formula,image
"\alpha = \frac { 3 6 0 } { N _ { d } } p = \frac { 3 6 0 } { 1 4 } \times 2 = \frac { 3 6 0 } { 7 }" ,000469d0-1fad-11e4-a8ab-001018b5eb5c__mathematical-expression-and-equation_2.jpg
"\le e _ { z } ^ { T } P ^ { - 1 } B _ { n } B _ { n } ^ { T } P ^ { - 1 } e _ { z } + v _ { 1 } ^ { 2 } ," ,0024bae7-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_17.jpg
"| | T _ { x } ( V ) | | _ { s } = | | V | | _ { s }" ,00283f86-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"A n n ( N _ { 1 } ) \varsubsetneqq A n n ( N _ { 2 } ) \varsubsetneqq \dots \varsubsetneqq A n n ( N _ { p } ) \varsubsetneqq \dots" ,0028424b-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"u = a = 2 n" ,00323708-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_15.jpg
"x \sin \omega - y \cos \omega = h \prime" ,006118d2-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"x _ { v + 1 } - x ." ,0061196e-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_9.jpg
"r = ( m + \frac { m \sin 2 \beta } { 2 \cos \beta } ) \sin \beta" ,00611988-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\pi r ^ { 2 } + \pi r ^ { 2 } ( \frac { 1 - \sin \alpha } { 1 + \sin \alpha } ) ^ { 2 } + \pi r ^ { 2 } ( \frac { 1 - \sin \alpha } { 1 + \sin \alpha } ) ^ { 4 } + \dots ," ,00611a3e-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\beta = \frac { \Delta l } { r }" ,0092e632-e0b0-4b42-9ff1-235aa83b8ad6__mathematical-expression-and-equation_2.jpg
"+ 2 [ ( P + f _ { 1 } ) - \frac { 3 } { 2 } ( R + f _ { 1 } ) ] ^ { 2 } + 2 [ ( S + f _ { 2 } ) - \frac { 3 } { 2 } ( Q + f _ { 2 } ) ] ^ { 2 }" ,00ff8d0d-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\Theta _ { 3 } ) _ { 1 3 } = \eta _ { 1 3 } ( \eta _ { 2 1 } + 9 - 3 \eta _ { 1 1 } + 3 \eta _ { 3 3 } ) - 3 \eta _ { 2 3 } ( 2 + \eta _ { 1 1 } +" ,00ff8d26-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_22.jpg
"= [ ( 1 - e ) \phi ( m ) ] + [ 1 - e _ { 1 } ] [ a + a ^ { 2 } + \dots + a ^ { v - 1 } ] ." ,00ff8d65-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"A _ { 0 } = L _ { p } ( \Omega , \sigma )" ,00ff8e31-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\theta \in [ 0 , \tau _ { 2 } ]" ,0101f9fb-ac0b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_12.jpg
"t = f ( n ; b _ { 1 } , b _ { 2 } , b _ { 3 } , b _ { 4 } , J )" ,0187f845-a25d-474f-baac-78c52b868e99__mathematical-expression-and-equation_2.jpg
"\_ | \_ \_ \cup | \_ \cup \_ \cup | \_ \_ \dots" ,01d01a76-4bfd-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"| | e ^ { P } | | \le e ^ { \Lambda } ( 1 + 2 | | P | | + \dots + 2 ^ { m - 1 } | | P | | ^ { m - 1 } )" ,01d9240c-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"= \int _ { - \infty } ^ { \infty } T ( s ) \delta ( s ) f ( t ) d s = T ( 0 ) f ( t ) = f ( t )" ,01d92410-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_4.jpg
"| | u | | \neq 0 \}" ,01d924b5-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\xi - x = - r \sin \tau , \eta - y = r \cos \tau ." ,0216fb80-d3b8-11e2-b791-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"d \prime A \equiv P \cdot d l = P ( \frac { \partial l } { \partial T } d T + \frac { \partial l } { \partial P } d P )" ,022d9bd2-40e4-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
"v ^ { 2 } = 4 g \frac { P } { M } s ; s = \frac { v t } { 2 }" ,0234f550-be25-11e4-9ade-005056825209__mathematical-expression-and-equation_2.jpg
"+ \int _ { \Omega } N _ { i } \frac { \partial } { \partial x } ( h n D _ { x x } \frac { \partial c } { \partial x } + h n D _ { x y } \frac { \partial c } { \partial y } ) d \Omega +" ,0272705f-bc38-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"[ D _ { l } ( s ) W ( s ) ] [ \begin{array} { c } C \\ s I _ { n } - A \end{array} ] = 0" ,02b32e7b-ac0b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"a b = z b a ," ,02b46933-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\int _ { a } ^ { + \infty } t ^ { 2 k } | u ^ { ( k ) } ( t ) | ^ { 2 } d t < + \infty" ,02b46b36-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\int _ { 0 } ^ { + \infty } | p ( t ) | | u ( t ) | ^ { 2 } d t < + \infty" ,02b46b3e-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\int _ { a } ^ { t } | u ^ { ( n _ { 0 } + 1 ) } ( \tau ) | ^ { 2 } d \tau = \sum _ { i = 1 } ^ { n _ { 0 } } ( - 1 ) ^ { n _ { 0 } - i } u ^ { ( n _ { - } i ) } ( t ) u ^ { ( i ) } ( t ) - u ^ { ( n _ { 0 } + 1 ) } ( a ) u ^ { ( n _ { 0 } ) } ( a ) +" ,02b46b48-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_5.jpg
"r d r = x _ { 1 } d x _ { 1 } + x _ { 2 } d x _ { 2 } + x _ { 3 } d x _ { 3 } ," ,02c23ac9-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_8.jpg
"c _ { i k } ^ { 2 } = S _ { i } S _ { k } ^ { 2 } = ( r - r _ { i } ) ^ { 2 } + ( r - r _ { k } ) ^ { 2 } - 2 ( r - r _ { i } ) ( r - r _ { k } ) \cos \phi" ,0300aa0d-2032-4769-9da4-007897df8944__mathematical-expression-and-equation_5.jpg
"p . d V = R . d T ," ,03144b40-dadf-11e2-9439-005056825209__mathematical-expression-and-equation_6.jpg
"a _ { 1 , k , l } \equiv 0 ; x _ { k } \equiv 1 , x _ { l } \equiv 1 , x _ { r } \equiv 1 ; k \neq l \neq r , k \neq" ,03618781-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\iint _ { A } [ u ( x , y ) ] ^ { 2 } d x d y = 1 ," ,03618794-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\sqrt { n } ( \hat { \beta } ^ { w } - \hat { \beta } ) = \frac { \frac { 1 } { \sqrt { n } } \sum _ { t = 1 } ^ { n } X _ { t - 1 } u _ { t } ^ { w } } { \frac { 1 } { n } \sum _ { t = 1 } ^ { n } X _ { t - 1 } ^ { 2 } } = \frac { \frac { 1 } { \sqrt { n } } \sum _ { t = 1 } ^ { n } X _ { t - 1 } \hat { u } _ { t } K _ { t } } { \frac { 1 } { n } \sum _ { t = 1 } ^ { n } X _ { t - 1 } ^ { 2 } }" ,039045fb-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { \partial W _ { \theta * } } { \partial \theta _ { i } } = - M _ { B \prime } X \prime ( \Sigma _ { \theta * } + X M _ { B \prime } X \prime ) ^ { + } V _ { i }" ,0390473d-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"p ^ { ( 6 n + 4 ) } ( 0 , 1 , 0 ) = g ( p ^ { ( 6 n + 3 ) } ( 0 , 1 , 1 ) , p ^ { ( 6 n + 3 ) } ( 0 , 1 , 0 ) )" ,039048d8-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_6.jpg
"d h _ { a } ( \tilde { p } _ { \{ Q \} } ) ( P ) = P ;" ,03921ebf-570b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"l = 1 , \dots , 4 ." ,03e49da4-bc38-11e1-8339-001143e3f55c__mathematical-expression-and-equation_14.jpg
"\alpha = \frac { \omega } { 2 n + 1 }" ,0460aece-4073-43ba-a89d-a67f02781d42__mathematical-expression-and-equation_9.jpg
"\Delta K ^ { * } _ { a s } = [ \begin{array} { c c c c c c c c c } 5 & \pm 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \pm 2 & 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{array} ]" ,0469de12-ac0b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_0.jpg
"D _ { 1 } \int _ { t _ { 0 } } ^ { t } \sum _ { l , j \in N } | y _ { k l } ( t ) | | y ^ { j l } ( s ) | \lambda _ { 1 } ( s , C | | m ( s ) | | , C | | m ( s ) | | ) | x _ { 1 }" ,046d3e19-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_5.jpg
"g ( c | a ) = g ( c | a )" ,046d3e82-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_11.jpg
"t \frac { a ^ { 3 } } { \sqrt { a ^ { 3 } z - a z ^ { 3 } } } ." ,04aec3db-e2b7-4407-b8ea-da28588fe9db__mathematical-expression-and-equation_0.jpg
"x _ { 2 } = \lambda ^ { 2 }" ,054798a9-570b-11e1-2069-001143e3f55c__mathematical-expression-and-equation_0.jpg
"+ \bigwedge \{ \omega ( z ) | z \in [ 1 - y _ { 2 } , x _ { 2 } ] \} - \bigwedge \{ \omega ( z ) | z \in [ 1 - y _ { 2 }" ,0549b71f-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"K ^ { ( n - s ) } _ { n - h + 2 } . C ^ { ( s ) } _ { 2 n - s - h + 2 } , c _ { ( s ) } k _ { ( n - s ) } I _ { n - h + 2 } ," ,05e649f9-6d00-4dcd-a482-e1a85fd0d88b__mathematical-expression-and-equation_8.jpg
"\Phi = \frac { v } { v - b }" ,05f7eb27-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"4 3 \frac { 1 } { 3 } : 5 8 = x" ,05fd0c1c-224c-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_15.jpg
"C _ { 2 } * C _ { 1 } = \max \{ Z \in \mathcal { C }" ,0620b909-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( d s ^ { \alpha } _ { ; i } - s ^ { \alpha } _ { ; j } \omega ^ { j } _ { i } + s ^ { \beta } _ { ; i } \tau ^ { \alpha } _ { \beta } ) \wedge \omega ^ { i } = - \frac { 1 } { 2 } S ^ { \alpha } _ { \beta i j } s ^ { \beta } \omega ^ { i } \wedge \omega ^ { j } ," ,0620b97e-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_8.jpg
"s i n \epsilon ^ { 2 } = | \begin{array} { c c } m & m \prime \\ n & n \prime \end{array} | | \begin{array} { c c } \beta & \gamma \\ \beta \prime & \gamma \prime \end{array} | + | \begin{array} { c c } n & n \prime \\ l & l \prime \end{array} | | \begin{array} { c c } \gamma & \alpha \\ \gamma \prime & \alpha \prime \end{array} | + | \begin{array} { c c } l & l \prime \\ m & m \prime \end{array} | | \begin{array} { c c } \alpha & \beta \\ \alpha \prime & \beta \prime \end{array} | ." ,06a3058c-bf88-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"( d , t ) = 1 2 2 ^ { \circ } 2 6 \prime - 9 0 ^ { \circ } = 3 2 ^ { \circ } 2 6 \prime ." ,06a30629-bf88-11e1-1586-001143e3f55c__mathematical-expression-and-equation_16.jpg
"U ( t ^ { j } , \frac { 1 } { 4 } \tilde { \rho } _ { j } ) \subset D ^ { j } \subset U ( t ^ { j } , \tilde { \rho } _ { j } )" ,06fb1310-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"[ 1 3 4 \dots p 2 ] \cup ( 1 p )" ,06fb14b7-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg
"S _ { - } ^ { 0 } = S _ { - u } ^ { 0 } = \{ y \in S _ { 0 } ^ { 1 } : y ( \infty ) = - \infty \}" ,06fb150b-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ c _ { 1 } h ^ { p + 1 } + c _ { 2 } h | | \Delta u _ { 1 } | | _ { p } ^ { p }" ,06fb15a9-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"W ^ { 1 , p } ( \Omega _ { n } ; v , v ) \circlearrowright L ^ { q } ( \Omega _ { n } ; w )" ,06fb1608-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_8.jpg
"s _ { y } = 2 s _ { x }" ,076da831-5333-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\frac { \partial F } { \partial u } \frac { \partial ( \psi \chi ) } { \partial ( v \alpha ) } + \frac { \partial F } { \partial v } \frac { \partial ( \psi \chi ) } { \partial ( \alpha u ) } + \frac { \partial F } { \partial \alpha } \frac { \partial ( \psi \chi ) } { \partial ( u v ) } = 0" ,07754679-5885-03d6-768f-952a8be614b7__mathematical-expression-and-equation_3.jpg
"i = n ( a , b )" ,07df0c5f-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d ( L _ { 1 } ) ^ { n _ { 2 } } d ( L _ { 2 } ) ^ { n _ { 1 } }" ,07df0c9c-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"3 \cdot 2 = 6" ,07df0cf7-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_18.jpg
"q ( A _ { * } , M _ { * \phi } ) = 1" ,081a8dd8-9864-4215-8d3f-cccc4802ae0b__mathematical-expression-and-equation_1.jpg
"K = \sqrt { \frac { x ^ { 2 } } { n \sqrt { ( r - 1 ) ( s - 1 ) } } }" ,084d8282-5333-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( \begin{array} { c c c c c c c } a & b & c & \dots . & h & k \\ 1 & 2 & 3 & \dots . & n - 2 , & n - 1 , & n \end{array} ) \dots K ." ,0888b54e-bf88-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { d } { d t } \{ W ( z ( t ) ) \exp [ - \int _ { t _ { 1 } } ^ { t } E _ { j } ( s ) d s ] \} \le 0" ,08bd5c97-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"2 \alpha \beta = \gamma ( \alpha + \beta )" ,08bd5dbc-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_12.jpg
"- \operatorname { d i v } \boldsymbol { u } \operatorname { g r a d } \phi _ { 0 } ] = \operatorname { g r a d } ( \lambda + 2 \mu ) \times \operatorname { g r a d } \operatorname { d i v } \boldsymbol { u } +" ,08c79582-d3b5-4a23-818a-96018e5888df__mathematical-expression-and-equation_7.jpg
"J ( a , b ) \subset J ( a ) \times J ( b )" ,099bb02f-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { 1 } { c ^ { 2 } } \frac { \partial ^ { 2 } U } { \partial t ^ { 2 } } - \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } + \frac { 4 \pi ^ { 2 } m _ { 0 } ^ { 2 } c ^ { 2 } } { h ^ { 2 } } U = 0" ,099cfd8c-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\int f ( x ) d x = \int _ { a } ^ { x } f ( x ) d x = F ( x ) - F ( a ) . \prime \prime" ,099cfd98-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p = \frac { k v _ { 1 } v _ { 2 } v _ { 3 } v _ { 4 } } { 3 0 0 N n _ { 1 } n _ { 2 } }" ,0a028a8e-6c45-11e5-a4fc-001b21d0d3a4__mathematical-expression-and-equation_0.jpg
