yuntian-deng/im2latex-animals-concat-moremix

formula stringlengths 5 245	filename stringlengths 14 14	preprocessing stringclasses 1 value
\partial _ { \mathrm { a } } \squid\boar 6 \sheep\overline{u}(k)v(k') = - \overline{v}(k)u(k')	956d0824e0.png	concat
\dolphin\crab 0 . 5 c m ] \eagle\seagul 2 9	44e8f41eea.png	concat
\toucan\label{eq4.12c}[L_S(m),J_S(n)] = -nJ_S(n+m)	4297a616e1.png	concat
\rho ( \tau ) = \delta ( \tau )\rat\bison \pi _ { i } = \peacock	2705962a71.png	concat
\cow \bird { \cal F } _ { 2 }	95d605cfef.png	concat
\shrimp\goat \varepsilon ( x \rightarrow \pm \infty ) \rightarrow 0 \panda \alligator	cda892f52c.png	concat
\mu \ll 1 \protect \protect \protect \protect \jellyfish d \theta + \theta \wedge \theta = 0 . \lobster \delta _ \kappa E _ 7 = \flamingo\swordfish	08d0276706.png	concat
\quail \goat v _ { j } = \leopard \bison v ^ 2\plankton\swordfish	4d17a51b98.png	concat
\langle \, \dolphin\pi ^ * \Omega = d \omega\eel\leopard A_J^\alpha = 0. \label{J3}	25da5486e5.png	concat
\Pi _ { \sigma } ( p )\flamingo\swordfish \phi(\xi) = \pm \tanh \xi, \label{stat}	57a30718e0.png	concat
H _ 0 = - \plankton J \wedge \Omega = 0 \ . \jellyfish\gorilla \delta _{iBRS}[\phi ]\delta \Lambda \protect	0c372349f1.png	concat
\gorilla\bigtriangleup ( \bigtriangleup \varphi ) = 0\tarantula\octopus \lambda + \mu - \nu \in Q \, , \turtle \crocodile	7ecf203c0a.png	concat
\cow \label{19.258}\rho \rightarrow \rho / f'.	80dd6a9fc1.png	concat
\pi _ i = \cat \urchin	34dfba303e.png	concat
\whale C(\vartheta )\left\| \Omega \right\rangle =0\lion\sloth	9495e6594d.png	concat
\epsilon = 0 ^ { + } \; . \fish	199ccc8d50.png	concat
\pi ^ * \Omega = d \omega \alligator m(\alpha,\alpha)=1,\,\forall \alpha\in \Pi\zebra\shrimp	e5410e46f3.png	concat
\left[ \Omega , \Omega \right] = 0 .\snake-2 \delta _ D \overline C = 0 , \eagle\seagul Q^2=H \label{B10}	9d962eba36.png	concat
\plankton\swordfish W_n(\varphi)=\exp(in\varphi) %(83)\quail \goat \varepsilon = \varepsilon _ \infty \hen\mouse	6a1abc675b.png	concat
S = - \frac T 2\tarantula\urchin 3 2\whale \beaver Q^2=H \label{B10} \moose \shrimp	a9be054b01.png	concat
\leopard {\bf d}\Omega=0. %35% \octopus \elephant	1042ee2ade.png	concat
B = d A \beaver \bar F(z)\equiv AF(z)+BzF'(z) \label{efnot1} \sheep	76227c335d.png	concat
\penguin \| \psi \| ^ 2 = \rho =\camel\alpha = \arg Z ( \Gamma )	a1d240de00.png	concat
\lemur\starfish\hat{\varepsilon }(x,y)=\varepsilon (x,y)\dolphin\crab	db36264027.png	concat
\donkey a(f) \equiv (f,\widehat\phi).\label{annih}	0643374b90.png	concat
\otter\squirrel A =\racoon	06bdd6f1d7.png	concat
n = 4 : \quad \otter\mole\tau \sheep s\Gamma[a,\theta]\,=\,0.\label{BRSGamma} \puffin	3abc7ab616.png	concat
\tau \starfish\camel\mu \frog \kappa \mu \sin \Theta \dot \Theta =	f380740cfa.png	concat
\crab \bugs a _ k \| 0 \rangle = 0 . \wolf J \wedge \Omega = 0 \ . \vulture	4025e3ce0e.png	concat
t = \theta \, \left \| \tau \right \|\mole\tiger B = d A	f2749b3d16.png	concat
\elephant \urchin ( 1 j ) : ~ ~ ~ \rooster	dc61dd663c.png	concat
1 3 \eagle \psi(x)=f(x)e^{i\theta(x)}.\label{eq:EQ1} \octopus\skunk \tau	6b0fcc810d.png	concat
