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52458.png | A _ { i } ( x ) \rightarrow \lambda A _ { i } ( \lambda x ) , |
38f3a208-884f-44f6-82c1-d8b4d6e92bd3.jpg | \operatorname* { l i m } _ { x \to 6 ^ { + } } e ^ { \cot { x } \ln { \left( 7 + x \right) } } |
oleehyo_latex_15_5110.png | \begin{array} { r } { \triangle ( u ( x + h ) - p _ { u , x } ( h ) - e _ { u , x } ( h ) ) = 0 B _ { \delta } . } \end{array} |
sume_data-00001-of-00009_119049.png | \displaystyle \dot { \bf R } _ { k } = \textbf { P } _ { k } / M _ { k } . |
b3c1474134c13e4_basic.png | i U _ { m } ^ { \lambda } \Delta _ { F } ^ { m - n } \left( \mathbf { z - x } \right) ; |
process_34_8319.bmp | \begin{array} { r } { \sigma ( t , \omega ) = \mathbf { s } ( \omega ( t ) ) = ( \mathbf { s } _ { i j } ( \omega ( t ) ) ) _ { 1 \le i , j \le n } \mathrm { a n d } \vartheta ( t , \omega ) = \boldsymbol { \theta } ( \omega ( t ) ) = ( \boldsymbol { \theta } _ { 1 } ( \omega ( t ) ) , \dots , \boldsymbol { \theta } _ { n } ( \omega ( t ) ) ) ^ { \prime } } \end{array} |
a300a77996d19d1_basic.png | n a _ { n } x + a _ { n - 1 } \in R ^ { p } |
oleehyo_latex_47_10892.png | \begin{array} { r } { Z = \left( \frac 1 6 C _ { I J K } q ^ { I } q ^ { J } q ^ { K } \right) ^ { \frac 1 3 } \, . } \end{array} |
process_42_1208.bmp | \begin{array} { r } { J ( A ) ^ { 2 } = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { m } ( 1 - 1 _ { B } ) R _ { i } 1 _ { B } 1 _ { B } L _ { j } ( 1 - 1 _ { B } ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { m } J _ { i * } ^ { 0 1 } J _ { * j } ^ { 1 0 } . } \end{array} |
sume_data-00003-of-00009_29407.png | \varepsilon ^ { \gamma \delta } F _ { \gamma } ^ { a , i } \bar { F } _ { a , N + 4 + i , \delta } \ , |
4b30ec4e8320717.png | \epsilon ( e ( \Lambda ) , m ( \Lambda ) ) = \Lambda ^ { - 1 } \epsilon ( e _ { 0 } , m _ { 0 } ) \tilde { \Lambda } ^ { - 1 } |
sume_data-00000-of-00009_4923.png | \dot { x } _ { t } ^ { \varepsilon } = f ( x _ { t } ^ { \varepsilon } ) d X _ { t } ^ { \varepsilon } , |
sume_data-00007-of-00009_6482.png | \displaystyle \gamma _ { R , \alpha \beta } \, , |
process_44_673.bmp | \begin{array} { r l } { \rho ^ { ( n ) } \left( P _ { n | 1 } \right) } & { { } = \tau \circ \rho ^ { ( n ) } \left( P _ { n | 0 } \right) } \\ { \rho ^ { ( n ) } \left( P _ { n | 0 } \right) } & { { } = \tau \circ \rho ^ { ( n ) } \left( P _ { n | 1 } \right) , } \end{array} |
oleehyo_latex_0_6265.png | \begin{array} { r } { I _ { 1 } = \int _ { \varepsilon \log ( \frac { 3 } { 2 } ) } ^ { 1 } \frac { e ^ { w } } { w } \, d w \leq \frac { e } { \varepsilon \log \frac { 3 } { 2 } } \int _ { \varepsilon \log ( \frac { 3 } { 2 } ) } ^ { 1 } \, d w \leq \frac { e } { \varepsilon \log \frac { 3 } { 2 } } \ll \frac { 1 } { \varepsilon } . } \end{array} |
process_10_8961.bmp | \begin{array} { r l } { \beta _ { a } ( I ) = \beta _ { a , b } ( I ) } & { { } = \ | \ \{ w \in \mathcal { L } _ { t } ^ { f } ( u ) : \operatorname* { m i n } ( u ) = 1 \ \} \ | - \ | \ \{ w \in \mathcal { L } _ { t } ^ { f } ( v ) \setminus \{ v \} : \operatorname* { m a x } ( w ) = n \ \} \ | } \end{array} |
7ba68c70d4c1322.png | A _ { 4 } = \int _ { - L / 2 } ^ { L / 2 } \! \! \! \! d x \, \left[ \left. \mathrm { I m } \left( \phi \partial _ { x } \bar { \phi } \right) \right| _ { t = - T / 2 } - \left. \mathrm { I m } \left( \phi \partial _ { x } \bar { \phi } \right) \right| _ { t = T / 2 } \right] . |