"1 + 2 + 3 + \dots + 2 n ," ,0a41b0a3-bf88-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x _ { n } = b - \frac { 1 } { n } ( b - a ) , y _ { n } = m + \frac { 1 } { n } ( M - m ) ( n = 1 , 2 , \dots )" ,0a742362-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"Y - X ^ { 2 \delta } = ( 0 )" ,0a74249b-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x ^ { 2 } - y ^ { 2 } = 2 ," ,0a7425c5-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_8.jpg
"M ( n , p , r ) \le ( b - a ) ^ { n - 1 } | | 2 | s _ { 0 } - s | ^ { n - 3 } g ( s , s _ { 0 } ) | | _ { p \prime }" ,0a7a76fd-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"| W _ { n - 1 } ( y ) - W _ { n - 1 } ( x ) | ^ { 2 } \le \int ( \int ^ { y _ { n } } p _ { n } ^ { - 1 } d x _ { n } ) d x \int _ { \Omega } p _ { n } | \frac { \partial v } { \partial x _ { n } } | ^ { 2 } d x" ,0a7a7768-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { | S u ( x \prime , 0 ) - S u ( x \prime - s \prime r , 0 ) | ^ { p } } { r ^ { p } } r ^ { N - k - 1 + \epsilon } d s \prime d r d x \prime" ,0b5a7863-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_14.jpg
"a _ { x } ^ { a i } = 1 e _ { x } ^ { a i } - \theta ^ { 2 } e _ { x } ^ { a i } + \dots + ( - 1 ) ^ { k } \cdot \theta ^ { k } \cdot { } ^ { k + 1 } e _ { x } ^ { a i }" ,0c1f1629-40e4-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"y ( t ) \le - M \text { f o r } t \ge T _ { 2 }" ,0c39db79-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_6.jpg
"V _ { - 1 } ( T _ { x } \overline { M } ) = \bigoplus _ { h = 0 } ^ { p } _ { N _ { x } } ^ { 2 h } M" ,0c39dbcd-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_2.jpg
"s = 3 4 . 9" ,0c6afc47-bf88-11e1-1232-001143e3f55c__mathematical-expression-and-equation_19.jpg
"\Psi _ { 1 } = - \frac { B } { 2 A } + \sqrt { \frac { B ^ { 2 } } { 4 A ^ { 2 } } + \frac { C } { A } }" ,0c708df2-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { E _ { 0 } } { I ^ { 0 } _ { 0 } } = Z _ { 0 }" ,0c708f65-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"u _ { L } ( t ) = R e e ^ { j \omega t } \int _ { 0 } ^ { t } f \prime ( \tau ) e ^ { j \omega \tau } d \tau" ,0c708f95-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"u _ { L } ( t ) = R e U e ^ { j \omega _ { i } t }" ,0c708fa1-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { \eta } { \xi } = t g \frac { \phi _ { 0 } } { 2 } , \frac { \eta } { \xi } = - c o t g \frac { \phi _ { 0 } } { 2 }" ,0ce39dff-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"+ \frac { 1 } { 2 } { \sum \sum } _ { p , q } \frac { \cos \omega _ { 3 } } { \sqrt { ( p + x ) ( q + x ) } } = S _ { 1 } + S _ { 2 } + S _ { 3 }" ,0d1d82f8-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg
"0 \phi _ { 1 } [ - ; q ^ { \alpha + k } , - t T _ { k , q } ] x ^ { \alpha + n } = x ^ { \alpha + n } e _ { q } ( - x t ) _ { 1 } \phi _ { 1 } [ \begin{array} { c c } q ^ { - n } ; & x t q ^ { n + \alpha + k - 1 } \\ q ^ { k + \alpha } ; & q \end{array} ]" ,0d1d841c-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_11.jpg
"S ( X ) = \frac { \partial } { \partial t } | _ { 0 } ( s \circ f ) \in T _ { s ( x ) } \mathcal { F } ( E _ { 1 } , E _ { 2 } )" ,0d1d8465-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_0.jpg
"q + r + s = n" ,0d99318b-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- \frac { 1 } { n } ^ { 0 } a _ { a b c } h ^ { a b } = U _ { c } ^ { \mu } p _ { \mu }" ,0d993224-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { P } { 4 } = 1 + \frac { 1 } { 2 \sqrt { 3 } } \lg ( 6 + 4 \sqrt { 3 } ) - \frac { 1 } { 2 \sqrt { 3 } } \lg ( 2 \sqrt { 3 } )" ,0dcbea6e-4056-444c-a101-0c57ca0d32e6__mathematical-expression-and-equation_6.jpg
"c _ { n } : = t _ { n } - t _ { n - 1 } = \frac { p _ { n } } { P _ { n } P _ { n - 1 } } \sum _ { v = 1 } ^ { n } p _ { v - 1 } x _ { v } , n \ge 1" ,0dfdd28d-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\sigma \prime ^ { 2 } ( x ) = \sigma ^ { 2 } ( x ) + \sigma ^ { 2 } ( y )" ,0e0278f6-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"r < l _ { m } < M i n ( | z | ; | z _ { 1 } | , | z _ { 2 } | , \dots , | z _ { m + 1 } | )" ,0e466194-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\tau _ { b } = \frac { P - Q } { \frac { 1 } { 2 } \sqrt { ( n ^ { 2 } - \sum n _ { i } ^ { 2 } ) ( n ^ { 2 } - \sum n _ { j } ^ { 2 } ) } }" ,0ebd9b2a-5333-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"T _ { 2 i , z } = - \frac { P _ { 2 } p _ { 2 } } { l _ { 2 } } - \frac { 3 k _ { 2 z } } { l _ { 2 } } ( \phi _ { g z } + \phi _ { j z } - 2 \psi _ { 2 z } ) - \frac { \mathfrak { M } _ { 2 g , z } + \mathfrak { M } _ { 2 j , z } } { l _ { 2 } }" ,0ecd6a28-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_19.jpg
"H _ { m } ^ { t } ( M ^ { \vee } ) \xrightarrow { a . } H _ { m } ^ { t } ( M ^ { \vee } ) \rightarrow H _ { m } ^ { t } ( ( \underline { M } _ { a } ) ^ { \vee } ) \rightarrow 0" ,0ee4b012-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- \int _ { \psi ( B \cap \mathcal { U } ( x ; \delta _ { 0 } ) ) } f ( \psi ^ { - 1 } ( w ) ) \mathrm { g r a d } h _ { \psi ( y ) } ( w ) \cdot n ^ { \psi ( G ) } ( w ) \mathrm { d } \mathcal { H } _ { m - 1 } ( w ) |" ,0ee4b061-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\mu - \alpha = \gamma" ,0f421a8a-7876-455a-8ea1-4904fbe2e26b__mathematical-expression-and-equation_4.jpg
"p = r ^ { 2 } \cdot \pi" ,0f7c1d0c-e3fa-11e6-aeaf-001b63bd97ba__mathematical-expression-and-equation_8.jpg
"y = - \frac { b } { c } x" ,0f980ed1-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_7.jpg
"e _ { \alpha } = \pm 1" ,0f980ed5-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_12.jpg
"y _ { j } = \sum _ { i = 1 } ^ { n } k R _ { i j } x _ { i }" ,0f9f606b-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\phi _ { 1 } = \frac { k \prime [ R _ { 2 } u _ { 2 } - ( R _ { 2 } + R _ { F e } ) u _ { 1 } ] } { ( R _ { 2 } + R _ { F e } ) \sqrt { p } + k \prime ( R _ { 1 } R _ { 2 } + R _ { 1 } R _ { F e } + R _ { 2 } R _ { F e } ) }" ,0f9f6086-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\alpha _ { n } = \frac { \alpha \prime \prime \alpha \prime ^ { n + 1 } - \alpha \prime \alpha \prime \prime ^ { n + 1 } } { \alpha \prime ^ { n + 1 } - \alpha \prime \prime ^ { n + 1 } }" ,0fcc41fe-1f58-47de-8324-b90ae9b07881__mathematical-expression-and-equation_2.jpg
"p _ { 1 } = \frac { d P _ { 2 } } { R _ { 1 - 2 } } = \frac { 3 , 5 \cdot 1 , 4 } { 3 , 7 } = \mathbf { 1 , 3 2 4 } n" ,0fd18bb0-5839-11e6-b155-001018b5eb5c__mathematical-expression-and-equation_3.jpg
"n _ { \psi \phi 5 } = - 0 , 0 0 0 5 \cdot 0 , 5 0 0 = + 0 , 0 0 0 2" ,10696651-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_42.jpg
"\phi ( s ) = \frac { \phi _ { 1 } ( s ) } { \int _ { d } ^ { d + k l } \phi _ { 1 } ( u ) d u } \int _ { d } ^ { d + k l } \phi _ { 1 } ( t ) d t \int _ { t } ^ { s } \frac { C + M \int _ { a } ^ { w } \phi _ { 1 } ( r ) d r } { w ^ { 4 } \phi _ { 1 } ^ { 2 } ( w ) } d w" ,106967a9-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_5.jpg
"X _ { d i f n } = X _ { d i f } \frac { k _ { c } } { k _ { c n } }" ,10696818-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x _ { 2 } = 0 , 1 8 2 0" ,1124640c-5333-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\bar { \sigma } = \frac { \sigma _ { T } } { c _ { L } c \prime }" ,1138eb88-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- H _ { 1 3 } + H _ { 3 3 } + C _ { 3 3 } \cos \beta - D _ { 2 2 } \cos \beta - C _ { 2 4 } \cos \beta + D _ { 3 3 } c" ,1138ec5b-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"C _ { \infty } = C _ { 3 } + C _ { 2 }" ,1138ecd0-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\sigma _ { B } = 3 2 / 5 0 k g / m m ^ { 2 }" ,1138ed92-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"1 1 = \frac { 9 3 ^ { 2 } } { 3 } \%" ,11dbcce0-5dc8-11e8-afe6-005056825209__mathematical-expression-and-equation_2.jpg
"w _ { 1 } = w _ { 0 5 } = - w _ { 2 3 } , w _ { 3 } = w _ { 2 3 } , w _ { 4 } = w _ { 2 2 }" ,11f9f2a5-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"p = [ y - y _ { 0 } ] ^ { 1 / 2 } \{ 2 [ P - f ( 0 ) - \phi ( y _ { 0 } ) ] - [ y - y _ { 0 } ] ^ { 1 / 2 } \frac { 4 } { 3 } f \prime ( 0 ) [ 2 [ P - f ( 0 ) - \phi ( y _ { 0 } ) ] ] ^ { 1 / 2 } -" ,11f9f2ff-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"z _ { 0 1 } = 2 0 0 0 \cdot 0 , 0 ^ { 3 } 4 4 2 \cdot 0 , 9 9 2 = 0 , 8 7 7 ," ,12067970-ee50-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_18.jpg
"- \Theta _ { v 2 } ( A _ { 0 } + A _ { 1 } X _ { 2 } + A _ { 2 } X _ { 2 } ^ { 2 } + \dots + X _ { 2 } ^ { r } ) + \dots +" ,12bdb7e4-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"A _ { 0 } \sum _ { v = 1 } ^ { m } \sum _ { i = 0 } ^ { n - r } \theta _ { v } [ ( i + 1 ) t _ { 1 } ] \theta _ { v } ( i t _ { 1 } ) + A _ { 1 } \sum _ { v = 1 } ^ { m } \sum _ { i = 1 } ^ { n - r + 1 } \theta _ { v } ^ { 2 } ( i t _ { 1 } ) + \dots +" ,12bdb7e8-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_5.jpg
"z = \frac { \alpha ( z _ { 0 } + \frac { p } { 4 } ) + \frac { p } { 4 } ( z _ { 0 } - \alpha ) \sin ^ { 2 } \phi } { ( z _ { 0 } + \frac { p } { 4 } ) - ( z _ { 0 } - \alpha ) \sin ^ { 2 } \phi }" ,12f6f803-c2c9-4e7b-930d-ae8a9f69adf7__mathematical-expression-and-equation_8.jpg
"U _ { v v } = U _ { v v 1 } - U _ { v v 2 } = \mathfrak { E } _ { v } ( 1 + A _ { v } e ^ { j ( r _ { v } + x ) } ) v n \cos \delta 2 j \sin ( \frac { \pi l } { \lambda } \cos \alpha \cos \delta )" ,133b25e5-40e4-11e1-3052-001143e3f55c__mathematical-expression-and-equation_4.jpg
"w _ { 3 - 1 } = ( 2 \cdot 0 , 0 6 3 7 - 0 , 0 0 0 0 ) k p \Delta _ { y } ^ { 4 } = 0 , 1 2 7 4 k p \Delta" ,1388332c-3c62-11e1-5298-001143e3f55c__mathematical-expression-and-equation_19.jpg
"x = X + \alpha t" ,13883458-3c62-11e1-5298-001143e3f55c__mathematical-expression-and-equation_6.jpg
"p ^ { 2 } = K \mu C ^ { - 2 } n ^ { 2 } + 4 \pi \mu \sigma n c" ,13faa0e8-3315-4d40-9805-6140669615d9__mathematical-expression-and-equation_4.jpg
"\alpha \prime \prime + 2 f _ { 1 } \prime f _ { 1 } \prime \prime = - \frac { 1 } { E ^ { * } t } ( p _ { 1 } ^ { U } - p _ { 1 } ^ { L } )" ,146720e1-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\lambda _ { 4 } = \frac { a _ { I , p l } } { a _ { I , e l } }" ,146721ec-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"N _ { 1 } ^ { H ( D ) } =" ,14672330-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { d _ { 0 } } { d } = \frac { c _ { m } } { 2 } ( \frac { 1 } { c _ { 1 } } + \frac { 1 } { c _ { 2 } } ) \frac { Z _ { 0 } } { Z }" ,14ebb1d9-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"\hat { \mathbf { A } } = [ \hat { 1 } ; \frac { 1 } { 2 } \vec { \mathbf { p } } ] [ \hat { e } ; \hat { 0 } ] [ \hat { 1 } ; - \frac { 1 } { 2 } \vec { \mathbf { p } } ] = [ \hat { e } ; \vec { \mathbf { p } } \times \vec { e } ]" ,1511d971-1159-4c74-9bf2-b39e7e945a2c__mathematical-expression-and-equation_8.jpg
"a = 1 \\ d = 6" ,151bd7c0-e382-11e8-9984-005056825209__mathematical-expression-and-equation_25.jpg
"B _ { F e } = 2 \cdot 5 B _ { d m a x } \frac { R } { p } \sqrt { ( \frac { B _ { F e } } { H _ { e } } \gamma s f _ { 1 } ) } \sin \xi" ,153e7027-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"r = \sqrt { ( x ^ { 2 } + y ^ { 2 } ) }" ,153e710a-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"1 ) x ^ { 2 } + y ^ { 2 } = 9 i x ^ { 2 } + y ^ { 2 } - 2 4 x + 1 0 8 = 0" ,15dff3f0-3a1a-11e9-9fd6-5ef3fc9ae867__mathematical-expression-and-equation_19.jpg
"+ \tau x y - \frac { p _ { x } y ^ { 2 } } { 2 } - \frac { p _ { y } x ^ { 2 } } { 2 }" ,1623c565-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\hat { H } = \hat { H } ^ { d } + \hat { H } ^ { r }" ,1623c707-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\mathbf { U } = u _ { \alpha } \mathbf { a } ^ { \alpha } + w \mathbf { a } _ { 3 }" ,1623c75b-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_5.jpg
"H _ { 1 } = \sigma a [ f _ { 1 } ( t ) \frac { x ^ { 2 } } { 2 } + f _ { 2 } ( t ) \frac { x ^ { 3 } } { 3 ! } ] + A + B x" ,1623c7d1-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\epsilon _ { 3 } G _ { 0 } ^ { ( 1 ) } [ \begin{array} { c } \sqrt { ( - \frac { \epsilon _ { 3 } } { \epsilon _ { 1 } } ) } g \tilde { \gamma } , h \sqrt { ( - \frac { \epsilon _ { 3 } } { \epsilon _ { 1 } } ) } g \tilde { \gamma } \end{array} ] = \epsilon _ { d } F _ { o } ( j g \tilde { \gamma } )" ,1623c84f-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_8.jpg
