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sume_data-00001-of-00009_67824.png | \displaystyle S _ { s t r } |
sume_data-00007-of-00009_124711.png | 4 3 6 9 0 1 5 0 9 9 2 |
process_2_4448.bmp | \begin{array} { r } { h ( \tau ) : = \mu \ ( ( \sqrt { \omega } - \tau ) ^ { 2 } , \frac { \mathbf { c } } { \sqrt { \omega } } ( \sqrt { \omega } - \tau ) \ ) = ( \sqrt { \omega } - \tau ) ^ { 4 - d } \mu \left( 1 , \frac { \mathbf { c } } { \sqrt { \omega } } \right) , } \end{array} |
sume_data-00003-of-00009_120847.png | A = \mathrm { M i n } \left[ e ^ { - ( { \cal H } ^ { \prime } - { \cal H } ) } , 1 \right] . |
process_3_3062.bmp | \begin{array} { r } { \int _ { Y } ( \partial _ { 1 } w _ { A } ) ( \partial _ { 2 2 } ^ { 2 } w _ { B } ) = \int _ { Y } ( \partial _ { 2 } w _ { A } ) ( \partial _ { 1 1 } ^ { 2 } w _ { B } ) = 0 . } \end{array} |
71f8838431ce968_basic.png | \ensuremath { \mathbf { A } } ^ { x } |
sume_data-00001-of-00009_93311.png | \displaystyle 1 - \operatorname* { m i n } \{ H ( p _ { y } + p _ { z } ) , H ( p _ { x } + p _ { z } ) , H ( p _ { x } + p _ { y } ) \} \; , |
process_20_5792.bmp | \begin{array} { r } { N _ { Y } = \prod _ { p } p ^ { f _ { p } } . } \end{array} |
33d3f5b6f84b092.png | \partial ^ { \mu } \, \langle 0 \vert \, T ( \, \, N _ { 3 } \, [ \, \, J _ { _ { \mu \, 5 } } ^ { ^ { B P H Z } } \, ] \, \, X \, \vert 0 \rangle \, = \, \, r \, \langle 0 \, \vert \, T \, ( \, N _ { 4 } \, [ \, F _ { \mu \nu } \, { \tilde { F } } ^ { \, \mu \nu } \, \, ] \, X \vert \, 0 \, \rangle |
sume_data-00008-of-00009_103902.png | \displaystyle \int _ { M } e ^ { - \frac { d ( \psi ( p ) , p ) ^ { 2 } } { 4 r ^ { 2 } } } \, d \mathrm { v o l } ( p ) \leq \int _ { M } \left( \int _ { \{ ( x , y ) \in A _ { r } | \Phi _ { r } ( x , y ) = p \} } e ^ { - \frac { d ( x , \Phi _ { r } ( x , y ) ) ^ { 2 } } { 4 r ^ { 2 } } } d \mathcal { H } ^ { 0 } \right) d \mathrm { v o l } ( p ) . |
sume_data-00007-of-00009_123803.png | ( \Omega ^ { - \bullet } ( A ) [ [ u ] ] , b + u d ) \to \mathrm { { C C } } _ { - \bullet } ^ { - } ( A ) |
sume_data-00003-of-00009_132350.png | \scriptstyle { \, \, \, \, d } |
f83d0cd71a40dbd_basic.png | \operatorname * { l i m } _ { x _ { 1 } \rightarrow + \infty } \; S ^ { ( l ) } ( x _ { 1 } ) \; \; = \; \; \operatorname * { l i m } _ { x _ { 1 } \rightarrow - \infty } \; S ^ { ( l ) } ( x _ { 1 } ) \; \; \; \; \; \forall \; l \; , |
sume_data-00006-of-00009_29713.png | \displaystyle | \delta { \omega } | _ { \mathrm { m i n } } = \frac { 1 } { \sqrt { M } \tau } , |
sume_data-00006-of-00009_170795.png | \displaystyle ( a g ) \circ x |