\platypus\flamingo\varphi \rightarrow \varphi - \Lambda .\label{diecisiete}	8ab1ac2a21.png	concat
\partial _ { \mathrm { a } } \penguin\koala = \; ( n + \frac p 2 )	d5fea7b7a2.png	concat
a _ { i i } = 1 . \iguana \cow a_k \|0\rangle=0. \label{vac} \elephant	1d7482a07c.png	concat
\beaver H _ { L C } \; = \;	6363c215fe.png	concat
\tau _ s \approx 1 0 . 1 5 \peacock \fish \Lambda_\mu(p,q) = S(p)\Gamma_\mu(p,q)S(q).	d530784280.png	concat
3 6 \seal\mouse\mu \ll1 \protect \protect \protect \protect \hen \cow	2f369b2e9f.png	concat
\Lambda_\mu(p,q) = S(p)\Gamma_\mu(p,q)S(q). \quail \gorilla	dd5fc4a663.png	concat
\tau \alligator \label{eq:Intertwiner} T \pi(A) = \varrho(A) T	774d579412.png	concat
\coyote\kangaroo c h a n g e d \kangaroo\quail	b64fe2ad74.png	concat
T\|\phi (x,a)\rangle =\|\phi (x,f(a))\rangle , \stingray \chicken	0896c4e299.png	concat
Backslash \\ %%%% Right bracket \seagul\seal	d6cd0bf641.png	concat
\partial ^ 2 \eta = 0 . \parrot \whale \Phi: S^3 \rightarrow S^2,\label{eq:II12}	a04408fb28.png	concat
\lbrack a,b,cd]=c[a,b,d]+[a,b,c]d, \label{der} \bat	428b4074e6.png	concat
D : S \rightarrow S + \lambda \ , \ostritch \penguin	dee3369a68.png	concat
\octopus\jellyfish\langle \,	f35893fb9c.png	concat
\seagul f ( - 2 p )\gorilla \pig	a0fcfcfb92.png	concat
\parrot\ostritch Backslash \\ %%%% Right bracket \lizard 3 5 \badger { \bf d } \Omega = 0 .	717bcb9ea6.png	concat
T\|\phi (x,a)\rangle =\|\phi (x,f(a))\rangle , \peacock	a44bbb65a5.png	concat
%13b\bar{x} \longrightarrow \bar{x}\hbar \hawk\jellyfish \pi \cdot \varepsilon = \varepsilon ~ ,	02185d76d8.png	concat
\psi(x)=f(x)e^{i\theta(x)}.\label{eq:EQ1}\cat\rhino	fc8539a7e3.png	concat
\langle I \| 0 \rangle = 1 \, ,\penguin\langle \rho,~~\rangle ~:~~\Xi \longrightarrow A \crab \quail	7ab4615f25.png	concat
\squid m _ { \! _ J } \dog \monkey b =	2d58b2763d.png	concat
\ \anteater \Phi =F_R\left( \varphi \right) \label{newphi2}	805ea40f4f.png	concat
\newt \turtle f =	53303df9fd.png	concat
\skunk\walrus \Delta_d \rightarrow \Delta, \qquad\Sigma_d \rightarrow \Sigma,\mole	5f03a72b42.png	concat
\skunk \Omega : \; \sigma \leftrightarrow -\sigma . \pig H ( \eta _ 0 ) = \Lambda .	6b765d2eba.png	concat
\tau_s \approx 10.15 \label{spinodaltime} \guinea-pig\mu \gg 1 \protect \protect \protect \protect \killer-whale X ^ i ~ \longrightarrow - X ^ i	432f34268f.png	concat
\lambda ^ { \ast } \omega = K . \shrimp\exp i \pi \kappa = \zeta \hawk \sheep \pi _ i = \dog\seagul	037dfd2181.png	concat
\camel \goat \label{eq:KMP} v\mapsto v-(v,x-ny)y+(v,y)x \squid \crocodile	259316c08b.png	concat
\eagle\lion Q \Psi = - \Psi \star \Psi . \dolphin\crab ( h + \lambda r ) = \lambda '	e87316020a.png	concat
\langle\phi(x)\phi(x')\rangle={1\over i}G(x,x'),\racoon\moose	7158e3821e.png	concat
\wolf\parrot { [ \, }	187533a507.png	concat
\label{eq:fundsusy}\pi \cdot \varepsilon = \varepsilon~, \goat \zebra\label{eq:nonabelianreality} \bar V = V \hyena\omega = \rho d(\cos \vartheta d \varphi),	0163946e74.png	concat
\parrot \whale { [ \, } \jellyfish\gorilla \partial _ 0 A _ 0 = 0 , \scorpion \moose	7f8f06c77b.png	concat