"1 8 M _ { 1 } + 3 M _ { 2 } + 1 8 9 0 0 = 0" ,16cf5bc0-e603-11ea-804d-005056827e51__mathematical-expression-and-equation_22.jpg
"H _ { t } \neq H _ { s }" ,16d2da29-9911-48b8-ab24-ee69bfe185e7__mathematical-expression-and-equation_2.jpg
"a _ { 1 1 } x ^ { 2 } + a _ { 2 2 } y ^ { 2 } + a _ { 3 3 } z ^ { 2 } = 0 ?" ,1717615a-901e-11ed-868a-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"e ( - 2 m k \prime _ { 1 } + k \prime _ { 2 } ) : k \prime _ { 1 } = - 2 k _ { 2 } : k _ { 1 } ; p" ,1717ae8d-901e-11ed-868a-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"x \approx \sqrt { ( 1 - \frac { \lambda _ { H _ { 1 } } } { \Delta D } ) }" ,17ebdad1-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg
"P = y _ { s } \frac { 1 6 \pi D } { r ^ { 2 } }" ,17ebdae6-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\int _ { 0 } ^ { \infty } s e ^ { - s } \theta d \Theta = 1" ,17ebdbfd-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg
"A + z - d z < ( x _ { 1 } - x _ { 2 } ) < A + z + d z" ,18c35087-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_8.jpg
"D = - ( \epsilon _ { 2 } ^ { 2 } - 1 ) ^ { 2 }" ,18c3512d-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"a ^ { 2 } + a \prime ^ { 2 } + a \prime \prime ^ { 2 } = 1 \dots a \beta \prime + a \prime \beta \prime + a \prime \gamma \prime = 0 \dots" ,18eae9ac-ae29-4cc3-af2e-fac30be568c0__mathematical-expression-and-equation_4.jpg
"\Sigma = \Sigma _ { 1 } + \Sigma _ { 2 } ," ,1959cb70-5d32-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"\frac { d ^ { 3 } v ( x _ { M } , t _ { m } ) } { d x ^ { 3 } } f ( t _ { m } ) + \sum _ { j = 1 } ^ { \infty } a _ { ( j ) } \frac { d ^ { 3 } v _ { ( j ) } ( x _ { M } ) } { d x ^ { 3 } } e ^ { - ( \gamma / 2 ) \omega _ { ( j ) } t _ { m } } \sin ( \omega _ { ( j ) } t _ { m } + \alpha _ { ( j ) } ) = 0" ,19993d2c-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_1.jpg
"y = 0 , 6 4 5 5 - 0 , 1 7 x" ,19af1840-af3e-11ea-9c77-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"\frac { \dot { \epsilon } _ { i j } } { \dot { \epsilon } _ { S } } = \frac { \mathrm { d } \epsilon _ { i j } } { \mathrm { d } \epsilon _ { S } }" ,1a5fd4b3-845e-49f9-b986-a1484ae11b55__mathematical-expression-and-equation_8.jpg
"\sigma _ { i j } = f _ { i j } [ \int _ { t _ { 0 } } ^ { t } L _ { 1 } ( t - \tau ) \epsilon _ { k l } ( \tau ) d \tau" ,1a69fad0-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { - y } { x ^ { 2 } } \psi \prime \sqrt { z } + \psi \frac { \partial z } { \partial x } \frac { 1 } { 2 \sqrt { z } } = \frac { x } { \sqrt { x ^ { 2 } + y ^ { 2 } } } + \frac { y } { x ^ { 2 } } \phi \prime ," ,1a6d1000-0a0b-11e3-9439-005056825209__mathematical-expression-and-equation_5.jpg
"D _ { 9 } = - D _ { 1 0 } = - D _ { 1 1 } = D _ { 1 2 } = D _ { 1 3 } = - D _ { 1 4 } = - D _ { 1 5 } =" ,1b3ded8d-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_25.jpg
"\frac { 1 } { \rho } = \chi : = \frac { 1 } { r } \cdot \frac { l } { q }" ,1b6e352a-8a4d-4a5a-9e1f-b7be2561eb9f__mathematical-expression-and-equation_3.jpg
"h = - \frac { S r _ { o } } { c o s \phi }" ,1b9acd32-8a2f-4f83-b531-c3444ec39f45__mathematical-expression-and-equation_1.jpg
"\frac { d L _ { 1 } } { d t } + J \frac { d _ { r } V } { d t } = \frac { d T } { d t }" ,1bc73cf2-3371-4931-bc3b-7c84eba4a9f9__mathematical-expression-and-equation_1.jpg
"\int r ( \sin x ) \cos x d x" ,1bff6570-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"+ \sum _ { K = 1 } ^ { N } \Phi _ { N + K } \int _ { t _ { 0 } } ^ { t } L _ { K } ( t - \tau ) \epsilon _ { i \lambda } ( \tau ) d \tau \int _ { t _ { 0 } } ^ { t } L _ { K } ( t - \tau ) \epsilon _ { \lambda j } ( \tau ) d \tau +" ,1c1d4f68-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_10.jpg
"W \prime _ { \tau } = W _ { 0 } + u \frac { x _ { d } - x \prime _ { d } } { x _ { d } x \prime _ { d \tau } } \cos \theta _ { 0 } e ^ { - B _ { 1 \tau } }" ,1c1d509d-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_3.jpg
"a + a q + a q ^ { 2 } + \dots + a q ^ { n - 1 } = a \sum _ { 1 } ^ { n } q ^ { v - 1 }" ,1cc60eb0-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg
"\nabla ( U \mathfrak { U } ) = U . \nabla \mathfrak { U } + \mathfrak { U } . \nabla U" ,1ce86c20-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_12.jpg
"\{ ( M _ { 1 } - h _ { 1 } N _ { 1 } ) \gamma _ { 1 } \} \prime _ { 0 } = 0" ,1cf7101e-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
"p _ { 1 k } + p _ { 2 k } + \dots + p _ { r k } = 1 . - P" ,1d6438d2-1fc9-40b8-9a11-9c44d421eba6__mathematical-expression-and-equation_6.jpg
"I _ { 1 0 } = - \frac { U _ { p } e ^ { j \theta } } { \omega L ( \alpha + j ) }" ,1dd05892-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\alpha ^ { 2 } - 1 ) + ( ( \alpha + \beta ) ^ { 2 } - \sigma ^ { 2 } - 2 \alpha \beta \sigma ) x ^ { 2 } + \sigma ^ { 2 } x ^ { 4 } ] ^ { 2 } + 4 \alpha ^ { 2 } ( \beta ^ { 2 } + \sigma" ,1dd05895-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\theta _ { B } = [ 1 - \frac { \varkappa _ { 0 } \omega } { \varkappa \omega _ { 0 } } \frac { ( 1 - m \frac { \omega _ { 0 } } { \varkappa _ { 0 } } ) } { ( 1 - m \frac { \omega } { \varkappa } ) } \frac { 1 } { \delta } \frac { \sinh \delta } { \cosh \delta } ] ^ { - 1 } \{ \frac { \Theta _ { A } - \Theta _ { B } } { 2 } ( - \frac { \varkappa _ { 0 } } { \omega _ { 0 } } \frac { 1 } { h } )" ,1dd058e6-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { n ( a ) _ { v 2 } ( t ) } { n ( a ) _ { \text { K R I T 2 } } } = \frac { \sigma _ { 2 } n ( a ) _ { k 1 } } { \sigma _ { 1 } n ( a ) _ { \text { K R I T 1 } } } \frac { t _ { 1 } } { t _ { p 1 } } + \frac { \bar { n } ( a ) _ { 2 } } { n ( a ) _ { \text { K R I T 2 } } } + \frac { a _ { 1 } ( t _ { 1 } ) } { a _ { 2 } ( 0 ) _ { \text { K R I T } } } +" ,1dd0597f-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"v = ( \frac { \partial g } { \partial p } ) _ { T } = \frac { R T } { p } + \frac { C } { p _ { r } } \sum _ { i , j } b _ { i j } . i \pi ^ { i - 1 } . \tau ^ { - j }" ,1ea66b3a-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"W = 1 8 3 . 6" ,1edd4b80-0af6-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"B = \sqrt { - \frac { q } { 2 } - \sqrt { ( \frac { q } { 2 } ) ^ { 2 } + ( \frac { p } { 3 } ) ^ { 3 } } }" ,1f9e8310-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg
"\mu _ { 1 , 2 , 3 } = \lambda _ { 1 , 2 , 3 }" ,1fd50e5c-1849-4f79-b638-03b29043bdb3__mathematical-expression-and-equation_18.jpg
"P K = \frac { V \text { k g } } { 6 0 ( \text { a ž } 8 0 ) \sqrt { v } }" ,201443bb-bbd0-481d-8dc9-9e942469e0fa__mathematical-expression-and-equation_0.jpg
"\mathbf { A } ^ { \mathbf { B } } _ { \mathbf { C L } } = - { } ^ { 2 } \mathbf { B }" ,2051ab40-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\lambda = \pm i \Omega _ { s } s = 1 , 2 , \dots , l" ,2051ab9d-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ 2 \sum _ { s = 1 } ^ { l } A _ { 1 s } B _ { 1 s } ] \Omega _ { s } ^ { k - 2 } \sin ( \phi _ { s } + k \frac { \pi } { 2 } ) \} + \epsilon ^ { 3 } \dots" ,2051ab9f-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\int _ { - 1 } ^ { 1 } \{ y ^ { 2 } c _ { 1 3 } [ \sigma ^ { 1 3 } ( 0 , y ) + \hat { z } _ { 3 } ( 0 , y ) ] + c _ { 3 3 } [ \hat { z } _ { 3 } \prime \prime ( 0 , y ) + 2 y \hat { z } _ { 1 } \prime ( 0 , y ) ] +" ,2051ac10-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_13.jpg
"f = \{ f ^ { U } , f ^ { C } , f ^ { L } \} ^ { T }" ,2051ac2b-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\epsilon _ { y 1 } = \prescript { 1 } { } { a _ { 2 2 } } \sigma _ { y 1 1 } + \prescript { 1 } { } a _ { 2 1 } ( \alpha _ { 1 } \sigma _ { x } + \alpha _ { 2 } \sigma _ { x 2 1 } ) = \prescript { 1 } { } a _ { 2 2 } \sigma _ { y 3 1 } + \prescript { 1 } { } a _ { 2 1 } \sigma _ { x 3 1 } ," ,2051aca6-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_11.jpg
"C _ { G } = K _ { d } \frac { r _ { F } } { x _ { F \sigma } }" ,21324831-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_16.jpg
"c _ { 0 } = \frac { \overline { A } _ { 0 } \rho _ { 0 } ( \rho _ { 1 } z _ { 2 } - \rho _ { 2 } z _ { 1 } ) + \overline { A } _ { 1 } \rho _ { 1 } ( \rho _ { 2 } z _ { 0 } - \rho _ { 0 } z _ { 2 } ) + \overline { A } _ { 2 } \rho _ { 2 } ( \rho _ { 0 } z _ { 1 } - \rho _ { 1 } z _ { 0 } ) } { 2 S }" ,21324875-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\Delta \phi / \phi = ( 7 7 . 0 8 \pm 1 . 1 6 ) [ 1 - \exp \{ - t 1 0 ^ { - 2 } ( 7 . 4 0 \pm 0 . 3 2 ) \} ]" ,2178cf1e-da9d-4eda-b00e-8288d4695f12__mathematical-expression-and-equation_5.jpg
"\ln K _ { c } = \frac { Q \prime _ { v } } { R T } + k o n s t ." ,22ae4110-d5e1-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_1.jpg
"( 4 1 . k - 1 ) H _ { z k \_ 1 } ^ { ( k ) } = \sum _ { v = 1 } ^ { \infty } \sum _ { n = 1 } ^ { \infty } \frac { 1 } { M _ { v n k } ^ { ( k ) } } \frac { 1 } { j \omega _ { v k - 1 } \mu _ { k - 1 } } [ - E _ { y v n k - 1 } ^ { ( k - 1 ) } ( x , y , z - \sum _ { i = k - 1 } ^ { k } d _ { i } ) ] \times" ,22e9bc53-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"M = E J : r" ,22e9bcf0-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"+ \{ [ \epsilon _ { 2 2 } ( \epsilon _ { 1 1 } ^ { 2 } + \epsilon _ { 1 2 } ^ { 2 } + \epsilon _ { 1 3 } ^ { 2 } ) - \epsilon _ { 1 1 } ( \epsilon _ { 2 2 } ^ { 2 } + \epsilon _ { 2 1 } ^ { 2 } + \epsilon _ { 2 3 } ^ { 2 } ) ] \delta _ { i j } +" ,23c01e42-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_6.jpg
"+ \frac { r _ { 0 k } z _ { 1 k } - r _ { 1 k } z _ { 0 k } } { r _ { 0 k } - r _ { 1 k } } \ln \frac { r _ { 0 k } } { r _ { 1 k } } + \frac { r _ { 1 k } z _ { 2 k } - r _ { 2 k } z _ { 1 k } } { r _ { 1 k } - r _ { 2 k } } \ln \frac { r _ { 1 k } } { r _ { 2 k } }" ,23c01e5a-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_6.jpg
"l _ { 1 } ( v _ { 1 } , \tau _ { 1 } ) = \cos \tau _ { 1 } + \frac { B } { v _ { 1 } } \sin \tau _ { 1 }" ,23c01f31-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\alpha . \frac { 2 \pi } { \tau \omega } b + ( a _ { 2 3 } + s _ { 1 } ) c = 0" ,240aeb4d-7162-4fb1-a768-c97c341814dc__mathematical-expression-and-equation_2.jpg
"\frac { 1 } { a + \frac { 1 } { b + \frac { 1 } { c + \dots } } }" ,24300bf1-e64d-4080-ad9f-a768bb010fe6__mathematical-expression-and-equation_1.jpg
"y \prime = a y" ,256bcd70-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_11.jpg
"C _ { b } = + 1 . ( 1 + \frac { l } { 2 l _ { 0 } } )" ,26488210-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_0.jpg
"F _ { 1 } : F _ { 2 } = m _ { 1 } : m _ { 2 }" ,265153d0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg
"T l ( S O _ { 4 } ) _ { 3 } ( N H _ { 4 } ) _ { 3 }" ,26cbc0bd-6719-4359-a155-508bb9f3b2a5__mathematical-expression-and-equation_8.jpg
"( - 5 a ) + ( - 3 . 4 ) + ( + 3 . 5 ) + ( + 3 a ) + ( + 3" ,27278ab0-14e4-11e5-9192-001018b5eb5c__mathematical-expression-and-equation_10.jpg
"q _ { 0 } = + 0 . 8 0 0 7 8 ," ,27a82360-3d62-11e8-baa7-5ef3fc9bb22f__mathematical-expression-and-equation_9.jpg
"( 4 1 x ) ^ { 2 } - ( 9 x ) ^ { 2 } = ( 3 0 x + 1 0 ) ^ { 2 } ." ,2843c93c-88d4-4d53-875c-92e058da3079__mathematical-expression-and-equation_25.jpg
"\frac { \partial \sigma _ { 1 } ( \mathbf { v } _ { 1 } , t ) } { \partial t } = - \frac { 1 } { v } m M _ { 1 } \sum _ { j = 2 } ^ { N } \int d \mathbf { v } _ { j } \frac { \partial \Phi _ { 1 j } } { \partial \mathbf { v } _ { 1 } } \frac { \partial \phi _ { 2 } ^ { ( 1 j ) } } { \partial \mathbf { v } _ { 1 } }" ,2856f826-d806-4f1f-992c-1e494a2d908d__mathematical-expression-and-equation_0.jpg
"( B - C ) \eta \xi + C \xi \prime \eta - A \eta \prime \xi = 0" ,28c60476-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\tau = \frac { 2 u - ( 2 m + 1 ) } { 2 n + 1 } ," ,28c604b5-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\int _ { 0 } ^ { \delta } \Phi ( x ) x ^ { \frac { 1 } { 2 } s - 1 } d x , \int _ { h } ^ { \infty } \phi ( x ) x ^ { \frac { 1 } { 2 } s - 1 } d x" ,28c604c6-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p = \frac { \partial z } { \partial x }" ,28f1a580-5d32-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_11.jpg
"p _ { d } = \frac { 4 } { 5 } \alpha" ,29002cb7-037a-48de-8ebb-7a2be3ce0824__mathematical-expression-and-equation_4.jpg