9686a4bea8f0338_basic.png | \lambda _ { \rho } = 1 . 0 6 \pm 0 . 1 5 , \; \; \; \; \; \; \lambda _ { \omega } = 0 . 3 1 \pm 0 . 0 6 , |
oleehyo_latex_31_1487.png | \begin{array} { r l } { \frac { d } { d t } ( f _ { t } ^ { H _ { 0 } } ( f _ { t } ^ { H _ { 1 } ^ { t } } ( z ) ) ) } & { { } = \frac { d } { d t } f _ { t } ^ { H _ { 0 } } ( f _ { t } ^ { H _ { 1 } ^ { t } } ( z ) ) + D f _ { t } ^ { H _ { 0 } } ( f _ { t } ^ { H _ { 1 } ^ { t } } ( z ) ) \frac { d } { d t } f _ { t } ^ { H _ { 1 } ^ { t } } ( z ) } \end{array} |
c2e6d0631476c5d.png | \begin{array} { r } { { \forall \, m , n \neq 0 , ~ ~ ~ \left[ a _ { m } ^ { r } , a _ { n } ^ { s } \right] = \mathrm { s g n } ( n ) \delta _ { m + n , 0 } \, \delta ^ { r s } ~ ~ ~ \mathrm { a n d } ~ ~ ~ \{ \theta _ { m } ^ { 1 a } , \theta _ { n } ^ { 1 b } \} = \frac { 1 } { 4 } ( \Gamma ^ { + } ) ^ { a b } \, \delta _ { m + n , 0 } } } \end{array} |
oleehyo_latex_41_6229.png | \begin{array} { r l } \end{array} |
oleehyo_latex_41_8147.png | \begin{array} { r } { \int _ { \mathbb { R } ^ { N } } | \nabla U | ^ { 2 } \, d x = T _ { N } \mathrm { ~ a n d ~ } \int _ { \mathbb { R } ^ { N } } | U | ^ { 2 ^ { * } } \, d x = 1 . } \end{array} |
5f20e56c1f.png | \delta _ { R } \, \, \Sigma ( r , u _ { i } ) = - 2 \epsilon \, \, \epsilon _ { z i j } \, \, u _ { i } \, \, \partial _ { u _ { j } } \ \Sigma ( r , u _ { i } ) \ . |
process_31_5137.bmp | \begin{array} { r l } { C } & { { } = [ \zeta ^ { 0 } ] P ( z _ { 1 } - z _ { 2 } ) P ( z _ { 1 } - z _ { 3 } ) P ( z _ { 1 } - z _ { 4 } ) P ( z _ { 2 } - z _ { 3 } ) P ( z _ { 2 } - z _ { 4 } ) P ( z _ { 3 } - z _ { 4 } ) } \end{array} |
758115ca10082b7_basic.png | X _ { 1 } - X _ { 3 } = Y _ { 1 } ( a ) = 0 |
sume_data-00003-of-00009_56668.png | \displaystyle \frac { V ( n , K ) } { L ( n , K ) } |
sume_data-00001-of-00009_35578.png | \displaystyle \frac { i - 1 } { N } = \int _ { \gamma _ { i } ( t ) } ^ { E _ { t } } \mathrm { d } \hat { \rho } _ { t } ( x ) . |
process_31_6638.bmp | \begin{array} { r } { \zeta ( s ) = \frac { 1 } { s - 1 } + \dots , \Gamma ( s ) = \frac { 1 } { s } + \dots , } \end{array} |
oleehyo_latex_2_6520.png | \begin{array} { r } { S T O ( z _ { 1 } ) : = \left\{ \begin{array} { l } { \displaystyle \operatorname* { m i n } _ { x , y } \, \, \mathbb { E } \left[ \theta \left( x , y , z _ { 1 } , \zeta ( \omega ) \right) \right] } \\ { \left\{ \begin{array} { l l } { x \in X } & { } \\ { y \in D ( x ) . } & { } \end{array} \right. } \end{array} \right. } \end{array} |
sume_data-00008-of-00009_144727.png | \mathrm { r n k } ( x y ) \leq \operatorname* { m i n } \left( \mathrm { r n k } ( x ) , \mathrm { r n k } ( y ) \right) , \quad x , y \in M _ { n } . |