\gamma ^a\partial _a\psi =0, \label{twodDirac}\owl\urchin m(\alpha,\alpha)=1,\,\forall \alpha\in \Pi \ostritch \tarantula	a49549fb13.png	concat
\cat\rhino\langle \rho,~~\rangle ~:~~\Xi \longrightarrow A\fish \frog	0546275a5a.png	concat
H ^ 0 _ { \alpha \beta } = \walrus	034ae78044.png	concat
\langle f,f\rangle = \langle g,g\rangle = 0. \lion \bear H _ { L C } \; = \;	663f813417.png	concat
\goat G _ { \zeta } ( q ) = \starfish\epsilon = 0 ^ { + } \; . \flamingo	c831cef291.png	concat
\Gamma \epsilon = \epsilon \, , \coyote \plankton f =\gorilla \pig e q . ( 1 )	2304e25509.png	concat
D _ i ^ \theta\walrus\hawk	3e6744850d.png	concat
A_J^\alpha = 0. \label{J3} \snake\label{3.3a} \alpha(P_0;\kappa) = \Phi(P_0) \duck \hyena { [ \, } \ostritch \eel	afb0c8aae8.png	concat
\elephant\turtle \phi ^ 6 \leftrightarrow - \phi ^ 6 .	9e8927d812.png	concat
f \diamond g \toucan\vartheta \, \rightarrow \, \vartheta -\alpha \anteater\plankton	5f862ef3bf.png	concat
\urchin \skunk 3 2\fish \tiger a _ { i i } = 1 .	c737eb86e3.png	concat
D a = d a - \zebra	e755c41b60.png	concat
\partial_x^3\Psi(x) +x\ \Psi(x)=E\Psi(x), \mole\tiger	be61b7e34b.png	concat
\label{eq:grav:einstein} \delta R^A_B=0. \ostritch \bat f _ { i } ( t ) = \owl\hyena T \rightarrow { 1 \over T } \, . \elephant \shark	03efb7bf55.png	concat
\llama \tau_s \approx 10.15 \label{spinodaltime} \pig\label{type2}(x,y,z) \to (e^{i \theta}x,y,z)	981d5c6829.png	concat
\guinea-pig\alpha = \arg Z ( \Gamma ) \hawk\Omega : \; \sigma \leftrightarrow -\sigma .	7806a93951.png	concat
\ast\gamma =\gamma_5 \gamma.\label{obh:g5}\skunk \leopard \psi \rightarrow \psi \coyote \snake f _ 0 ( q ) \doteq \ostritch	98c76191f4.png	concat
. \cat \leopard	2688d232c0.png	concat
\tiger \skunk 0 . 5 c m ]	23cbfacd91.png	concat
\fox \starfish \phi(\xi) = \pm \tanh \xi, \label{stat} \sloth	2a6cafda17.png	concat
\octopus \elephant \sigma _ 3 \, \theta \, = \theta	014e185802.png	concat
\lambda _ 0 \sim \tilde \lambda \to 0 \squid \stingray Q ^ 2 = H \alligator\cdot : G \times G \rightarrow G .	dbfa8e8e8e.png	concat
Z \longrightarrow u(z) \longrightarrow w(u(z)) \ostritch Backslash \\ %%%% Right bracket	eecbf7cdcc.png	concat
3 1 \dolphin	956282c571.png	concat
i v _ b d x ^ b \moose\pi(d a) = i[D, \pi(a)]. \label{3.1} \crab \bugs v ^ { 2 }	6cb61e3725.png	concat
\wolf\varepsilon(p,q)=\varepsilon(q,-p-q).\label{A12} \racoon\partial ^ 2 \eta = 0 . \eel\leopard	2530544c70.png	concat
3 2 \lemur h(\lambda) =\rho \Theta(\lambda)H(\lambda)	7c759a9620.png	concat
B = d A \racoon \pig\Gamma \epsilon = \epsilon \, ,	aa91b8cca3.png	concat
\dot { \varphi } = \partial _ x \varphi \eagle \rhino\varphi(\omega,y)= \varphi(\omega, -y, y)\,. \racoon	91c05c5d64.png	concat
\tiger\langle S \rangle = N \langle \Delta S \rangle	20a2f13a8e.png	concat
\hen \cow s\Gamma[a,\theta]\,=\,0.\label{BRSGamma} \bugs\scorpion	bf3587506a.png	concat
\coyote \snake \bar { R } =\shrimp \hedgehog \lambda ^ { \ast } \omega = K . \eel\leopard	5d7a26e25c.png	concat
\rat v ^ 2 \lizard \sheep	08774043f4.png	concat
\owl\urchin \frac { \partial \rho } { \partial L } \seal\hedgehog 2 9 \ostritch \tarantula G _ { \zeta } ( q ) =	db6fcc93a7.png	concat