"\frac { R } { ( m + a ) ^ { 2 } }" ,2939a170-1b94-11e4-8e0d-005056827e51__mathematical-expression-and-equation_4.jpg
"\frac { 1 } { 2 } \cdot \frac { m - 2 } { 2 } ( \frac { m - 2 } { 2 } + 3 ) = \frac { m ^ { 2 } + 2 m - 8 } { 8 }" ,29a7639c-df3d-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg
"N = C - S - H" ,2a863820-0af6-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"+ \frac { 1 } { 2 } \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } \sum _ { i } \sum _ { k } ( m _ { i } c _ { i } ^ { 2 } + m _ { k } c _ { k } ^ { 2 } ) f ( \mu r ^ { 2 } )" ,2ad7710b-0f8c-48e7-821e-2c05b3a380e4__mathematical-expression-and-equation_5.jpg
"E = R _ { v } I + R I" ,2b220600-d996-11e5-ac59-005056825209__mathematical-expression-and-equation_1.jpg
"7 \frac { 1 } { 2 } + 2 \frac { 1 } { 4 } = 9 \frac { 3 } { 4 }" ,2bf6c701-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_19.jpg
"u _ { 1 } = u" ,2db59880-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_8.jpg
"[ E ( z + 1 , p ) ] ^ { 2 } - [ E ( z - 1 , p ) ] ^ { 2 } = 4 z ^ { p } E \prime ( z , p )" ,2db5993d-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_6.jpg
"2 Q _ { n - 1 } = ( 1 + i x ) ^ { n - 1 } + ( 1 - i x ) ^ { n - 1 }" ,2db599c0-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_9.jpg
"E = \frac { m a ^ { 2 } } { 2 \omega ^ { 2 } } \frac { 1 } { ( \frac { 1 } { x } - x ) ^ { 2 } + \frac { 4 b ^ { 2 } } { \omega ^ { 2 } } }" ,2dc8cbc0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg
"- k ( x ^ { 2 } + y ^ { 2 } )" ,2df1075b-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_5.jpg
"+ m [ ( l + l _ { 0 } + u ) ^ { 2 } \ddot { \phi } + 2 ( l + l _ { 0 } + u ) \dot { u } \dot { \phi } + ( l + l _ { 0 } + u ) g \sin \phi ] = 0" ,2e19abae-712c-11e2-83a5-005056a60003__mathematical-expression-and-equation_11.jpg
"\mu = \frac { 1 } { h \sqrt { 2 } } = \frac { 0 , 7 0 7 1 1 } { h }" ,2e3bee70-ee52-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"\phi _ { 2 } = x _ { 3 } , \phi _ { 3 } = x _ { 1 } ;" ,2eadb482-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_5.jpg
"0 \le v \le n ," ,2eadb503-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_12.jpg
"d = 0 . 2 5" ,2fe35530-452d-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_4.jpg
"T _ { 1 } = 2 7 3 + 2 6 . 7" ,3007b381-290b-11e8-8c71-001b63bd97ba__mathematical-expression-and-equation_7.jpg
"s = 6 + 0 . 0 0 2 l" ,3026f900-e718-11e5-8d5f-005056827e51__mathematical-expression-and-equation_2.jpg
"\frac { d l n K } { d T } = - \frac { Q } { R T ^ { 2 } }" ,304587f2-cf0a-4167-a7db-d667edee2473__mathematical-expression-and-equation_1.jpg
"- 2 \pi < \rho < 2 \pi , - \infty < y < + \infty" ,30655015-df3d-11e1-1287-001143e3f55c__mathematical-expression-and-equation_15.jpg
"S = l i m \sum _ { a } ^ { b } x ^ { 2 } \Delta x" ,30897b53-2a1c-4223-85e3-77c70237ba0a__mathematical-expression-and-equation_0.jpg
"f \prime _ { i n 1 } , f _ { i n 1 } , f _ { i n 2 } \in [ 0 . 1 , 1 . 0 ]" ,317ec11a-8178-4ab0-8d1d-21361c153341__mathematical-expression-and-equation_9.jpg
"= \sum _ { n = 0 } \frac { \partial ^ { n } } { \partial t ^ { n } } [ D ^ { ( n ) } ( v ) + \frac { \partial W ^ { ( n ) } } { \partial x } - \frac { \partial U ^ { ( n ) } } { \partial z } + \Delta ( \frac { \partial \Theta ^ { ( n ) } } { \partial v } ) - \frac { \partial J ^ { ( n ) } } { \partial y } ]" ,324ab161-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\{ A ^ { 2 } B ^ { 2 } C ^ { 2 } | \begin{array} { c c c } A ^ { 2 } , & A , & 1 \\ B ^ { 2 } , & A , & 1 \\ C ^ { 2 } , & C , & 1 \end{array} | + | \begin{array} { c c c } A ^ { 3 } , & A ^ { 2 } , & 1 \\ B ^ { 3 } , & B ^ { 2 } , & 1 \\ C ^ { 3 } , & C ^ { 2 } , & 1 \end{array} | - A B C | \begin{array} { c c c } A ^ { 3 } , & A , & 1 \\ B ^ { 3 } , & B , & 1 \\ C ^ { 3 } , & C , & 1 \end{array} | - | \begin{array} { c c c } A ^ { 2 } , & A , & 1 \\ B ^ { 2 } , & B , & 1 \\ C ^ { 2 } , & C , & 1 \end{array} |" ,324ab183-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"= 4 s e n \frac { \beta - \gamma } { 2 } s e n \frac { \gamma - \alpha } { 2 } s e n \frac { \alpha - \beta } { 2 }" ,324ab185-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"1 6 + 4 = 2 0" ,32ba4150-1030-11e5-ae7e-001018b5eb5c__mathematical-expression-and-equation_1.jpg
"T _ { 0 } ^ { H } = ( 0 , 8 6 0 6 \pm 0 , 0 0 0 2 ) s" ,33618f1b-c29b-4037-b3da-2a9a499a5f60__mathematical-expression-and-equation_1.jpg
"R = \frac { 1 \cdot 2 2 , 4 0 7 } { 2 7 3 , 1 } = 0 , 0 8 2 0 5 \frac { 1 \cdot \text { a t m } } { \text { g r a d } }" ,33c822a0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg
"\tau _ { 2 } = \tau _ { 0 } \sqrt { 1 - K }" ,341f3af5-aaa3-40fa-8a7f-103463cee081__mathematical-expression-and-equation_1.jpg
"K _ { e x t r } = \sum _ { i = 1 } ^ { p } ( \delta X _ { i } \prime ^ { 2 } + \delta Y _ { i } \prime ^ { 2 } )" ,3552fe12-3f4a-4c38-a095-1d0ca601f428__mathematical-expression-and-equation_10.jpg
"+ \epsilon k ^ { - 2 } \int _ { 0 } ^ { t } F _ { k } ( u ) ( \tau ) \sin k ^ { 2 } ( t - \tau ) d \tau , \text { f o r } k = 1 , 2 , \dots" ,35a8c565-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg
"S _ { m } = P - ( D - d ) ( V - v )" ,36a804d0-3b45-11e3-9053-005056825209__mathematical-expression-and-equation_1.jpg
"= ( F O + O P ) ^ { 2 } - ( F O - O P ) ^ { 2 }" ,36e248a4-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_10.jpg
"d _ { \phi } ( \omega _ { 1 } \wedge \omega _ { 2 } ) = d _ { \phi } \omega _ { 1 } \wedge \omega _ { 2 } + ( - 1 ) ^ { p r } \omega _ { 1 } \wedge d _ { \phi } \omega _ { 2 } ," ,36ff538c-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"q _ { \mu } = W _ { \mu } + \mathbf { x } _ { 1 } + \mathbf { x } _ { 2 } + \dots + \mathbf { x } _ { \mu - 1 }" ,37577c54-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg
"+ [ l g \frac { ( n + 1 ) s - 1 } { n s - 1 } + J _ { 1 } ( ( n - 1 ) s - 1 ) ] \frac { 1 } { n - 1 ! } l g ^ { n - 1 } \frac { ( n + 1 ) s + t - 1 } { ( n + 1 ) s - 1 } +" ,375d4960-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg
"= \frac { ( \beta - 1 ) ( 2 n + \alpha + \beta - 2 ) - ( n + \beta - 1 ) ( n + \alpha + \beta - 2 ) } { 2 n + \alpha + \beta - 2 }" ,37670cc7-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_10.jpg
"\frac { t g \alpha } { \alpha } = 1 ^ { * } )" ,37877fe0-9f32-43ac-bfb5-0d53df96d3aa__mathematical-expression-and-equation_12.jpg
"| \begin{array} { c c c c c } a _ { 1 } & 2 a _ { 2 } & 3 a _ { 3 } & 4 a _ { 4 } & 5 a _ { 5 } \\ o & \phi _ { 1 } ( x ) & ( x + a _ { 1 } ) \phi _ { 1 } ( x ) & ( x ^ { 2 } + a _ { 1 } x + a _ { 2 } ) \phi _ { 1 } ( x ) & ( x ^ { 3 } + a _ { 1 } x ^ { 2 } + a _ { 2 } x + a _ { 3 } ) \phi _ { 1 } ( x ) \end{array} |" ,37985967-ff6a-4aa2-8d85-e98177e55f0c__mathematical-expression-and-equation_9.jpg
"= x + B \vee _ { p } C ( 0 ) = B \vee _ { p } C ( 0 ) + x" ,37a92900-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"2 l h - v ( 2 l - d ) = \emptyset ," ,37c50b96-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"\S 1 4" ,37c532ab-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_3.jpg
"\alpha = [ \alpha ] \cdot l \cdot \frac { p s } { 1 0 0 } = 0 . 6 6 4 9 l p s" ,37d69c70-dadf-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg
"\frac { \epsilon } { 2 \pi } = \frac { \tau } { T _ { 2 } } = 0 , \frac { 2 } { 1 2 } , \frac { 4 } { 1 2 } , \frac { 6 } { 1 2 } , \frac { 8 } { 1 2 } , \frac { 1 0 } { 1 2 }" ,37e9221c-df3d-11e1-1090-001143e3f55c__mathematical-expression-and-equation_1.jpg
"l = ( 1 1 0 ) \infty P ; s = ( 1 0 0 ) \infty P \infty ; x = ( 3 1 1 ) 3 P 3" ,37fc966d-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_0.jpg
"p V = \frac { 1 } { 3 } \mu c ^ { 2 } = R T ," ,3800ea50-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_2.jpg
"A = \mathcal { F } _ { 1 } A _ { 1 } \pm \mathcal { F } _ { 2 } A _ { 2 }" ,3818f820-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg
"\beta = 0 . 1 8 9 3 7 \times 1 0 ^ { 1 0 }" ,386913a1-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg
"( Q , D _ { 0 } ) = Q \prod _ { q } ( 1 - ( \frac { D _ { 0 } } { q } ) \frac { 1 } { q } )" ,38b6beb8-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"\frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } k ^ { a + i x } \frac { d x } { a + i x } = \{ \begin{array} { c c } 0 & \text { p r o } k < 1 \\ 1 & \text { p r o } k > 1 \end{array}" ,38feeb4e-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_8.jpg
"V \le k _ { 2 } L ^ { 3 }" ,3903fdec-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- \pi i R ( x _ { 0 } ) + ( \epsilon )" ,3904de86-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg
"+ y _ { 2 } G _ { 3 } ( y _ { 3 } , \epsilon ) + y _ { 2 } ^ { 2 } \Psi _ { 1 } ( y , \epsilon ) + y _ { 3 } ^ { 2 } \Psi _ { 2 } ( y , \epsilon )" ,39b0deb9-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_10.jpg
"m = \frac { ( 1 - r _ { 2 } ) m _ { 1 } + ( 1 - r _ { 1 } ) m _ { 2 } } { ( 1 - r _ { 1 } ) + ( 1 - r _ { 2 } ) }" ,39b0df11-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"= \log \sin ( w + v ) \pi \cdot \sin ( w - v ) \pi + 2 ( w \log w - ( 1 - w ) \log ( 1 -" ,39b43105-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_13.jpg
"\frac { a : \frac { 1 } { 1 \pm \alpha } } { b } = \frac { a ( 1 \pm \alpha ) } { b }" ,39dd815e-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\frac { r _ { k - 1 } } { r _ { k } } = b _ { k - 1 } + b _ { k } \frac { r _ { k + 1 } } { r _ { k } }" ,39de9313-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"r ( I ^ { j } ) \ge \alpha" ,3a5e8555-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { \partial b } { \partial a _ { 2 } } = b" ,3b219a05-36ea-41c9-ae32-145d748c32e1__mathematical-expression-and-equation_6.jpg
"y _ { 0 } \prime \prime = f ( x _ { 0 } ) - \phi ( x _ { 0 } ) y _ { 0 } \prime - \psi ( x _ { 0 } ) y _ { 0 }" ,3b713842-df3d-11e1-1090-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\sigma _ { x } \sigma _ { \eta } = \sigma _ { \tau }" ,3bb9a71a-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"F = \sum _ { h = 1 } ^ { n } y _ { h } \overline { A } ( x ) _ { h }" ,3c10016e-3105-11e9-8847-005056a2b051__mathematical-expression-and-equation_0.jpg
"g \equiv x - \frac { a } { 2 } = 0" ,3c550942-df3d-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg
"( 1 + \alpha x ) ^ { \frac { 1 } { \alpha x } } = e ^ { \theta }" ,3d127178-df28-11e1-4047-001143e3f55c__mathematical-expression-and-equation_3.jpg
"+ k _ { 2 } ( t , y ( h _ { 3 } ( t ) ) , y \prime ( h _ { 4 } ( t ) ) )" ,3d165157-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x \in G _ { L } ( a , b )" ,3d1651a5-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"y - m _ { 2 } x = 0" ,3da1f8f3-ebac-11ec-90b7-00155d01210b__mathematical-expression-and-equation_9.jpg
"t _ { 3 } = \sup X _ { 3 }" ,3dc3d002-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"d \eta _ { i } / d t = \sum _ { j = 1 } ^ { n } \phi _ { j } ( \zeta _ { i j } ) - \rho _ { i } ( \eta _ { i } ) ," ,3e087085-7a41-4006-b159-0a2e10718893__mathematical-expression-and-equation_1.jpg
"\text { t í } \lim \mathbf { a } ^ { \mu \nu } = \mathbf { a } _ { \mu \nu } , 1 \le \mu \le r , \nu = 1 , 2 , \dots , \alpha _ { r - \mu + 1 } ." ,3e71ea15-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\log b = \log c + \log \cos \alpha" ,3e7c3820-ad11-4f01-a7e6-2408915dddc8__mathematical-expression-and-equation_5.jpg
"u _ { n } = \alpha a ^ { n } + \beta b ^ { n }" ,3ea4c46b-df3d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"c ^ { 8 } - 2 c ^ { 7 } + 3 c ^ { 6 } - 3 c ^ { 5 } + 2 c ^ { 4 } - c ^ { 3 } + 2 c ^ { 2 } - 2 c + 1 = 0" ,3f277f37-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_46.jpg
"\frac { \lambda _ { b } } { \lambda _ { a } } = ( a b )" ,3f3ca460-df28-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"9 x ^ { 2 } - 4 y ^ { 2 } + 4 y z - z ^ { 2 }" ,3f3f122c-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_11.jpg
"2 x - 4 y + 9 z = 2 8" ,3f3fadba-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_31.jpg
"| i n d _ { h } z _ { 1 } - i n d _ { h } z _ { 2 } | = 1" ,3fdf0e1f-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lim _ { \Theta \rightarrow \frac { \omega } { 2 } } \int _ { 0 } ^ { 1 } [ f _ { 1 2 } ( r ) - u _ { 2 } ( r , \Theta ) ] ^ { 2 } r ^ { 2 \gamma - 1 } d r = 0" ,3fdf0ed8-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"s _ { 1 } ^ { 1 } = \frac { 1 } { 2 } g \sin \alpha t ^ { 2 }" ,3fec87d0-04d1-11e5-bdc1-001018b5eb5c__mathematical-expression-and-equation_2.jpg