sume_data-00008-of-00009_91086.png | \displaystyle V = \alpha k ( \theta ) \sigma _ { < } |
sume_data-00007-of-00009_114936.png | \displaystyle P _ { | X | | Y | } ^ { d } ( q ) |
sume_data-00001-of-00009_159946.png | ( g ^ { - 1 } x ) ( e ) = x ( g ) = g \neq e |
sume_data-00004-of-00009_31726.png | g ^ { \ast } T ^ { 1 } ( X ) = T ^ { 1 } ( X _ { m - 2 } ) \otimes L |
process_43_8350.bmp | \begin{array} { r } { ( a f ) ( x ) : = \sum _ { t ( g ) = x } a ( g ) ( g \cdot f ( s ( g ) ) ) } \end{array} |
4faaeef1-274d-4af3-b6a0-64c97ff6c652.jpg | \operatorname* { l i m } _ { v \to 8 } 0 \cos { v } |
sume_data-00000-of-00009_76309.png | { \mathcal { B } } \mathrm { ~ i s ~ b o u n d e d ~ i n ~ } \mathcal { I } . |
sume_data-00003-of-00009_125442.png | \frac { \partial c } { \partial t } + u _ { F } \frac { \partial c } { \partial x } + \frac { \partial ( v _ { p } c ) } { \partial y } = D \frac { \partial ^ { 2 } c } { \partial x ^ { 2 } } + \frac { \partial } { \partial y } \left( D \frac { \partial c } { \partial y } \right) . |
sume_data-00005-of-00009_12157.png | \displaystyle = \frac { r - 1 } { q } \log P + \Theta ( P ) |
sume_data-00006-of-00009_96529.png | K _ { n } : = F ^ { - 1 } ( ( - \infty , n + \operatorname* { s u p } _ { K _ { 0 } } F ] ) . |
sume_data-00000-of-00009_126107.png | \overline { { W } } _ { n _ { 0 } } = \sum _ { \alpha } \left| C _ { n _ { 0 } } ^ { \alpha } \right| ^ { 4 } . |
process_37_2683.bmp | \begin{array} { r } { \int _ { Q _ { - } ^ { + } } \ ( u \cdot ( \partial _ { t } \varphi + \Delta \varphi ) + u \otimes u : \nabla \varphi + p \mathrm { d i v } \ , \varphi \ ) d x d t = 0 } \end{array} |
process_39_3643.bmp | \begin{array} { r } { \left( 1 - \frac { 2 } { \sqrt { \prod _ { i = 1 } ^ { s } d _ { i } } } \right) \frac { 1 } { \sum _ { i = 1 } ^ { s } d _ { i } - 5 s - 2 \delta - \nu - 1 } > \lambda > \frac { 1 } { \sum _ { i = 1 } ^ { s } d _ { i } + 1 } } \end{array} |
process_34_6658.bmp | \begin{array} { r } { \left| \Pi _ { n } \right| = \left( n ! \right) ^ { 2 n } } \end{array} |
9d0d89e5-7023-4aea-9d39-3b98f82740c4.jpg | \operatorname* { l i m } _ { u \to 9 ^ { + } } \frac { \frac { d } { d u } \left( 3 + - 7 \sin ^ { 0 } { u } \right) } { \frac { d } { d u } \left( \sin { u } + u \cos ^ { 3 } { u } \right) } |
process_21_5831.bmp | \begin{array} { r } { 5 F _ { u } { } ^ { 2 } = L _ { 2 u } - ( - 1 ) ^ { u } 2 \ , , u \in \Z \ , , } \end{array} |
sume_data-00000-of-00009_95928.png | \frac { \Lambda } { \kappa } \gg 1 . |
sume_data-00002-of-00009_24000.png | \sigma ^ { 2 } \rightarrow \infty |