\partial _ { \mathrm { a } } \squid\boar 6 \sheep\overline{u}(k)v(k') = - \overline{v}(k)u(k')

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\dolphin\crab 0 . 5 c m ] \eagle\seagul 2 9

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\toucan\label{eq4.12c}[L_S(m),J_S(n)] = -nJ_S(n+m)

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\rho ( \tau ) = \delta ( \tau )\rat\bison \pi _ { i } = \peacock

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\cow \bird { \cal F } _ { 2 }

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\shrimp\goat \varepsilon ( x \rightarrow \pm \infty ) \rightarrow 0 \panda \alligator

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\mu \ll 1 \protect \protect \protect \protect \jellyfish d \theta + \theta \wedge \theta = 0 . \lobster \delta _ \kappa E _ 7 = \flamingo\swordfish

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\quail \goat v _ { j } = \leopard \bison v ^ 2\plankton\swordfish

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\langle \, \dolphin\pi ^ * \Omega = d \omega\eel\leopard A_J^\alpha = 0. \label{J3}

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\Pi _ { \sigma } ( p )\flamingo\swordfish \phi(\xi) = \pm \tanh \xi, \label{stat}

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H _ 0 = - \plankton J \wedge \Omega = 0 \ . \jellyfish\gorilla \delta _{iBRS}[\phi ]\delta \Lambda \protect

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\gorilla\bigtriangleup ( \bigtriangleup \varphi ) = 0\tarantula\octopus \lambda + \mu - \nu \in Q \, , \turtle \crocodile

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\cow \label{19.258}\rho \rightarrow \rho / f'.

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\pi _ i = \cat \urchin

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\whale C(\vartheta )\left| \Omega \right\rangle =0\lion\sloth

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\epsilon = 0 ^ { + } \; . \fish

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\pi ^ * \Omega = d \omega \alligator m(\alpha,\alpha)=1,\,\forall \alpha\in \Pi\zebra\shrimp

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\left[ \Omega , \Omega \right] = 0 .\snake-2 \delta _ D \overline C = 0 , \eagle\seagul Q^2=H \label{B10}

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\plankton\swordfish W_n(\varphi)=\exp(in\varphi) %(83)\quail \goat \varepsilon = \varepsilon _ \infty \hen\mouse

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S = - \frac T 2\tarantula\urchin 3 2\whale \beaver Q^2=H \label{B10} \moose \shrimp

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\leopard {\bf d}\Omega=0. %35% \octopus \elephant

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B = d A \beaver \bar F(z)\equiv AF(z)+BzF'(z) \label{efnot1} \sheep

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\penguin | \psi | ^ 2 = \rho =\camel\alpha = \arg Z ( \Gamma )