"r _ { i } = [ \frac { n + k } { k } ] \text { p r o } j < i \le k , \text { k d e } j = k [ \frac { n + k } { k } ] - n" ,4094a233-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"A x = f" ,414afb0d-408b-11e1-2238-001143e3f55c__mathematical-expression-and-equation_5.jpg
"u _ { 1 } \prime = - ( \frac { h n ^ { 2 } \sin n t } { \omega } + \frac { 1 } { 3 } \frac { n ^ { 2 } + 2 } { n } \cot { n t } ) u + \frac { b } { \omega } u ^ { 2 }" ,41fe1d79-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"- M ( x ) \rightarrow P ( x ) , S ( \iota ) \rightarrow M ( \iota ) \vdash S ( \iota ) \rightarrow P ( \iota ) :" ,42109d9e-6183-49d7-9d40-c6f21a685579__mathematical-expression-and-equation_18.jpg
"\{ s \in \mathbb { R } ; ( t , s ) \in \Psi \}" ,42a8f853-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg
"C \prime = ( p _ { 1 } + \beta \prime ) \mathbf { u _ { 1 } } + ( p _ { 2 } + \beta q ) \mathbf { u _ { 2 } } + \beta c _ { 1 } \mathbf { u _ { 3 } } + \sqrt { ( 1 - p _ { 1 } ^ { 2 } - p _ { 2 } ^ { 2 } ) } \mathbf { u _ { 5 } }" ,42b33c6a-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\mathbf { P _ { v 1 } } , \dots , \mathbf { p _ { v n } } ) ( \mathbf { x } _ { \mathbf { v } } - \mathbf { a } ) = \mathbf { A } ( \mathbf { x _ { v } } ) ( \mathbf { x _ { v } } - \mathbf { a } ) - \mathbf { P } ^ { - 1 } ( \mathbf { x _ { v } } ) ( \mathbf { F } ( \mathbf { p _ { v 1 } } , \dots , \mathbf { p _ { v } n } ) )" ,42b33e05-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_14.jpg
"k \prime ( t ) = - \frac { 1 } { u ( t _ { 1 } + \omega ) } ( u \prime ( t _ { 1 } + \omega ) - 1 ) ( u ( t _ { 1 } + \omega ) v \prime ( t ) - u \prime ( t ) v ( t _ { 1 } + \omega ) )" ,4365e0fb-f33d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"f ( x ) = \sum _ { j = 0 } ^ { n } [ a _ { j } x ^ { n - j } / j ! ( n - j ) ! ]" ,4371aa6c-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"| \omega ( t ) - \omega ( t _ { 0 } ) | = | \lambda _ { n } ( t ) - \gamma ( t _ { 0 } ) | \le" ,4371ab44-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"P ^ { ( n ) } ( G _ { - \epsilon } ) \rightarrow \sqrt { ( \frac { q _ { 1 } , \dots , q _ { k } } { ( 2 \pi ) ^ { k - 1 } \sum p _ { i } q _ { i } } ) } \int _ { G _ { - \epsilon } } e ^ { - \frac { 1 } { 2 } \sum q _ { i } x _ { i } ^ { 2 } } d v" ,4371ac01-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"a + ( + b ) + ( + c ) + ( - d ) + ( + m )" ,43d27151-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_4.jpg
"7 z ^ { 3 } ) ] = ?" ,43d27156-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\phi _ { 4 } ^ { k 2 } = \kappa _ { 4 } ^ { 1 2 } \phi _ { 1 } ^ { k 1 } + \kappa _ { 4 } ^ { 3 2 } \phi _ { 3 } ^ { k 3 } + \kappa _ { 4 } ^ { 4 2 } \phi _ { 4 } ^ { k 4 }" ,4419c736-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_5.jpg
"| a _ { 2 } ^ { ( 6 ) } | + \frac { k + 1 } { 2 } | a _ { 1 } ^ { ( 6 ) } | \le 3 k ^ { 2 }" ,4419c777-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_5.jpg
"A _ { 2 } = \{ x \in \ell _ { 2 } : x _ { 1 } < 0 \}" ,4419c7ea-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
"- n _ { 1 } \xi _ { 1 j } ( \lambda _ { 1 } ) \xi _ { 1 k } ( \lambda _ { 2 } ) - \dots ]" ,44282a8c-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x \prime \prime \prime = \frac { 1 - \sqrt { - 8 } } { 3 }" ,44560197-e4c8-4637-b6f2-60779bfdf255__mathematical-expression-and-equation_9.jpg
"V = \frac { k _ { 2 1 } } { k _ { 1 2 } }" ,448d94d4-a681-11e6-adc0-d485646517a0__mathematical-expression-and-equation_8.jpg
"N _ { v } = ( 4 0 0 0 0 + 1 0 0 0 0 ) \times 0 . 0 8 + 3 4 0 0 0 \times 0 . 0 2 1 8 5 + 8 0 0 + ( 5 2 5 6 0 +" ,44c46e84-8bcd-11e7-b19b-005056a54372__mathematical-expression-and-equation_3.jpg
"I I ( c _ { 1 } + d _ { 2 } + e _ { 3 } ) = a ^ { 2 } + b ^ { 2 } + c ^ { 3 } + d ^ { 2 } \dots" ,44e3f94e-722e-43bc-a1b3-48542b571dd9__mathematical-expression-and-equation_4.jpg
"\bar { \Lambda } _ { m n } ( x , y ) = \int _ { x } ^ { \pi } \int _ { y } ^ { \pi } D _ { m } ( s ) D _ { n } ( t ) d s d t" ,458711ec-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
"G _ { k } ^ { l } x ( z ) = z ^ { l } \sum _ { s = 0 } ^ { \infty } a _ { l + s k } z ^ { s } \text { a n d } \Theta _ { z E _ { k } } x _ { l } = \sum _ { s = 0 } ^ { \infty } a _ { l + s k } z ^ { s }" ,458711fa-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_3.jpg
"D = B ^ { 1 - p } \{ \frac { p ( B - 1 ) ^ { p - 1 } } { B ^ { p } - ( B - 1 ) ^ { p } } - 1 \}" ,458712b0-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
"P _ { 3 } ( 1 0 , 4 , 2 ) = \{ 1 2 3 4 , 5 6 7 8 , 1 5 9 1 0 \} ," ,45871363-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_5.jpg
"p + 2 q \le 8" ,45935389-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"+ ( B - A ) [ ( - 1 ) ^ { k } \frac { 1 } { 2 } ( - \frac { 1 } { k + 1 } - 1 ) \delta ^ { k + 1 } + ( - 1 ) ^ { k } \frac { 1 } { 2 } \delta ^ { k + 3 } -" ,45c96850-78dc-4b05-bcd6-fefb26adaa68__mathematical-expression-and-equation_5.jpg
"f ( \mathbf { V } ) = \mathbf { W }" ,463fdb31-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathbf { R } \prime = \varkappa _ { 1 } \mathbf { T }" ,46490e17-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\overline { \lim } _ { n \rightarrow \infty } B _ { n } ^ { - 2 } \sum _ { k = 1 } ^ { n } | \xi _ { k } - \mathbf { E } \xi _ { k } | ^ { 3 } < \infty , g _ { k } ( x ) \le C _ { k } < \infty , \sum _ { k = 1 } ^ { \infty } a _ { k } C _ { k } ^ { - 2 } = \infty , \text { t h e n }" ,46490e3d-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"2 - 3 - 0" ,46fe53c1-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_17.jpg
"( x , \alpha ) \in E , g ( x , \alpha ) \le x _ { 1 } \implies V ( x , \alpha ) \le \varkappa _ { 0 } ," ,46fe5460-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\{ n - 2 , 1 ^ { 2 } \} \otimes \{ n - 5 , 5 \} = \{ n - 4 , 4 \} + \{ n - 4 , 3 , 1 \} + \{ n - 5 , 5 \} +" ,46fe5508-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_17.jpg
"B _ { R } ( a + i b ) : = \{ z \in \mathbb { C } | | z - ( a + i b ) | < R \}" ,4702b6af-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"S _ { 2 } \dots ( d _ { 1 2 } , 0 , 0 )" ,47595c6e-4789-498c-92ef-93f23e9434a1__mathematical-expression-and-equation_12.jpg
"t ^ { l k } _ { ; l } + \rho ( f ^ { k } - a ^ { k } ) = 0" ,477424c1-8934-4625-8740-13b7e778cd82__mathematical-expression-and-equation_3.jpg
"v ( t ) ( \xi ) = \int _ { 0 } ^ { t } I _ { 0 } ( c \sqrt { ( t ^ { 2 } - \tau ^ { 2 } ) } ) w ( \tau ) ( \xi ) d \tau ," ,47ac2174-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"L ( y ) \equiv 0" ,47babaf6-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_3.jpg
"s \in [ 0 , 1 )" ,47babb92-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\parallel D _ { r } ( x ( \phi _ { \epsilon } , t ) - R _ { y } ( \phi _ { \epsilon } , t ) \parallel _ { K } \le C _ { r } \epsilon ^ { \alpha ( q ) - N _ { r } \prime }" ,47babc03-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_7.jpg
"p = p ( u , v )" ,48592940-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"x ( t + ) = [ I + \Delta ^ { + } A ( t ) ] x ( t ) + \Delta ^ { + } f ( t )" ,49056f09-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\phi ( f , a , x ) = \hat { \phi } ( f , \langle a , x \rangle )" ,49b13eb5-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { G v ^ { 2 } } { 2 g } = G \omega l + T f l" ,4b1821b0-6022-48c6-8dbc-76a5d2dac712__mathematical-expression-and-equation_0.jpg
"t = \frac { x - M } { \sigma }" ,4b897eae-420f-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"- 1 2 7 -" ,4ceca400-50ad-11e6-8746-005056825209__mathematical-expression-and-equation_0.jpg
"f ( r , \theta , \phi , t ) = \sum _ { n = 0 } ^ { \infty } V _ { n } ( r ) S _ { n } ( \theta , \phi ) e ^ { i \omega _ { n } t }" ,4d87ad9c-2c1e-443e-a6e2-4a5785b76c83__mathematical-expression-and-equation_2.jpg
"h V _ { 0 } - h V _ { 1 } = h V" ,4dc8d6a1-e492-4ba2-8b05-9bfb5b3b4327__mathematical-expression-and-equation_0.jpg
"\frac { d y } { d x } = \cos x" ,4dd36bda-1aa7-4b1d-a641-fdaf08fe58bf__mathematical-expression-and-equation_3.jpg
"1 2 . \dot { 6 } = 1 2 + \frac { 6 } { 9 } = \frac { 1 1 4 } { 9 }" ,4dd3ab0e-5030-48e6-a567-56b9c7accdb7__mathematical-expression-and-equation_2.jpg
"N = ( a + c + e \& c . ) - ( b + d + \& c . ) + 1 1 ( b + 9 c" ,4df1699c-22be-11ec-b1c8-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"v _ { 1 } = a i , v _ { 2 } = b i , v _ { 3 } = c i" ,4e6ce4c6-c3dd-4c73-9895-651fb01b9e71__mathematical-expression-and-equation_6.jpg
"\pi ^ { 2 } = 0 . 1 0 1 3 2 1" ,4e7ff729-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_35.jpg
"\frac { P _ { 1 } } { P _ { 2 } } = t g ( \alpha _ { 1 } + 2 \phi )" ,4e8045c1-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"D _ { v 4 } = \frac { 2 , 6 \times 1 7 , 8 \times 4 } { 1 0 + 5 , 5 + 1 4 , 1 + 1 7 , 8 } = 3 , 9 \%" ,4ec741d0-cfd0-11ea-9a89-005056825209__mathematical-expression-and-equation_4.jpg
"k ^ { V } _ { m } = \frac { M _ { m } } { W _ { m } } = \frac { 5 , 8 0 4 . 9 3 5 } { 6 7 7 7 } = 8 5 6 k g" ,5003e0b7-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"G _ { 1 } \cos \epsilon = Q . [ \pm \sqrt { r ^ { 2 } \cos ^ { 2 } ( \lambda - \epsilon ) + ( r ^ { 2 } + \Delta ^ { 2 } ) - 2 \Delta r \cos ( \lambda - \epsilon ) } -" ,516e9310-ef98-11ea-b427-005056825209__mathematical-expression-and-equation_1.jpg
"\sigma = \frac { 2 ^ { \frac { 5 } { 3 } } } { 3 ^ { \frac { 3 } { 2 } } } \frac { \Delta ^ { \frac { 1 } { 4 } } } { A ^ { \frac { 1 } { 2 } } }" ,51e63f8a-9bf0-4173-8d97-c536ec4d8589__mathematical-expression-and-equation_11.jpg
"e _ { a } = \phi _ { 1 } ( \nu _ { a } , \nu _ { b } )" ,527af49a-e425-4234-b4f9-ed8bd03fca36__mathematical-expression-and-equation_5.jpg
"\phi = 0 , p x = x y , p y = 0 , m y = l x = p m = 0" ,52c4dde6-46da-4f69-8de3-d7f87c68c462__mathematical-expression-and-equation_8.jpg
"| \begin{array} { c c c } 1 & 1 & 1 \\ a & 1 & c \\ 1 & 0 & 0 \end{array} | = o" ,53809e72-21ae-410a-9d5a-bd420a7fc312__mathematical-expression-and-equation_7.jpg
"( 0 , 9 - ) 1 , 0 - 1 , 1 ( - 1 , 3 )" ,53c08570-66fa-11e3-99ab-005056825209__mathematical-expression-and-equation_1.jpg
"v _ 2 = \frac { 2 \Delta _ 2 } { \overline { P _ 3 P _ 6 } }" ,555c3120-5d9e-11e6-95c7-005056825209__mathematical-expression-and-equation_10.jpg
"- \frac { x } { \sqrt { \frac { r _ m } { r _ i } } }" ,55eb9718-4d9e-11e1-2028-001143e3f55c__mathematical-expression-and-equation_6.jpg
"l o g \overline { A C } ^ 2 = 9 . 4 5 9 0 3 1 4" ,56387d15-8141-4335-8ffa-eb36d657a788__mathematical-expression-and-equation_0.jpg
"+ ( \partial _ j f _ i ( \xi _ i ) - q _ { i j } ) ( \partial _ l f _ i ( \xi _ i ) - q _ { i l } ) \} ( u _ j - v _ j ) ( u _ l - v _ l )" ,572a5f83-8937-4f48-a97a-53dfeb78a409__mathematical-expression-and-equation_7.jpg
"( y ^ 2 - 2 p x ) - ( y y _ 1 - p x - p x _ 1 ) ( p x + y y _ 1 - 3 p x _ 1 ) = 0" ,5793b3d8-4516-4638-847f-497036d9c972__mathematical-expression-and-equation_9.jpg
"p = 1 1 . 5" ,58e1b3ac-c4d7-11e9-b0b4-001999480be2__mathematical-expression-and-equation_11.jpg
"R M S = \sqrt { \frac { 1 } { N } } \sum _ { i = 1 } ^ { N } ( y _ i ) ^ 2" ,5942e576-5012-46a2-b311-5215ae5e34c2__mathematical-expression-and-equation_0.jpg
"\int _ 0 ^ \pi \sin x d x = 2 \int _ 0 ^ { \frac { \pi } { 2 } } \sin x d x = 2" ,594daf58-7d00-4997-a803-30229e56b062__mathematical-expression-and-equation_3.jpg
"( m _ 1 ^ 2 - p ^ 2 ) A _ 1 x ^ { m _ 1 } + ( m _ 2 ^ 2 - p ^ 2 ) A _ 2 x ^ { m _ 2 } + ( m _ 3 ^ 2 - p ^ 2 ) A _ 3 x ^ { m }" ,594e5e40-39db-11e9-9656-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"P : P _ { \prime } = \frac { \mu J l } { r ^ 2 } : \frac { \mu _ { \prime } J _ { \prime } l _ { \prime } } { r _ { \prime } ^ 2 }" ,597e1ae0-ff1a-11e9-8c48-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"\frac { 1 } { s ^ 2 } + 2 \frac { ( x _ 1 - a ) \cos \alpha + ( y _ 1 - b ) \sin \alpha } { t ^ 2 } \cdot \frac { 1 } { s } + 1 = 0" ,5ada3860-10f9-11e5-b269-5ef3fc9bb22f__mathematical-expression-and-equation_10.jpg
"a _ { n , 0 } + a _ { n - 1 , 1 } y \prime _ { \infty } + a _ { n - 2 , 2 } ( y \prime _ { \infty } ) ^ 2 + \dots + a _ { 1 , n - 1 } y \prime _ { \infty } + a _ { 0 , n } y \prime ^ n _ { \infty } = 0" ,5b2383fb-ae6a-11e7-884e-00155d012102__mathematical-expression-and-equation_10.jpg
"k = 2 , 3" ,5b733212-6769-462d-9a22-f32ca5f4ff75__mathematical-expression-and-equation_5.jpg