process_49_274.bmp | \begin{array} { r } { D _ { k } ( n + 1 ) - D _ { k } ( n ) = \left\{ \begin{array} { l l } { 1 , } & { p \frac { D _ { k } ( n ) } { n } , } \\ { 0 , } & { 1 - p \frac { D _ { k } ( n ) } { n } } \end{array} \right. } \end{array} |
sume_data-00007-of-00009_149829.png | \displaystyle \mathrm { e } ^ { 2 K t } g _ { \eta , \sigma } \leq C ( n , K , \alpha , V , \Theta , \eta ) \, . |
sume_data-00008-of-00009_73317.png | \displaystyle L _ { s o ( 2 n + 1 ) } ( k , 0 ) \otimes |
process_8_2770.bmp | \begin{array} { r } { \tilde { V } ( x ) = \frac { 1 } { T } \int _ { 0 } ^ { T } \mathcal { P } _ { t } V ( x ) d t } \end{array} |
sume_data-00002-of-00009_119285.png | \displaystyle ( 0 , 2 ) , ( 0 , 4 ) , ( 2 , 4 ) , ( 0 , 0 ) , ( 2 , 2 ) , ( 4 , 4 ) \, . |
sume_data-00000-of-00009_26607.png | P _ { r } ( L ) = \int _ { 0 } ^ { \infty } f ( L , t ) d t . |
sume_data-00005-of-00009_106906.png | \displaystyle W ( \cos \Theta ) |
sume_data-00005-of-00009_39360.png | \displaystyle g _ { x _ { i } x _ { i } } ^ { ( 1 ) } |
process_33_9362.bmp | \begin{array} { r } { { \hat { h } } _ { 0 } ( n ) = n \ , , { \hat { h } } _ { 1 } ( n ) = n ^ { 2 } + \sum _ { i > 0 } i p _ { i } \frac { \partial } { \partial p _ { i } } \ , , } \end{array} |
oleehyo_latex_42_6605.png | \begin{array} { r } { | T _ { 0 } ^ { ( n ) } | \le \frac { N } { h } D _ { e t } ^ { - n + 1 } \| \widetilde { C _ { o } } \| _ { l , 0 } ^ { n - 1 } \left( \sum _ { m = 2 } ^ { N } 2 ^ { 2 m } D _ { e t } ^ { \frac { m } { 2 } } \| J _ { m } \| _ { l , 0 } \right) ^ { n } . } \end{array} |
9f83fdc6d71eacd.png | \delta | \Psi \rangle = a ^ { A } \Bigl ( p ^ { A } + \mathrm { i } ( E _ { 0 } + \frac { 3 } { 2 } - d ) y ^ { A } \Bigr ) | \Lambda \rangle \, , |
sume_data-00008-of-00009_75718.png | \sigma _ { n } = 2 \pi \ \int \ P _ { n } ( b ) \ b d b \; . |
sume_data-00007-of-00009_17968.png | \| h _ { \delta } \| _ { L ^ { 2 } ( \tilde { Q } ) } \leq C \| \tilde { y } _ { 0 } \| _ { L ^ { 2 } ( Q _ { A , 1 } ) } , |
84bee794b8030ae.png | \sum _ { i } \kappa _ { i } = 2 ( m _ { 1 } + m _ { 2 } + m _ { 3 } ) . |
oleehyo_latex_48_1871.png | \begin{array} { r } { \Im \left( U _ { 2 } \right) | _ { \partial M } = 0 , \qquad \Im \left( \phi ^ { * } V _ { 1 } \right) | _ { \partial M } = 0 \, . } \end{array} |
oleehyo_latex_6_4863.png | \begin{array} { r } { \begin{array} { r l } { = } & { { } \xi _ { 0 } E _ { P } \biggl [ \varphi \biggl ( x + \sum _ { i = 1 } ^ { n } Z _ { i } ^ { \theta } \biggr ) \vert H _ { 1 } \biggr ] + ( 1 - \xi _ { 0 } ) E _ { P } \biggl [ \varphi \biggl ( x + \sum _ { i = 1 } ^ { n } Z _ { i } ^ { \theta } \biggr ) \vert H _ { 2 } \biggr ] , } \end{array} } \end{array} |
