { 2 } } } ~ ,"
"58c383b1ae.png"
"normalized"
"\psi _ { \scriptscriptstyle W } = \frac { 1 } { 2 } ( \psi \pm \gamma _ 5 \psi \gamma _ { 2 1 } ) ."
"5aefee37e5.png"
"tokenized"
End of preview (truncated to 100 rows)

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