"K _ { d 1 } = D + \frac { V _ 1 q ^ { n - t _ 1 } + V _ 2 q ^ { n - t _ 2 } + \dots + D _ 1 } { q ^ n - 1 }" ,5cc40374-4f71-479e-9878-8038f24cc9b4__mathematical-expression-and-equation_2.jpg
"2 6 \times 1 7" ,5ccb6fde-9e21-48ea-93bf-5b3af72d0fe8__mathematical-expression-and-equation_3.jpg
"y = - x \sqrt { 2 } + \sqrt { 3 } , y = - x \sqrt { 2 } - \sqrt { 3 }" ,5d65fa2c-ae6a-11e7-884e-00155d012102__mathematical-expression-and-equation_5.jpg
"\eta = \frac { 2 m n } { r }" ,5dbfadfd-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_5.jpg
"P _ { 1 3 } = - v _ 3 X _ 3 ," ,5deb049e-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_11.jpg
"J . + 2 2 9 , 6 E" ,5e4d48cf-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"F = \frac { 8 0 0 } { 3 6 0 0 \times 1 . 4 5 } = 0 . 1 6 5 m ^ 2" ,5ea2b4a7-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\sphericalangle \alpha + \gamma = 2 R" ,5f12264b-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"\delta ^ { 1 3 } C ( \permil ) = [ \frac { ( R _ { \text { s a m p l e } } - R _ { \text { s t a n d a r d } } ) } { R _ { \text { s t a n d a r d } } } ] \times 1 0 ^ 3" ,615568d0-2a24-11ed-bd55-0050568d9066__mathematical-expression-and-equation_0.jpg
"k = \frac { P } { t . s } ( 1 \pm \frac { d } { z } ) = \frac { P } { t . s } ( \frac { z \pm d } { z } )" ,628dcb96-5e8e-11ed-9d94-00155d01210b__mathematical-expression-and-equation_1.jpg
"N p = 1 4 , 7 2" ,629441bf-03bd-464a-854b-04a15d49b2ec__mathematical-expression-and-equation_7.jpg
"4 6 7 - 4 6 9" ,63def930-6f41-11e1-a6d4-005056a60003__mathematical-expression-and-equation_2.jpg
"\frac { \partial ^ 2 F } { \partial x ^ 2 } = F _ { 1 1 } , \frac { \partial ^ 2 F } { \partial y ^ 2 } = F _ { 2 2 } , \frac { \partial ^ 2 F } { \partial z ^ 2 } = F _ { 3 3 }" ,655f7563-e61c-436f-976f-3d743a4cdb27__mathematical-expression-and-equation_1.jpg
"( 2 . ) x = - \frac { a v + b } { a u v - d }" ,65f60120-da08-4c04-b02b-c24a431f7854__mathematical-expression-and-equation_7.jpg
"\gather* 1 2 . 3 5 \times \frac { 8 } { 1 3 } = 9 8 . 8 0 : 1 3 = \text { z l . } 7 . 6 0 \\ 7 8 \gather*" ,65fd0d9f-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"2 8 8 - 1 3 = 2 7 5 ; 2 7 5 : 5 = 5 5" ,6602b2bc-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"+ a q + b q + c q" ,66204b23-1218-11ec-aa85-00155d012102__mathematical-expression-and-equation_4.jpg
"\rcases x = D M . + 1 9 ^ o . 2 7 6 4 ( 9 ^ m . 5 ) A R 1 4 ^ h 5 ^ m 7 ^ s . 8 D + 1 9 ^ o 4 7 \prime . 8 \\ y = D M . + 1 9 ^ o . 2 7 7 3 ( 9 ^ m . 5 ) A R 1 4 ^ h 7 ^ m 5 3 ^ s . 1 D + 1 9 ^ o 4 8 \prime . 8 \rcases \text { B }" ,6685504d-1001-4741-a1c1-6929aeafe7d2__mathematical-expression-and-equation_1.jpg
"\mathcal { S } F _ 1 = \frac { 1 } { T - 1 } ( M A _ { 2 , 1 } + M A _ { 3 , 1 } + \dots + M A _ { T , 1 } )" ,6747ffe3-7fd6-4c47-9955-e290fd3f8e96__mathematical-expression-and-equation_2.jpg
"N _ 1 = 2 \frac { D \cdot \check { S } \cdot L } { P d \cdot V } ( 1 + p ) ," ,69a8ca3c-6bff-11e5-aeea-001b21d0d3a4__mathematical-expression-and-equation_0.jpg
"m = \frac { 1 } { a } ( b + \sqrt { b ^ 2 - a c } )" ,6c30484c-a2fa-4cfc-86c5-f161e5e88f17__mathematical-expression-and-equation_2.jpg
"C _ n . q = J _ n . p \text { č i l i } \frac { C _ n } { J _ n } = \frac { p } { q }" ,6c89b373-cb50-a6e8-fd93-5c7f79165568__mathematical-expression-and-equation_15.jpg
"= m a x \{ \frac { 1 } { 2 } V , \frac { 3 } { 2 } V - \frac { 1 } { 2 } \} + m i n \{ V , 1 - V \} \mu _ 0 ," ,6d095e7f-e0d0-4fb7-9ca3-0720c7141d84__mathematical-expression-and-equation_4.jpg
"d ) \frac { 3 2 5 } { 9 7 5 } = \frac { 1 3 } { 3 9 }" ,6d1cc91f-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"D \delta \phi x = \log ( 1 + v ) . f v = f v ( v - \frac { 1 } { 2 } v ^ 2 + \frac { 1 } { 3 } v ^ 3 - \dots ) ;" ,6e869985-935a-4428-a037-4fa45182a958__mathematical-expression-and-equation_11.jpg
"= \frac { 2 } { d } \frac { \partial u } { \partial \eta } + \frac { 2 } { q } \frac { \partial w } { \partial \xi }" ,70159dc3-4cb3-443c-9e83-00bfb8e76bc7__mathematical-expression-and-equation_3.jpg
"p _ 1 = 1 ; p _ 1 v _ 1 ^ 2 = 7 2 9" ,7144bc56-68d7-42f9-b7b3-3bedb8ef0ed7__mathematical-expression-and-equation_17.jpg
"\frac { 4 6 0 . 1 4 2 } { 2 2 8 . 6 8 0 } = 2 0 1 . 2 \%" ,714d4e0f-e23e-11e6-b2b2-001999480be2__mathematical-expression-and-equation_0.jpg
"L = 4 2 7 c _ p ( T _ 2 - T _ 0 ) \cdot ( 1 - \frac { T _ 1 } { T _ 2 } )" ,71c2f2d9-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\alpha _ { 0 t \prime } = \frac { 1 } { n }" ,7252c5cb-8ab0-46bb-b523-71f989545e95__mathematical-expression-and-equation_2.jpg
"= l \cotg ( \frac { \pi } { 4 } - \frac { y } { 2 } ) + C = l \tg [ \frac { \pi } { 2 } - ( \frac { \pi } { 4 } - \frac { y } { 2 } ) ] + C =" ,72cdbaae-2d84-4623-93e6-96451b26f19e__mathematical-expression-and-equation_10.jpg
"P e = \frac { 2 \alpha _ r a ^ 3 } { D _ 0 }" ,7327168c-8061-447e-b519-043aead03015__mathematical-expression-and-equation_2.jpg
"\frac { c } { h } = 0 , 0 6 6" ,734c5eab-818e-4df1-963c-87c2dad20ce0__mathematical-expression-and-equation_2.jpg
"y \prime = \overset { n } { \underset { i } { \mathcal { C O } } } \{ U _ \rho x \prime + V _ \rho \} = \phi ( x \prime )" ,73f552d1-b934-11e1-1457-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\omega ^ { 0 } = 1 8 0 ^ { 0 } - ( 2 \arcsin ( \cos \rho - \frac { a } { r } \sin \rho ) + \rho ^ { 0 } )" ,74df3cd6-b934-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"m _ c = \pm \sqrt { ( 1 , 5 \text { m m } ) ^ 2 + ( ( 2 , 5 \dots 7 , 5 ) \cdot 1 0 ^ { - 5 } . s ) ^ 2 } ." ,75284eba-2622-11e9-9a7b-801844f3cd1c__mathematical-expression-and-equation_0.jpg
"C A : A B = P _ 2 : ( P _ 1 - P _ 2 )" ,774bd660-de9d-11e7-8cdd-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"p _ 2 = a \sqrt { \tau ^ 2 + \omega ^ 4 }" ,795146b0-3b33-11e7-ad2f-005056827e51__mathematical-expression-and-equation_11.jpg
"a _ 0 = a - \alpha , b _ 0 = b - \beta" ,799a3ff0-ee5e-11ea-8ce6-005056825209__mathematical-expression-and-equation_4.jpg
"C _ K = \int _ 0 ^ \infty \cos [ \frac { 2 \pi } { \lambda } \rho _ K + \delta _ K + \xi ^ 2 - u _ K ^ 2 ] d \xi ," ,7a50a752-a805-44e3-9fda-7e569b4752d5__mathematical-expression-and-equation_10.jpg
"\frac { p _ 1 } { p } = \frac { P _ 1 + Q _ 1 } { P + Q } = \frac { v _ 1 ^ { \prime 2 } V } { v ^ 2 V _ 1 }" ,7a98cafa-32cb-439f-ad32-fba522327aef__mathematical-expression-and-equation_1.jpg
"n = p ( 1 - V s )" ,7b8da8c2-0d86-11e8-8ee8-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\log { \frac { 4 3 3 8 8 2 3 7 } { 3 1 7 } } = 5 . 1 3 6 3 1 = \log { 1 3 6 8 7 _ 0 }" ,7c1f6430-ee5e-11ea-8ce6-005056825209__mathematical-expression-and-equation_6.jpg
"\Omega _ { z } \equiv \Omega = - ( \frac { \partial ^ 2 \Psi } { \partial x ^ 2 } + \frac { \partial ^ 2 \Psi } { \partial y ^ 2 } ) = - \Delta \Psi" ,7c61492c-f978-4981-a152-bd3aa8149e16__mathematical-expression-and-equation_3.jpg
"M = \Sigma m" ,7dd1da43-bfb1-4b0b-bfa7-ed54862859a7__mathematical-expression-and-equation_13.jpg
"S _ { 2 } = \sum _ { \mu = 0 } ^ { p - 1 } f ^ { ( 2 n ) } ( a + \mu h + w k )" ,7e160d06-9859-49b8-9054-d2a109facbba__mathematical-expression-and-equation_0.jpg
"\frac { d x _ j } { d t } = I _ j - a _ j x _ j - f ( \sum _ { i } c _ { j i } I _ i ) x _ j + b _ j" ,7e949218-7754-455b-9699-c13ee205b79e__mathematical-expression-and-equation_2.jpg
"\cos . ( \alpha + \beta ) + \cos . ( \alpha - \beta ) = 2 \cos . \alpha \cos . \beta" ,7f1f9cfe-3402-4cdf-a912-a7558cc662d9__mathematical-expression-and-equation_11.jpg
"- \frac { P _ 2 \prime - P _ 2 } { 2 P _ 2 } = \frac { k ^ 2 - 1 } { 2 } ( \frac { P _ 0 } { P _ 2 } - 1 )" ,81f016b5-2606-47d6-b90f-ae9580ea85c1__mathematical-expression-and-equation_3.jpg
"[ l ( 1 + \frac { 1 } { K } ) - \frac { 1 } { K } ] < \frac { 1 } { K ^ 2 } \cdot \frac { 1 } { 2 m ^ 2 } ." ,8242bf10-eec1-11e6-8d33-005056825209__mathematical-expression-and-equation_5.jpg
"K _ 1 ( \frac { \partial ^ 2 \xi } { \partial t ^ 2 } + \sum A _ a \ddot { \phi } _ a ) = 4 \xi - \frac { \partial \sigma } { \partial x }" ,82595389-5d76-49d0-b1e4-5370cb0894f3__mathematical-expression-and-equation_1.jpg
"b _ y = 2 ( \frac { 1 } { L } ( \sum x _ i \sum z _ i - \sum x _ i z _ i ) ," ,82893839-43ab-4520-95aa-199f206771b6__mathematical-expression-and-equation_1.jpg
"\sigma = \frac { 1 } { G } \cdot p" ,8377aea0-de9d-11e7-8cdd-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"7 = 4 + 2 + 1" ,845e7fe7-bf5b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\tilde { g } ( \boldsymbol { u } ) = ( 1 + u ^ 2 ) ^ { \sigma / 2 } g ( \boldsymbol { u } ) ( \boldsymbol { u } \in \mathbb { R } ^ 3 )" ,85e168ce-f8fd-4c4d-84b4-d6bba9049639__mathematical-expression-and-equation_10.jpg
"b _ 1 ^ 2 = \frac { b ^ 4 \cos ^ 2 \alpha + a ^ 4 . \sin ^ 2 \alpha } { b ^ 2 \cos ^ 2 \alpha - a ^ 2 . \sin ^ 2 \alpha }" ,86dd6160-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_5.jpg
"S = x X + y Y + z Z" ,87273b68-67ca-11e8-bf34-00155d012102__mathematical-expression-and-equation_0.jpg
"N e = \frac { P \cdot x \cdot v } { 7 5 }" ,877c41c0-ee60-11ea-9e1b-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"x _ 3 = x _ 1 + \frac { 1 } { 3 } ( \mu h _ 2 + 2 \nu h _ 3 ) = x _ 1 + \frac { 1 } { 3 } ( \nu h _ 3 - \lambda h _ 1 )" ,87992165-316f-11e7-bc1a-00155d012102__mathematical-expression-and-equation_11.jpg
"C _ { \mu - 2 } = \cos . s \theta" ,879e2940-e348-11e8-9445-5ef3fc9bb22f__mathematical-expression-and-equation_28.jpg
"\bar { \eta } \prime \prime \prime + 3 Q \bar { \eta } \prime + ( 3 Q \prime - R ) \bar { \eta } = 0" ,889a8a21-118d-47a5-9fed-6727f92fcce2__mathematical-expression-and-equation_3.jpg
"T _ 1 = 0 . 2 7 6 ( p _ 1 - p _ 2 ) [ \frac { 2 7 3 } { T } ] ^ 2" ,88cfe1f0-fe4a-437b-b20d-044bb0e61e03__mathematical-expression-and-equation_0.jpg
"\frac { \Delta } { \rho _ n } = \frac { \cos ^ 2 \theta } { \rho _ 1 } + \frac { \sin ^ 2 \theta } { \rho _ 2 }" ,88d6e480-7aa3-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"t \ge t _ 0" ,89a156dc-7b0b-44e7-b977-0c7222a88c58__mathematical-expression-and-equation_6.jpg
"r a _ y - y a _ n = - \frac { y z g } { r }" ,89c817f5-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_8.jpg
"B _ 1 = - B _ 2 = \frac { c } { \gamma - \omega }" ,89c81804-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_8.jpg
"\frac { A _ 3 } { B _ 3 } = \frac { - \cos \alpha z } { - \cos \beta z } = \frac { \sin A z . \sin t } { \cos A z . \sin t } = \tan A z" ,8a21df8e-b9f4-11e1-2544-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\alpha = 9 0 ^ { \circ } - \frac { \alpha + \beta } { 2 } \equiv 8 8 ^ { \circ } 5 1 \prime 1 5 \prime \prime" ,8ae2daf0-ef95-11ea-819e-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"a _ 2 : a _ 5 = b _ 2 : b _ 5 ," ,8b5bd3b0-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_6.jpg
"u = v + \frac { v } { 3 } = \frac { 4 } { 3 } v . ^ { 2 2 5 } )" ,8b867240-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_1.jpg
"A = \frac { 1 } { 2 } M ( r _ 1 ^ 2 + r _ 2 ^ 2 )" ,8c2f73b0-7a06-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"e x p [ i ( \rho _ 1 ^ + + \rho _ 2 ^ - + \rho _ 3 ^ - - A _ 1 + A _ 2 - A _ 3 - A _ 4 + A _ 5 + A _ 6 )" ,8cc2343c-8d2c-4a4d-8999-950f9861d3b0__mathematical-expression-and-equation_9.jpg
"a _ 0 + \frac { 1 } { a _ 1 } + \frac { 1 } { a _ 2 } + \dots + \frac { 1 } { a _ { k - 1 } } + \frac { 1 } { a _ k } ," ,8d084b30-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_4.jpg
"c f m + a d f n + b c g m + b d g n = a c f m + a d g m + b c f n + b d g n" ,8d64290e-22b1-11ec-af09-001b63bd97ba__mathematical-expression-and-equation_13.jpg
"+ [ p b c . 1 ] \{ y + \frac { [ p b c . 1 ] } { [ p b b . 1 ] } z - \frac { [ p b o . 1 ] } { [ p b b . 1 ] } \}" ,8e3eb95a-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"x K = 1 1 \cdot 4 1 K" ,8e4b5c30-1012-11e9-91df-005056825209__mathematical-expression-and-equation_10.jpg
"\frac { b } { u ^ 4 } + \frac { b } { u ^ 5 } + \dots + \frac { b } { u ^ n } +" ,8e76e4a0-6b5a-11e0-9737-0013d398622b__mathematical-expression-and-equation_3.jpg
"O q r n = \frac { x \prime y } { 2 } + \frac { b ^ 2 } { 2 } \arcsin \frac { y } { b }" ,8f3c1934-285c-4c44-b1aa-ab85df79287d__mathematical-expression-and-equation_7.jpg
"\Bmatrix S _ x \\ S _ y \\ S _ z \Bmatrix" ,9003dc90-ef3a-11e2-a0b3-5ef3fc9bb22f__mathematical-expression-and-equation_12.jpg