12acbe7f2e62c0d_basic.png | \Psi _ { s } ( P ) = \frac { 2 ^ { - 1 / 4 } \Gamma ( 1 + 2 i b P ) \Gamma \left( 1 + \frac { 2 i P } { b } \right) \cos ( 2 \pi s P ) } { - 2 i \pi P } ( \pi \mu \gamma ( b ^ { 2 } ) ) ^ { - i P / b } ~ . |
process_32_8492.bmp | \begin{array} { r } { \| b \| _ { \lesssim } \operatorname* { s u p } _ { \| u \| _ { W ^ { 1 , n } } \le 1 } \int _ { \C } b J u = \operatorname* { s u p } _ { u \neq 0 } \frac { \int _ { \C } b J u } { \| u \| _ { W ^ { 1 , n } } ^ { n } } } \end{array} |
sume_data-00008-of-00009_173011.png | 2 \cdot ( n + 1 ) - 1 = 2 n + 1 . |
oleehyo_latex_29_1197.png | \begin{array} { r l r l } \end{array} |
sume_data-00004-of-00009_48640.png | \displaystyle \lambda _ { 2 } q _ { 2 } \leq \sum _ { i = 1 } ^ { 3 } \sum _ { j = m + 1 } ^ { n _ { 2 } } a _ { i , j } . |
sume_data-00006-of-00009_135027.png | Z ( t ) = B ( t ) + v _ { L } \, Y _ { L } ( t ) + v _ { R } \, Y _ { R } ( t ) , |
sume_data-00008-of-00009_97344.png | \displaystyle I _ { n } ^ { k } |
5ffea8e4-ba1f-4438-8978-e1cdef751f98.jpg | \operatorname* { l i m } _ { w \to \pi / 5 ^ { - } } 2 / 3 \tan ^ { 6 } { w } \left( 9 w + \left( - 5 \pi \right) ^ { 8 } \right) |
b95ec43a3081b2c.png | f _ { Q } ( E _ { Q } ) \simeq \beta _ { H } E _ { Q } ~ ~ ~ . |
oleehyo_latex_1_6259.png | \begin{array} { r } { \begin{array} { r l } \end{array} } \end{array} |
sume_data-00002-of-00009_28467.png | \displaystyle ( v _ { n } , \vartheta _ { n } ) \rightarrow ( v , \vartheta ) , \quad \mathrm { ~ i n ~ } L ^ { 2 } ( 0 , T ; C ^ { 2 } ( [ - k , k ] ) ) , |
b18023b5ef654e2.png | \left. \frac { \delta S [ \{ \varphi _ { i } \} ] } { \delta \varphi _ { i } } \right| _ { \varphi _ { i } = 0 } = 0 . |
sume_data-00005-of-00009_60455.png | \Lambda _ { A } ( X ) : = \ell ^ { p _ { A } } ( X , A ) . |
sume_data-00003-of-00009_169037.png | \displaystyle \psi _ { \phi } - N \psi _ { w } = c _ { i n } \, , |
process_8_1730.bmp | \begin{array} { r } { X X ^ { \top } = l \ , V ^ { \top } V \mathrm { ~ a ~ n ~ d ~ } X ^ { \top } X = k \ , W ^ { \top } W . } \end{array} |
process_19_3607.bmp | \begin{array} { r } { \left( \sum _ { \hat { x } \in \hat { X } } \alpha _ { \hat { x } } \hat { x } \right) ^ { \hat { \psi } _ { \sigma } } = \sum _ { \hat { x } \in \hat { X } } \alpha _ { \hat { x } } ^ { \hat { \phi } _ { \sigma } } \hat { x } ^ { \hat { \psi } _ { \sigma } } . } \end{array} |
sume_data-00001-of-00009_176124.png | \displaystyle \frac { a } { 1 0 \pi } K ( x ) , |
sume_data-00002-of-00009_156406.png | \displaystyle + \left. \sum _ { i = 1 } ^ { K } \sum _ { k : i \notin k } \beta _ { t } ^ { * } ( i ) a ( k ) v _ { T } ( t + 1 , l ( m , a , - i ) ) \right) . |