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\lemur\starfish\hat{\varepsilon }(x,y)=\varepsilon (x,y)\dolphin\crab

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\donkey a(f) \equiv (f,\widehat\phi).\label{annih}

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\otter\squirrel A =\racoon

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n = 4 : \quad \otter\mole\tau \sheep s\Gamma[a,\theta]\,=\,0.\label{BRSGamma} \puffin

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\tau \starfish\camel\mu \frog \kappa \mu \sin \Theta \dot \Theta =

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\crab \bugs a _ k | 0 \rangle = 0 . \wolf J \wedge \Omega = 0 \ . \vulture

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t = \theta \, \left | \tau \right |\mole\tiger B = d A

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\elephant \urchin ( 1 j ) : ~ ~ ~ \rooster

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1 3 \eagle \psi(x)=f(x)e^{i\theta(x)}.\label{eq:EQ1} \octopus\skunk \tau

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\platypus\flamingo\varphi \rightarrow \varphi - \Lambda .\label{diecisiete}

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\partial _ { \mathrm { a } } \penguin\koala = \; ( n + \frac p 2 )

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a _ { i i } = 1 . \iguana \cow a_k |0\rangle=0. \label{vac} \elephant

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\beaver H _ { L C } \; = \;

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\tau _ s \approx 1 0 . 1 5 \peacock \fish \Lambda_\mu(p,q) = S(p)\Gamma_\mu(p,q)S(q).

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3 6 \seal\mouse\mu \ll1 \protect \protect \protect \protect \hen \cow

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\Lambda_\mu(p,q) = S(p)\Gamma_\mu(p,q)S(q). \quail \gorilla

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\tau \alligator \label{eq:Intertwiner} T \pi(A) = \varrho(A) T

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\coyote\kangaroo c h a n g e d \kangaroo\quail

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T|\phi (x,a)\rangle =|\phi (x,f(a))\rangle , \stingray \chicken

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Backslash \\ %%%% Right bracket \seagul\seal

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\partial ^ 2 \eta = 0 . \parrot \whale \Phi: S^3 \rightarrow S^2,\label{eq:II12}

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\lbrack a,b,cd]=c[a,b,d]+[a,b,c]d, \label{der} \bat

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D : S \rightarrow S + \lambda \ , \ostritch \penguin

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\octopus\jellyfish\langle \,

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\seagul f ( - 2 p )\gorilla \pig

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\parrot\ostritch Backslash \\ %%%% Right bracket \lizard 3 5 \badger { \bf d } \Omega = 0 .

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T|\phi (x,a)\rangle =|\phi (x,f(a))\rangle , \peacock

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%13b\bar{x} \longrightarrow \bar{x}\hbar \hawk\jellyfish \pi \cdot \varepsilon = \varepsilon ~ ,

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\psi(x)=f(x)e^{i\theta(x)}.\label{eq:EQ1}\cat\rhino

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\langle I | 0 \rangle = 1 \, ,\penguin\langle \rho,~~\rangle ~:~~\Xi \longrightarrow A \crab \quail

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\squid m _ { \! _ J } \dog \monkey b =

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\ \anteater \Phi =F_R\left( \varphi \right) \label{newphi2}

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\newt \turtle f =

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\skunk\walrus \Delta_d \rightarrow \Delta, \qquad\Sigma_d \rightarrow \Sigma,\mole

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\skunk \Omega : \; \sigma \leftrightarrow -\sigma . \pig H ( \eta _ 0 ) = \Lambda .

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\tau_s \approx 10.15 \label{spinodaltime} \guinea-pig\mu \gg 1 \protect \protect \protect \protect \killer-whale X ^ i ~ \longrightarrow - X ^ i

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\lambda ^ { \ast } \omega = K . \shrimp\exp i \pi \kappa = \zeta \hawk \sheep \pi _ i = \dog\seagul

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\camel \goat \label{eq:KMP} v\mapsto v-(v,x-ny)y+(v,y)x \squid \crocodile

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\eagle\lion Q \Psi = - \Psi \star \Psi . \dolphin\crab ( h + \lambda r ) = \lambda '

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\langle\phi(x)\phi(x')\rangle={1\over i}G(x,x'),\racoon\moose