"O C : O C \prime = O D : O D \prime = q" ,9050bde0-0ae4-11e5-ae7e-001018b5eb5c__mathematical-expression-and-equation_0.jpg
"2 R = 1 7 2 . 4 c / m = 1 7 . 2 4 d m" ,907f431f-099e-4a2f-9d62-2ed3a0f06877__mathematical-expression-and-equation_0.jpg
"u = \frac { a + x } { x } \sqrt { a ^ 2 + x ^ 2 - 2 a x \cos \alpha } ;" ,92143609-460d-4acf-a65c-d576f8a8388d__mathematical-expression-and-equation_1.jpg
"N P = \xi + \delta" ,92c855e0-76ad-11e4-9605-005056825209__mathematical-expression-and-equation_5.jpg
"u _ z = \frac { 4 U } { \pi } \sum _ { n = 1 , 3 , 5 \dots } ^ { \infty } \frac { 1 } { n } \frac { s h ( n \pi \frac { y } { W } ) } { s h ( n \pi \frac { H } { W } ) } \sin ( n \pi \frac { x } { W } )" ,92efa340-2578-45fd-aa43-dc63fcf5ae05__mathematical-expression-and-equation_0.jpg
"\int _ { \Theta } \exp { ( - \sum _ { i = 1 } ^ { n } \rho ( X _ i , \theta ) + \ln { \pi ( \theta ) ) } } d \theta =" ,9348f0cf-3e83-452d-b7ad-4b1bd1aab328__mathematical-expression-and-equation_5.jpg
"\mathcal { M } ( 1 3 6 5 , 3 3 4 5 ) = 3 . 5 = 1 5" ,93a64d05-72c6-4388-a163-ec44cfc0c60e__mathematical-expression-and-equation_11.jpg
"1 , 2 , 3 , \dots ( n - 1 ) , n ." ,93fcd780-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_8.jpg
"\frac { 2 \xi _ \sigma } { \sigma } = \sqrt { \frac { \alpha _ 0 } { \alpha _ 2 } \frac { 1 - \eta } { \eta } } \{ 1 - \frac { 1 } { 2 } ( \frac { 1 - \eta } { \eta } - \frac { \alpha \prime _ 2 } { \alpha \prime _ 0 } + \frac { 1 } { 4 } [ ( \frac { \alpha _ 1 } { \alpha _ 0 } ) ^ 2 -" ,941346f5-62d2-4a86-be7e-803471d3c3b9__mathematical-expression-and-equation_2.jpg
"m = \frac { 3 } { 2 } , m ^ 2 = \frac { 3 ^ 2 } { 2 ^ 2 } , m ^ 3 = \frac { 3 ^ 3 } { 2 ^ 3 }" ,94407eed-c789-4ea0-b2b7-61f54ff2a80e__mathematical-expression-and-equation_0.jpg
"u = a ^ 2 ( 3 \pm 2 \sqrt { 2 } )" ,951dbcc4-5fc9-41c6-bc91-9b30e467aa87__mathematical-expression-and-equation_14.jpg
"B = \frac { g } { q ^ { 2 ( m + n ) - 1 } } \frac { q ^ { 2 m } - 1 } { q - 1 }" ,954f9987-c467-4bda-a9d6-18ea90db1d0f__mathematical-expression-and-equation_3.jpg
"k = \frac { K } { a _ m a _ z } ( \frac { a _ m - a _ { m + 1 } } { q } a _ { z + 1 } + \frac { a _ { m + 1 } - a _ { m + 2 } } { q ^ 2 } a _ { z + 2 } + \frac { a _ { m + 2 } - a _ { m + 3 } } { q ^ 3 } a _ { z + 3 } + \dots )" ,967fb1d0-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_2.jpg
"\frac { d } { d x } ( E - 2 H I _ s x ) = 0" ,97198d2f-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { d i _ o } { d t } + \frac { i _ o } { T } = K" ,97d208e3-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\theta _ { n j } ^ 2 = ( \frac { s _ { n j } } { a } ) ^ 2" ,97d20994-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"Y _ { s = i \omega } = - \frac { i \omega } { 2 \pi \Omega _ 1 } \int _ { 0 } \int _ { 0 } \frac { 2 \cos \theta } { n ^ 2 \cos \theta + \sqrt { n ^ 2 - 1 + \cos ^ 2 \theta } }" ,98a5fa6c-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"S ^ e _ { p \text { m a x } } = 3 7 5 0 0 0" ,98a5fbe6-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\rcases d X = \frac { \mu i } { r ^ 3 } \{ \eta \cos { \phi } + \zeta \sin { \phi } - \rho \} \rho d \phi \\ d Y = \frac { \mu i } { r ^ 3 } ( x - \xi ) \rho \cos \phi d \phi \\ d Z = \frac { \mu i } { r ^ 3 } ( x - \xi ) \rho \sin \phi d \phi \rcases \text" ,99614460-eea2-11e6-a8e7-001018b5eb5c__mathematical-expression-and-equation_6.jpg
"\epsilon = k _ 1 \log A + k _ 2" ,9979c53c-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"y _ x = \mu _ 1 \rho _ 1 ^ x + \mu _ 2 \rho _ 2 ^ x" ,99fd1b6d-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_10.jpg
"J _ A \cdot 8 5 0 - 1 5 . 5 7 5 - 1 5 . 4 2 5 = 0" ,9a3c4f40-f597-11e7-b30f-5ef3fc9ae867__mathematical-expression-and-equation_4.jpg
"\int _ { \bar { M } } [ \psi \Delta \phi + ( \nabla \phi , \nabla \psi ) ] d v = \int _ { \partial M } \psi ( n , \nabla \phi ) d \eta" ,9a5bae78-7fd0-4bfa-8a5d-85565d54a6f1__mathematical-expression-and-equation_4.jpg
"\frac { \tan \alpha + \tan \beta } { 1 - \tan \alpha \tan \beta } = 1" ,9ac966a2-9aa1-4a99-b0f2-07df75d18f4a__mathematical-expression-and-equation_0.jpg
"y = m x + \frac { p } { 2 m }" ,9b130268-f5f2-48f3-bd79-8c77578d506d__mathematical-expression-and-equation_1.jpg
"\frac { 1 } { \bar { n } } = \frac { N A } { \xi } \bar { t } _ k + \frac { 1 - q } { q ( p - 1 ) } \cdot \frac { N B } { \xi } \cdot \bar { t } _ k ^ 2" ,9b285e84-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\omega = | \gamma _ e | \mathrm { H } _ 0" ,9b285eed-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\S 7" ,9bcf05ab-72ff-4aa5-8cb5-0f4c614c5bdf__mathematical-expression-and-equation_9.jpg
"V _ { g z } < V _ { g } < 0" ,9bff5f2f-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\bar { \psi } \prime = \bar { \psi } \mathrm { e } ^ { i \frac { 1 } { 2 } \alpha \gamma _ 3 }" ,9bff5fb0-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_14.jpg
"K \prime \prime ( \mu ) = \pi \sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k + 1 } E _ k ^ * \sinh k \pi \frac { \cosh k \pi \frac { 1 } { 2 } \mu } { \cosh k \pi \mu }" ,9bff5fc4-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( x _ 2 - \alpha _ 1 ) ^ 2 + ( y _ 2 - \beta _ 1 ) ^ 2 + ( z _ 2 - \gamma _ 1 ) ^ 2 = a ^ 2" ,9c56abd5-b9f4-11e1-2544-001143e3f55c__mathematical-expression-and-equation_1.jpg
"1 8 d m - 1 d m =" ,9d386e76-2dbe-11ec-b584-001b63bd97ba__mathematical-expression-and-equation_28.jpg
"- ? = 7 | 1 3 m - ? m = 4 m" ,9d38e3ab-2dbe-11ec-b584-001b63bd97ba__mathematical-expression-and-equation_31.jpg
"+ \dots + A _ k ( \frac { 1 } { w _ k - u } + \frac { 1 } { u - \frac { 1 } { 2 } } ) \egroup" ,9dad3de5-969a-45f1-bc65-df09fcf376e5__mathematical-expression-and-equation_6.jpg
"\frac { v _ 2 } { v _ 1 } \ge \sqrt { 1 + [ ( \frac { D _ 2 } { D _ 1 } ) ^ 2 - 1 ] ( \frac { u _ 1 } { v _ 1 } ) ^ 2 }" ,9e5d29a0-32d4-11e6-a344-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"S _ { n + 1 } = S _ n e ^ { \mu \alpha }" ,9f114080-7704-11e4-9605-005056825209__mathematical-expression-and-equation_0.jpg
"\frac { d \epsilon } { d t } = \frac { 1 } { E } \frac { d \tau } { d t } + \frac { 1 } { \eta } \tau" ,9f213832-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"d N _ 2 = ( B N _ 1 \rho _ v - B N _ 2 \rho _ v - \frac { N _ 2 } { \tau } ) d t" ,9fdd82dc-4334-11e1-1729-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\mu = \text { c o n s t } > 0" ,9fdd8316-4334-11e1-1729-001143e3f55c__mathematical-expression-and-equation_10.jpg
"D _ f = a K _ a ^ { ( h k 0 ) }" ,a09e12f0-4334-11e1-1121-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\epsilon _ { i j } = \sqrt { ( \epsilon _ i \epsilon _ j ) } ." ,a09e1314-4334-11e1-1121-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\sin \delta = \sqrt { \sin ^ 2 \alpha - \sin ^ 2 \delta _ k } ." ,a0d237b0-c548-11ea-9a89-005056825209__mathematical-expression-and-equation_3.jpg
"( \frac { \partial \xi } { \partial t } ) _ { i , 0 } = 2 ( \frac { \partial \xi } { \partial t } ) _ { i , 1 } - ( \frac { \partial \xi } { \partial t } ) _ { i , 2 }" ,a10bd4ad-d696-4a45-ad1f-1c7270d9aad9__mathematical-expression-and-equation_3.jpg
"P ( C _ { p y r } ) = P ( n c ) ^ { n ( L - 1 ) + 1 }" ,a1a1f3da-c1bd-4912-b209-908cda004072__mathematical-expression-and-equation_2.jpg
"\le \mu ^ { 1 - \frac { 2 } { p } } ( \Omega ) \epsilon _ { i k l } \epsilon _ { j m n } | v _ { k } | _ { L _ { \infty } ( \Omega ) } | u _ { l m } - y _ { m } ^ { s } | _ { L _ { p } ( \Omega ) } | y _ { n , l } ^ { s } | _ { L _ { p } ( \Omega ) }" ,a31341b3-89e6-400f-85d9-9c42397f2881__mathematical-expression-and-equation_8.jpg
"f x = x ( a - x )" ,a3df5e00-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"\cos h \cos a = - \sin \delta \cos \phi + \cos \delta \sin \phi \cos" ,a4814792-effa-49cb-960c-a8bf91bca344__mathematical-expression-and-equation_9.jpg
"y ^ 2 = 3 x ; ( \frac { 1 } { 3 } , 1 ) ; ( \frac { 4 } { 3 } , 2 ) ; ( 3 , 3 ) ; ( \frac { 1 6 } { 3 } , 4 ) ; ( \frac { 2 5 } { 3 } , 5 ) ; ( 1 2 , 6 ) ; ( \frac { 4 9 } { 3 } , 7 ) ." ,a51465cc-1467-49a7-a89e-6893dab3f8e0__mathematical-expression-and-equation_25.jpg
"q _ 0 + r s = H \frac { \partial Q \prime } { \partial x } + Q \prime \frac { \partial H } { \partial x } + \delta \frac { \partial M \prime } { \partial x } + \delta \prime \frac { \partial N \prime } { \partial x } + M \prime x + N \prime x \prime" ,a56a687e-1e2d-4b11-a004-158fc3bfdd0c__mathematical-expression-and-equation_13.jpg
"\xi = - \frac { q } { y }" ,a5c2ccb9-0b67-4488-a9d6-a87ad8f64c71__mathematical-expression-and-equation_17.jpg
"V _ i ^ 1 ( P ) = - ( 4 \pi ) ^ { - 1 } \iint _ S V _ i ( Q ) \frac { \partial G _ 1 } { \partial n } d \sigma" ,a6393426-3728-46cf-bcff-5d5e8529836d__mathematical-expression-and-equation_2.jpg
"y = - \frac { c ^ 2 } { b ^ 2 } y" ,a66627b2-f28a-49d4-9365-aab09ecd80e1__mathematical-expression-and-equation_10.jpg
"u ^ 2 = r \prime + r \prime \prime - 2 \sqrt { \Sigma ( \Sigma - s ) }" ,a6e8dd6d-335b-11e9-8d85-00155d012102__mathematical-expression-and-equation_10.jpg
"g \cos \phi - b R \cos \psi = c" ,a6e952cd-335b-11e9-8d85-00155d012102__mathematical-expression-and-equation_18.jpg
"\lg K _ x = \frac { 1 } { R } \sum _ { i = 1 } ^ { h } v _ i ( C _ { p i } \lg T - \frac { a _ i } { T } - C _ { p i } + b \prime _ i ) - \lg p \sum _ { i = 1 } ^ { h } v _ i ;" ,a78a1940-35d1-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"\eta _ i ^ 1 = \frac { \text { p l . } K } { \text { p l . } a b c e f h i a }" ,a7c31092-8617-11ea-a4a1-001999480be2__mathematical-expression-and-equation_0.jpg
"x = 0" ,a7cd93bb-edf6-4a7a-81e5-eeba8c9eddfc__mathematical-expression-and-equation_14.jpg
"E _ 5 = 0 , 0 8 8 \mathrm { M P a }" ,a886a6f0-d351-11ea-903c-5ef3fc9ae867__mathematical-expression-and-equation_6.jpg
"d J = \frac { n } { D } \frac { 1 } { r } \frac { d } { d r } ( r \frac { d u } { d r } )" ,a906770b-e6aa-11e5-bc5e-001b21d0d3a4__mathematical-expression-and-equation_9.jpg
"p _ 1 ^ { - 3 } p _ 2 ^ { - 1 } p _ 3 ^ 2 = K _ p" ,a984fee0-35d1-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_4.jpg
"C = \frac { G } { g } \frac { ( 0 . 4 6 \sqrt { 2 g H } ) ^ 2 } { R _ s } = \frac { 0 . 4 2 3 G H } { R _ s }" ,aac4ab50-32d4-11e6-a344-5ef3fc9ae867__mathematical-expression-and-equation_6.jpg
"v _ k = g _ { k l } v ^ l , v ^ k = g ^ { k l } v _ l" ,ab2cc4aa-7ff1-43d9-96e4-7e7fbb89afeb__mathematical-expression-and-equation_0.jpg
"p | _ { \partial \Omega } = p _ \Omega" ,ac56741b-a261-4153-921f-3013a4f0ab5a__mathematical-expression-and-equation_5.jpg
"A O B D + \triangle A O B ." ,ac9c52a0-b5c9-11e8-b888-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg
"w = \sqrt { z . }" ,acb0c620-77e1-11e3-ae4b-001018b5eb5c__mathematical-expression-and-equation_3.jpg
"\frac { C A } { C N \prime } , \frac { B A } { B M \prime }" ,ae69e7bd-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"f _ { m a x } = \frac { g l \prime { ^ 2 } + 2 l \prime _ Q } { 8 T _ Q }" ,ae726c80-d035-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"2 \alpha \beta c x _ s = z _ s" ,aed13c20-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_11.jpg
"T = 1 2 0 0 \text { h o d i n . }" ,af851210-f597-11e7-b30f-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"\overline { J Z } = \overline { H Z } \sin \epsilon = \rho \sin \epsilon" ,b00d0e47-dc31-41af-a394-156dd81b6a9f__mathematical-expression-and-equation_4.jpg
"f ( x ) = A _ 0 B _ 0 ( x ) + \frac { A _ 1 } { 1 ! } + B _ 1 ( x ) + \frac { A _ 2 } { 2 ! } B _ 2 ( x ) \dots ( 1 1 )" ,b116a519-3348-4da9-8a70-7d1a7dc7f1da__mathematical-expression-and-equation_3.jpg
"K = \frac { 3 } { 4 } n a ^ 3 = 9 4 3 , 2 9 6 c m ^ 3" ,b2ae966f-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"K = \frac { a ^ 3 v } { 6 \sqrt { a ^ 2 - 2 v ^ 2 } } = 1 , 1 2 5 \mathrm { d m } ^ 3" ,b2aebd9c-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"D = \sqrt { \frac { 5 + \sqrt { 5 } } { 3 0 } } \cdot P \sqrt { 3 } = 5 8 , 8 1 7 \dots c m" ,b2af330f-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_4.jpg
"6 0 = 2 9 ^ \circ + 4 2 \prime + 3 3 \prime \prime" ,b2afa871-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_11.jpg
"k = \frac { V \pi } { 3 R } [ R ^ 3 - \sqrt { ( r _ 1 r _ 2 ) ^ 3 } ] = 7 , 9 3 9 4 3 3 \mathrm { d m } ^ 3" ,b2b01cee-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"K = n R ^ 3 \pi \sin ( \frac { 3 6 0 } { n } ) = 6 , 5 7 4 3 . . d m ^ 3" ,b2b04420-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"x = 1 1 , 0 8 0" ,b2bc51b1-e881-11e6-a880-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"\alpha - \beta = \frac { \pi } { 2 }" ,b30c8603-a4f8-40c0-b4d1-9fb0ba3d1ced__mathematical-expression-and-equation_9.jpg