oleehyo_latex_24_4774.png | \begin{array} { r } { \frac { 1 + \sqrt { d } } { 2 } = \frac { 1 + d + 2 \sqrt { d } } { 4 } - \frac { d - 1 } { 4 } } \end{array} |
process_29_7231.bmp | \begin{array} { r l } { I _ { 4 , r } = \sum _ { \xi = 0 } ^ { r } \frac { r ! } { ( r - \xi ) ! } } & { { } \left[ \frac { ( - 1 ) ^ { r - \xi - 1 } } { g _ { 0 } ^ { r - \xi } } e ^ { 1 / g _ { 0 } } \textrm { E i } \left( \frac { - 1 } { g _ { 0 } } \right) + \right. } \end{array} |
sume_data-00005-of-00009_11966.png | \displaystyle F _ { L } ( \bar { x } ) |
sume_data-00002-of-00009_132498.png | \displaystyle { \frac { d s } { d a } } |
68226.png | \operatorname* { l i m } _ { q \to 1 - 0 } R _ { 2 } ( a , b : q ) = \frac { b } { 1 2 a } - \frac 1 2 \log ( 2 \pi ) - \frac { a } { 2 b } - \left( \frac { a } { b } - \frac 1 2 \right) \log \frac { a } { b } + \log \Gamma ( \frac { a } { b } ) . |
sume_data-00002-of-00009_167271.png | \displaystyle \| \chi ( v ) g _ { 2 , 1 } ^ { < } ( v ) \| _ { L ^ { 2 } } ^ { 2 } |
31487c60f9.png | \nu ^ { \mu } = \psi \varphi ^ { ; i } x _ { \, , i } ^ { \mu } \, . |
7f6a4c6a03.png | c _ { 1 } \frac { \Gamma ( c ) \Gamma ( a - b ) } { \Gamma ( a ) \Gamma ( c - b ) } + c _ { 2 } \frac { \Gamma ( 2 - c ) \Gamma ( a - b ) } { \Gamma ( a - c + 1 ) \Gamma ( 1 - b ) } = 0 . |
process_10_5396.bmp | \begin{array} { r } { \partial _ { i } R ( x ) = \bar { \nu } _ { i } ( x ) R ( x ) \overline { { W } } ( x ) R ( x ) + d ( x ) R ( x ) \partial _ { i } \overline { { W } } ( x ) R ( x ) . } \end{array} |
6b5f1fc161ae08a_basic.png | a _ { U ( 1 ) } = - c ( U ( 1 ) ) + \sum _ { C } T _ { U ( 1 ) } ( 1 + 2 n _ { U ( 1 ) } ) , |
process_13_5050.bmp | \begin{array} { r } { \beta _ { \Gamma } ( n ) \gg n ^ { 3 } \beta _ { \Gamma } ( 1 ) } \end{array} |
oleehyo_latex_4_2997.png | \begin{array} { r } { K \phi \varphi _ { i } ( \gamma ) + K \phi \gamma \varphi _ { i } ^ { \prime } ( \gamma ) = \theta . } \end{array} |
process_35_6526.bmp | \begin{array} { r } { \left( \begin{array} { l l } { I _ { p , q } } & { 0 } \\ { 0 } & { I _ { p , q } } \end{array} \right) . } \end{array} |
sume_data-00002-of-00009_149255.png | \displaystyle \frac { d S _ { 3 } ( t ) } { d t } |
sume_data-00004-of-00009_150550.png | \displaystyle 1 0 ^ { 7 } n ( N , t ) [ x ( N , t ) + 0 . 5 5 ] |
sume_data-00004-of-00009_74845.png | c _ { t } ( S _ { t } , t ) |
sume_data-00000-of-00009_157764.png | \displaystyle = \, \hat { \nabla } _ { \mu } T ^ { \mu \nu } + \tilde { K } ^ { \mu } { } _ { \lambda \mu } T ^ { \lambda \nu } + \tilde { K } ^ { \nu } { } _ { \lambda \mu } T ^ { \mu \lambda } |
process_1_3612.bmp | \begin{array} { r } { f \left( x \right) = \left\{ { \begin{array} { r l } \end{array} } \right. . } \end{array} |
51745ba377f303e.png | \bar { \psi } \psi \to - \bar { \psi } \psi |
oleehyo_latex_1_4550.png | \begin{array} { r } { \tau = \alpha _ { 1 } + 2 \alpha _ { 2 } + 3 \alpha _ { 3 } + 4 \alpha _ { 4 } + 3 \alpha _ { 5 } + 3 \alpha _ { 6 } + 2 \alpha _ { 7 } + \alpha _ { 8 } . } \end{array} |
sume_data-00005-of-00009_8927.png | \textstyle { B \ignorespaces \ignorespaces \ignorespaces \ignorespaces \ignorespaces \ignorespaces \ignorespaces \ignorespaces } |
c2bb3730ab19656_basic.png | \operatorname * { l i m } _ { y _ { 0 } \rightarrow 0 } y _ { 0 } k ( \delta , y _ { 0 } ) = L _ { \delta } |