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\wolf\parrot { [ \, }

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\label{eq:fundsusy}\pi \cdot \varepsilon = \varepsilon~, \goat \zebra\label{eq:nonabelianreality} \bar V = V \hyena\omega = \rho d(\cos \vartheta d \varphi),

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\parrot \whale { [ \, } \jellyfish\gorilla \partial _ 0 A _ 0 = 0 , \scorpion \moose

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\gamma ^a\partial _a\psi =0, \label{twodDirac}\owl\urchin m(\alpha,\alpha)=1,\,\forall \alpha\in \Pi \ostritch \tarantula

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\cat\rhino\langle \rho,~~\rangle ~:~~\Xi \longrightarrow A\fish \frog

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H ^ 0 _ { \alpha \beta } = \walrus

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\langle f,f\rangle = \langle g,g\rangle = 0. \lion \bear H _ { L C } \; = \;

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\goat G _ { \zeta } ( q ) = \starfish\epsilon = 0 ^ { + } \; . \flamingo

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\Gamma \epsilon = \epsilon \, , \coyote \plankton f =\gorilla \pig e q . ( 1 )

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D _ i ^ \theta\walrus\hawk

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A_J^\alpha = 0. \label{J3} \snake\label{3.3a} \alpha(P_0;\kappa) = \Phi(P_0) \duck \hyena { [ \, } \ostritch \eel

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\elephant\turtle \phi ^ 6 \leftrightarrow - \phi ^ 6 .

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f \diamond g \toucan\vartheta \, \rightarrow \, \vartheta -\alpha \anteater\plankton

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\urchin \skunk 3 2\fish \tiger a _ { i i } = 1 .

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D a = d a - \zebra

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\partial_x^3\Psi(x) +x\ \Psi(x)=E\Psi(x), \mole\tiger

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\label{eq:grav:einstein} \delta R^A_B=0. \ostritch \bat f _ { i } ( t ) = \owl\hyena T \rightarrow { 1 \over T } \, . \elephant \shark

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\llama \tau_s \approx 10.15 \label{spinodaltime} \pig\label{type2}(x,y,z) \to (e^{i \theta}x,y,z)

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\guinea-pig\alpha = \arg Z ( \Gamma ) \hawk\Omega : \; \sigma \leftrightarrow -\sigma .

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\ast\gamma =\gamma_5 \gamma.\label{obh:g5}\skunk \leopard \psi \rightarrow \psi \coyote \snake f _ 0 ( q ) \doteq \ostritch

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. \cat \leopard

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\tiger \skunk 0 . 5 c m ]

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\fox \starfish \phi(\xi) = \pm \tanh \xi, \label{stat} \sloth

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\octopus \elephant \sigma _ 3 \, \theta \, = \theta

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\lambda _ 0 \sim \tilde \lambda \to 0 \squid \stingray Q ^ 2 = H \alligator\cdot : G \times G \rightarrow G .

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Z \longrightarrow u(z) \longrightarrow w(u(z)) \ostritch Backslash \\ %%%% Right bracket

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3 1 \dolphin

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i v _ b d x ^ b \moose\pi(d a) = i[D, \pi(a)]. \label{3.1} \crab \bugs v ^ { 2 }

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\wolf\varepsilon(p,q)=\varepsilon(q,-p-q).\label{A12} \racoon\partial ^ 2 \eta = 0 . \eel\leopard

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3 2 \lemur h(\lambda) =\rho \Theta(\lambda)H(\lambda)

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B = d A \racoon \pig\Gamma \epsilon = \epsilon \, ,

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\dot { \varphi } = \partial _ x \varphi \eagle \rhino\varphi(\omega,y)= \varphi(\omega, -y, y)\,. \racoon

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\tiger\langle S \rangle = N \langle \Delta S \rangle

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\hen \cow s\Gamma[a,\theta]\,=\,0.\label{BRSGamma} \bugs\scorpion

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\coyote \snake \bar { R } =\shrimp \hedgehog \lambda ^ { \ast } \omega = K . \eel\leopard

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\rat v ^ 2 \lizard \sheep

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\owl\urchin \frac { \partial \rho } { \partial L } \seal\hedgehog 2 9 \ostritch \tarantula G _ { \zeta } ( q ) =

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