784c29379a.png | z _ { \mathrm { Y M } } ^ { ( l ) } = 0 \qquad \mathrm { f o r } \quad l \geq 2 \ . |
sume_data-00002-of-00009_14078.png | t _ { r } = { \frac { 1 } { r } } \sum _ { j } n _ { j } z _ { j } ^ { - r } |
sume_data-00002-of-00009_122196.png | \displaystyle L ^ { \lambda _ { 1 } } ( s ) - L ^ { \lambda _ { 2 } } ( s ) |
sume_data-00004-of-00009_49204.png | \displaystyle ( k _ { 1 } , k _ { 2 } , k _ { 3 } , k _ { 4 } ) |
sume_data-00001-of-00009_42717.png | \displaystyle = | \{ L \in S ; \delta ( L ) \leq T \} | . |
sume_data-00003-of-00009_124238.png | { \frac { \partial \eta } { \partial a } } + \vec { \nabla } _ { x } ( \vec { u } \eta ) = 0 |
e20dbfa3-0de3-416a-892d-eeb63bcd7ccc.jpg | \operatorname* { l i m } _ { w \to \infty } \frac { 3 \cdot 2 w ^ { 5 } + - 8 w } { 4 \cdot 3 w ^ { 3 } } |
sume_data-00004-of-00009_82913.png | \displaystyle \overline { { a ( 2 a m s + 1 ) , \, 2 a m { ( 2 a m s + 1 ) } ^ { k - 2 } , } } |
sume_data-00007-of-00009_103053.png | \displaystyle a _ { \phi K _ { S } } ( t ) |
sume_data-00004-of-00009_137895.png | z = { \frac { 1 } { p q } } \left[ { \frac { 1 } { 2 } } ( M ^ { 2 } - m ^ { 2 } - M _ { D } ^ { 2 } ) + { \frac { s } { 4 } } \right] |
oleehyo_latex_47_19613.png | \begin{array} { r } { V = \Psi _ { i _ { 1 } . . . i _ { l } } n _ { i _ { 1 } } . . . n _ { i _ { l } } + . . . } \end{array} |
sume_data-00006-of-00009_165569.png | \displaystyle = a _ { 0 } 0 ^ { k } . |
oleehyo_latex_36_7319.png | \begin{array} { r } { d _ { \rho } = d e g _ { L S } ( I d + T _ { \rho } , 0 , B _ { R } ( 0 ) ) } \end{array} |
92936acf4dfbf6e_basic.png | z _ { 3 } : = ( s _ { 1 } , s _ { 2 } , x _ { 1 } , x _ { 2 } ) |
sume_data-00006-of-00009_63000.png | \Psi ( z _ { 1 } , . . . z _ { N } ) = \phi ( z _ { 1 } , \dots , z _ { N } ) \Psi _ { \mathrm { L a u g h } } ( z _ { 1 } , . . . z _ { N } ) |
sume_data-00001-of-00009_102233.png | \displaystyle - k v _ { b } - { \frac { \dot { h } } { 2 } } \, , |
sume_data-00006-of-00009_16725.png | \tau ( E ) = \frac { 4 \Gamma ^ { 2 } } { ( E - E _ { 0 } ) ^ { 2 } + 4 \Gamma ^ { 2 } } |
sume_data-00006-of-00009_88474.png | \displaystyle = X _ { n } \beta + e _ { n } ; \quad e _ { n } \sim N ( 0 , \sigma ^ { 2 } V _ { n } ) \; ; \quad \beta = \mu _ { \beta } ^ { ( d ) } + \omega ; \quad \omega \sim N ( 0 , \sigma ^ { 2 } V _ { \beta } ^ { ( d ) } ) \; , |
e998ffd06a71bd5_basic.png | \delta \Omega ^ { \delta - 1 } D \Omega \cdot D f + \Omega ^ { \delta } D \cdot D f = 0 , |
sume_data-00000-of-00009_113998.png | w _ { v } = c \times \prod _ { l \in L _ { v } } { \log ( s _ { l } ) } + b \, , |