process_43_4700.bmp | \begin{array} { r } { C ( N , \sigma ) : = \left\{ i \in \{ 1 , \ldots , N \} ^ { 2 m } : i _ { u - 1 } = i _ { v } , \ , i _ { u } = i _ { v - 1 } ( u , v ) \in \sigma \right\} \ , . } \end{array} |
sume_data-00001-of-00009_81961.png | \displaystyle p ( y , t ) |
sume_data-00006-of-00009_163443.png | \displaystyle < i \; j \; k \; l \; m \; n > \psi \; ( ( A \; o p _ { \times } \; B ) \; o p _ { \times } \; A ) |
sume_data-00006-of-00009_104578.png | \displaystyle \sum _ { i } \frac { m _ { i , j , d } ^ { \ast 3 / 2 } } { m _ { i , j , \xi } ^ { \ast } } \int _ { 0 } ^ { \infty } \eta _ { i , j } ^ { n } \gamma ^ { \frac { 3 } { 2 } } ( \eta _ { i , j } ) \tau _ { i , j } ^ { t o t } ( - \frac { \partial f _ { 0 } } { \partial \eta _ { i , j } } ) d \eta _ { i , j } |
oleehyo_latex_9_2153.png | \begin{array} { r } { ( - \alpha ^ { i - h } ( g ) , - h ) \circ ( b , j ) = ( \alpha ^ { - h } ( b ) - \alpha ^ { i - h } ( g ) , j - h ) , } \end{array} |
process_27_2055.bmp | \begin{array} { r } { \tilde { v } _ { k } = \frac { \| E _ { 2 } w _ { k } \| ^ { 1 / 2 } } { \| E _ { 1 } v _ { k } \| ^ { 1 / 2 } } v _ { k } , \tilde { w } _ { k } = \frac { \| E _ { 1 } v _ { k } \| ^ { 1 / 2 } } { \| E _ { 2 } w _ { k } \| ^ { 1 / 2 } } w _ { k } } \end{array} |
24149f4b6b46c46.png | \xi ^ { \alpha } \mapsto \xi ^ { \alpha } + t ^ { \alpha } ( \xi ) . |
d04e5ecce878564_basic.png | \nu _ { E _ { D } } ( \operatorname { N r d } _ { E _ { D } } ( v ^ { - 1 } g _ { 0 } ) ) |
sume_data-00003-of-00009_75399.png | \displaystyle \sum _ { \nu } \hat { N } _ { \lambda \mu } ^ { \ \ \nu } |
c9439100300c832_basic.png | \delta \eta _ { a } ^ { * } = \left( D _ { \mu } \right) _ { a } ^ { \; \; b } A _ { b } ^ { * \mu } , \; \gamma \eta _ { a } ^ { * } = - f _ { \; \; a c } ^ { b } \eta _ { b } ^ { * } \eta ^ { c } , |
76fcf20ad0c37ba.png | j _ { \mu \alpha } ^ { c a n } = - 8 i \sigma _ { \mu } ^ { \beta { \dot { \beta } } } \ D _ { \alpha } \left( { \mathcal F } ^ { \prime \prime } D _ { \beta } G { \bar { D } } _ { \dot { \beta } } G \right) \ . |
sume_data-00000-of-00009_85710.png | H _ { B } = \sum _ { k } E _ { k } P _ { k } \, , |
sume_data-00008-of-00009_85910.png | \displaystyle - 9 t ^ { 2 } - 3 t + 1 ) U ^ { 2 } , |
oleehyo_latex_12_3841.png | \begin{array} { r } { ( d ^ { A } \alpha ) ( X , Y ) = \nabla _ { X } ^ { A } ( \alpha ( Y ) ) - \nabla _ { Y } ^ { A } ( \alpha ( X ) ) - \alpha ( [ X , Y ] ) \, . } \end{array} |
sume_data-00002-of-00009_126209.png | \displaystyle \{ r : z ( r ) = k \} , \qquad | R _ { k } | = n _ { k } |
process_29_6486.bmp | \begin{array} { r } { \omega _ { \infty , \Lambda } = ( \Omega _ { \Lambda } , \cdot \Omega _ { \Lambda } ) ) \ , } \end{array} |
sume_data-00001-of-00009_170536.png | \sum _ { i = 1 } ^ { k } \nu f _ { i } \mathbin { { \scriptstyle \circ } } \pi | _ { ( c _ { i } ) _ { W } } = 0 \; . |
oleehyo_latex_48_18039.png | \begin{array} { r } { \hat { R } _ { m n } \epsilon \equiv \left[ \hat { \nabla } _ { m } , \hat { \nabla } _ { n } \right] \epsilon = 0 , } \end{array} |
sume_data-00004-of-00009_23673.png | \displaystyle v _ { i } ^ { l + 1 } = |
sume_data-00003-of-00009_97669.png | \displaystyle J _ { \nu } ( j _ { \nu + 1 , 1 } ) |
1f835835bb2e888.png | { \cal G } ( x , x ^ { \prime } ) = { \cal G } _ { 0 } ( x , x ^ { \prime } ) - \lambda \, { \cal G } _ { 0 } ( x , x _ { 0 } ) \, { \cal G } ( x _ { 0 } , x ^ { \prime } ) , |