"P O _ 4 H _ 3 = 3 1 + 6 4 + 3 = 9 8" ,b3663cb0-40ba-11ed-9c0c-0050568d9066__mathematical-expression-and-equation_0.jpg
"q _ v = \sqrt { 0 . 0 5 5 \times 0 . 0 3 4 \times 5 7 } = \sqrt { 0 . 1 0 6 6 } \doteq \mathbf { 0 . 3 2 7 }" ,b3762020-e3d1-11e3-bbd5-5ef3fc9bb22f__mathematical-expression-and-equation_13.jpg
"x = ( 2 k + 1 ) \frac { \pi } { 2 } , x = \frac { \pi } { 6 } + k \pi , x = \frac { 1 1 } { 6 } \pi + k \pi ;" ,b3c36184-cd17-443c-a00b-529731c0e213__mathematical-expression-and-equation_0.jpg
"j < \frac { n } { 4 }" ,b3e4aa19-f2d1-4fdd-b83d-af79d014ad16__mathematical-expression-and-equation_2.jpg
"\frac { 1 } { 2 } ( - 1 ) ^ { \frac { n } { 2 } } \frac { E _ n } { 3 ! ( n - 4 ) ! } + 4 x ^ 3 U _ { n - 1 } - \frac { h ^ { n - 4 } x ^ 3 } { 3 ! ( n - 4 ) ! } \int _ 0 ^ 1 E _ { n - 4 } ( 1 - t ) \phi _ n ( t ) d t" ,b43ef77d-2e19-46ba-a468-c686c9585d96__mathematical-expression-and-equation_11.jpg
"l o g ( \frac { c } { V } + \sqrt { 1 + \frac { c ^ 2 } { V ^ 2 } } ) =" ,b498be3c-59d6-44f1-81b0-f93f7cc57ac2__mathematical-expression-and-equation_2.jpg
"\phi _ 1 \theta = \phi \theta . \phi ( \alpha + \theta ) . \phi ( \alpha - \theta ) . \phi ( 2 \alpha + \theta ) . \phi ( 2 \alpha - \theta ) . \dots . \phi ( n \alpha +" ,b5318c85-24f9-4083-a028-1587f5a65fb5__mathematical-expression-and-equation_10.jpg
"M _ H = 2 . 1 \cdot 0 0 8 , M _ { C l } = 2 . 3 5 \cdot 4 5 7" ,b6ec0ac0-d5e0-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_5.jpg
"( 1 7 3 1 - 2 9 . 4 . 1 7 8 5 . )" ,b77ee830-9325-11e7-8167-005056825209__mathematical-expression-and-equation_0.jpg
"z _ 1 = H - S _ 1 ; z _ 2 = H - S _ 2" ,b792e970-87bf-11e5-bf6c-005056825209__mathematical-expression-and-equation_2.jpg
"\lambda _ y | _ { y = 0 } < b" ,b7c735e2-b4ee-4ed4-af81-fbc797c2a9da__mathematical-expression-and-equation_7.jpg
"\frac { ( \bar { \sigma } _ Y ^ { ( f ) } ) ^ 2 } { \bar { \sigma } _ Y ^ 2 } = 1 - \bar { \eta } _ { Y ( Z ) } ^ 2 ," ,b8ca83a0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"+ 2 ( \eta _ 2 z _ 2 ^ 2 + \eta _ 4 z _ 4 ^ 2 + \dots + \eta _ { n - 2 } z _ { n - 2 } ^ 2 ) | =" ,b9094d60-e228-11e2-a0b3-5ef3fc9bb22f__mathematical-expression-and-equation_15.jpg
"D p _ 3 = p _ 3 - p _ 2 = \eta _ 2 + \frac { 1 } { 2 } D \eta _ 2 + \frac { 5 } { 1 2 } D ^ 2 \eta _ 2" ,b963afb0-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"\frac { L \prime } { L } = - h \Theta ^ { 2 } _ { 0 , 0 }" ,b9de8b75-9cc3-4575-b71b-aee709ed054f__mathematical-expression-and-equation_2.jpg
"1 9 5 1 - 1 9 5 2 / - 1 3 2" ,bc73f8eb-443e-11eb-836c-00505684fda5__mathematical-expression-and-equation_11.jpg
"o = 2 [ \frac { ( d + 1 ) } { 2 } h + \frac { ( d - 1 ) } { 2 } ( h - 2 ) ] + 2" ,bd210bb2-6bff-11e5-aeea-001b21d0d3a4__mathematical-expression-and-equation_0.jpg
"\frac { H _ \delta } { H _ \phi ( a ) } \cdot \frac { a } { R } > q" ,be4b29ff-ba2f-448d-81df-16ed1163c6ce__mathematical-expression-and-equation_0.jpg
"\frac { R } { x } - \frac { R - \lambda } { \rho }" ,be5d0053-4cfd-4970-a5c9-832dfb375c2c__mathematical-expression-and-equation_1.jpg
"I _ 0 + a \cos L + \beta \sin L" ,beab403a-01c7-11e2-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { A ( u v - a - l \primenyj ) } { m } + \frac { N } { S }" ,bf0a51a3-530d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"A B C \rightarrow A - B - C" ,bfb7d00b-530d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_22.jpg
"G X Y = G _ { 1 2 }" ,bfecd758-f93a-4867-90bd-88d1d8463074__mathematical-expression-and-equation_3.jpg
"\frac { T _ 1 } { T _ 2 } = n = \frac { N _ 2 } { N _ 1 }" ,c0d31e30-40bf-11e4-bdb5-005056825209__mathematical-expression-and-equation_1.jpg
"f x + n x = v" ,c154b7ee-ef43-4428-941f-1b90c301eb1b__mathematical-expression-and-equation_10.jpg
"u _ 1 ^ 0 = \frac { 1 - 2 \nu } { 4 \nu ( 1 - 2 \nu ) } X _ 1 x _ 1 ^ 2 + \text { c o n s t . , }" ,c1b285db-3c53-11e1-2544-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\gamma = 2 [ 2 \arcsin \frac { I } { N } \frac { \sqrt { 4 - N ^ 2 } } { 3 } - \arcsin \frac { \sqrt { 4 - N ^ 2 } } { 3 } ] , \text { o ù } N = \frac { \sqrt { n ^ 2 - \sin ^ 2 \alpha } } { \cos \alpha } ." ,c1cb8d5a-e9e7-4d43-86d8-71e381df916b__mathematical-expression-and-equation_1.jpg
"+ 2 t r \mathbf { A } _ 3 \mathbf { T D T } - 2 \sum _ { 1 } ^ { m } \varkappa _ i t r \mathbf { S } \mathbf { V } ^ { - 1 } \mathbf { V } _ i \mathbf { V } ^ { - 1 } \mathbf { S D }" ,c1eef0db-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\Omega ^ 2 = K / M" ,c1fdb883-9efe-412a-8440-5ba6914cd981__mathematical-expression-and-equation_5.jpg
"s a _ { 2 2 } = 2 s ^ 2 \beta _ 1 \beta _ 2" ,c22f9271-49d0-4b53-84da-05825dab778f__mathematical-expression-and-equation_14.jpg
"= \bigcap _ s ( ( x ( R ^ 1 ) \cup B _ y ^ \perp ( t - s ) ) \cap ( y ( R ^ 1 ) \cup B _ x ^ \perp ( s ) ) \cap x ( R ^ 1 ) \cup B _ y ^ \perp ( t - s ) ) \cap" ,c2afa868-e09b-11e1-8202-001143e3f55c__mathematical-expression-and-equation_2.jpg
"u , v , w , z \in [ u _ 0 , v _ 0 ] , u \le w \le z \le v :" ,c2afa8be-e09b-11e1-8202-001143e3f55c__mathematical-expression-and-equation_35.jpg
"L = \hat { L } + \tilde { L }" ,c2afa9e7-e09b-11e1-8202-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathcal { M } ( x , s , z ) = - ( \begin{array} { c } g _ { x } ( x , s , z ) \\ g _ { x x } ( x , s , z ) \end{array} )" ,c36e1799-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\nabla . \tilde { u } ^ m - k \Delta p ^ m = 0 , \partial _ n p ^ m | \partial \Omega = 0 ." ,c36e17ba-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { 2 7 } { 6 4 } ( 1 - 2 0 m ^ 3 - 8 m ^ 6 ) = \lambda ^ 3 g _ 3" ,c383f097-57a6-412c-be43-8e53328085d0__mathematical-expression-and-equation_4.jpg
"\Theta _ m [ \begin{array} { c } g \\ n \end{array} ] ( v , \tau )" ,c3edd8b0-1e5b-11e5-b642-005056827e51__mathematical-expression-and-equation_4.jpg
"Y _ h = \{ z _ h \in C ( \overline { \Omega } ) | z _ h | _ T \in P _ 1 ( T ) \forall T \in \mathcal { T } _ h \}" ,c42ece4b-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"u : = u _ 0 ( F ( \alpha ) )" ,c42ed013-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\widehat { \delta \beta } ( Y , \delta \beta ) = [ ( F + \Delta ) \prime \Sigma ^ { - 1 } ( F + \Delta ) ] ^ { - 1 } ( F + \Delta ) \prime \Sigma ^ { - 1 } ( Y - f _ 0 )" ,c4ed6375-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"a _ { i j } = a _ { i j } ( u _ { 2 } )" ,c4ed63c3-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"F ( t ^ * ) \le \frac { C _ 4 } { 2 } \mathcal { E } ( T )" ,c4ed6420-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"u ( a ) - \sum _ { b \in R ( a ) } \gamma ( a b ) u ( b ) = \rho _ a + e _ t + e _ x" ,c4ed64c2-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"S ( a ) = \{ b _ 1 , b _ 2 , b _ 3 \} \cap \Gamma" ,c4ed64c5-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"8 a ^ 2 b ^ 2 c ^ 2 : 2 a ^ 2 = 4 b ^ 2 c ^ 2" ,c537a1a0-ceaf-4e9a-9603-8cc1b8c99b39__mathematical-expression-and-equation_16.jpg
"s p a n \{ M r ( x _ 0 ) , S M r ( x _ 0 ) , \dots , S ^ { k - 1 } M r ( x _ 0 ) \}" ,c5b7b82e-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\langle \epsilon \mathcal { A } ( e _ { \epsilon } ^ { n } ) u _ { \epsilon } ^ { n } + \mathcal { B } ( e _ { \epsilon } ^ { n } ) u _ { \epsilon } ^ { n } , v - u _ { \epsilon } ^ { n } \rangle _ { V ( \Omega ) } \ge \langle f + B e _ { \epsilon } ^ { n } , v - u _ { \epsilon } ^ { n } \rangle _ { W ( \Omega ) }" ,c5b7b953-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\delta ^ { 2 s } \cos j x = ( i 2 \sin j h ) ^ { 2 s } \cos j x ," ,c5b7b9c2-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\lambda _ { \text { h o m } } ( \xi ) \ge \sup _ { \sigma \in V } \int _ Y \langle \sigma , \xi \rangle - \frac { 1 } { q } \lambda ^ { 1 - q } | \sigma | ^ q d y ." ,c681712d-e09b-11e1-1121-001143e3f55c__mathematical-expression-and-equation_1.jpg
"P _ h U ^ n | _ { \Omega _ { k l } } = \frac { 1 } { | \Omega _ { k l } | } \int _ { \Omega _ { k l } } U ( x , y , t _ n ) d x d y" ,c681726b-e09b-11e1-1121-001143e3f55c__mathematical-expression-and-equation_2.jpg
"y \prime = b _ 2 \cdot y ." ,c7b26b60-7e4c-11e3-989f-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg
"c o s \frac { 2 \pi } { n } = \frac { a _ 1 } { 2 ^ \lambda } ," ,c830c886-6344-486b-8a40-4e3737ddb66e__mathematical-expression-and-equation_2.jpg
"= - 4 ^ 4 \cdot 6 ^ 3 A ^ 5 + 6 \cdot 4 ^ 3 \cdot 5 ^ 3 A ^ 3 B + 4 ^ 3 \cdot 5 ^ 4 A ^ 2 C - \frac { 8 } { 3 } 5 ^ 5 A B ^ 2 - \frac { 8 } { 3 } 5 ^ 5 B C - 5 ^ 5 D" ,c92bfce2-61c3-4c7a-bed6-e8aba36424a9__mathematical-expression-and-equation_5.jpg
"\sqrt { a } = \sqrt { \frac { a c ^ 3 } { c ^ 3 } } = \frac { \sqrt { a c ^ 3 } } { c }" ,c933ee75-a8dc-11e0-b4e4-0050569d679d__mathematical-expression-and-equation_1.jpg
"\frac { \phi _ 3 } { \phi _ 4 } = - \frac { \delta _ 3 f _ 3 } { f _ 3 ( \alpha ^ 2 - \delta _ 3 - \theta _ 3 \gamma _ 2 ) - \delta _ 2 \gamma _ 2 \theta _ 3 f _ 2 } = - \frac { \delta _ 3 f _ 3 } { f _ 4 }" ,c9552120-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"D ( \partial t ) = [ 2 V + 2 N _ m ] \frac { D t ^ s } { 2 }" ,c99b2520-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_8.jpg
": s \prime \equiv w \prime : w \equiv \frac { 1 } { w } : \frac { 1 } { w \prime } ( 1 )" ,c9bd29d0-e83e-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_7.jpg
"( - 1 ) ^ { b + \beta } \sqrt { [ \frac { ( 2 c + 1 ) } { ( 2 a + 1 ) } ] } C _ { c - \gamma b \beta } ^ { a - a }" ,ca62d531-e862-4639-a47e-b05cdf77b66e__mathematical-expression-and-equation_6.jpg
"M _ { ( x ) } = - \int _ x ^ { \frac { h } { 2 } } ( \xi - x ) d T = - \int _ x ^ { \frac { h } { 2 } } ( \xi - x ) q _ A d \xi =" ,ca7d5422-0de2-49c4-a241-94c315c18dd0__mathematical-expression-and-equation_6.jpg
"b ^ 2 y \prime ^ 2 + a ^ 2 z ^ 2 = a ^ 2 b ^ 2" ,cae15370-e228-11e2-a0b3-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"B _ 0 = 0 , 8 7 8 1 K + 0 , 1 1 2 5" ,cb79fd6a-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_49.jpg
"c = a \sqrt { \frac { h f S } { \delta . } \cdot \frac { g } { s . f } } = a \sqrt { \frac { g . h . S } { \delta . s } }" ,cba51d10-0bb5-11e5-b309-005056825209__mathematical-expression-and-equation_2.jpg
"\mu - k _ { 1 2 } s _ \mu \text { r e s p . } \mu + k _ { 1 2 } \cdot s _ \mu" ,cc2cab0b-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_12.jpg
"C = 1 0 ^ 3 p F , L = 1 0 ^ { - 4 } H , R = 2 , 1 \Omega ," ,cce376ff-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"a _ 6 r ^ 6 = - 0 , 1 4 1 ^ { \circ } \text { C }" ,cce37830-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"a _ n \prime = a _ n + \sum _ { \lambda = 0 } ^ { n - 1 } [ \sum _ { v = 3 \lambda - 1 } ^ { 3 \lambda + 2 } \binom { 3 n - 1 } { v } ] a _ \lambda a \prime _ { n - 1 - \lambda }" ,cce37840-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"1 3 - 1 3 . 5 0" ,cd2ee750-7905-11e7-89ee-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"a _ { 0 1 } ( \lambda ) = \frac { ^ { ( 1 ) } a _ { 0 1 } ( \lambda ) ^ { ( 2 ) } a _ { 0 1 } ( \lambda ) } { ^ { ( 1 ) } a _ { 1 1 } ( \lambda ) + ^ { ( 2 ) } a _ { 0 0 } ( \lambda ) } ," ,cd978589-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\tau _ 3 = 2 , 9 7" ,cd9785ed-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_3.jpg
"d \prime _ i \ge 0" ,ce4a81db-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_10.jpg
"E ( P ) = \frac { 1 } { 4 \cdot \pi } \cdot \iint _ S ( E \cdot \frac { \partial \psi } { \partial n } - \psi \cdot \frac { \partial E } { \partial n } ) \cdot d S ," ,ced6f4f7-cb1b-4d62-a0e7-1ebd18b08259__mathematical-expression-and-equation_0.jpg
"L [ \frac { 1 - e ^ { - \lambda [ t ] } } { e ^ { \lambda } - 1 } ] = \frac { 1 } { p ( e ^ { p + \lambda } - 1 ) }" ,cf0100a5-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lambda \frac { \partial \sigma _ x } { \partial y } + \eta \frac { \partial \sigma _ y } { \partial y } - \chi \frac { \partial \sigma _ x } { \partial x } + B = 0" ,cfb534d4-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { \sin ^ 2 2 p } { 2 \cos 2 p } = \frac { 2 \gamma ^ 2 } { x + y }" ,cfb53691-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\rho _ s \prime = \rho _ s ( 1 - f _ H )" ,d01cc423-4ca2-42b5-a0ad-7775ecedb8a8__mathematical-expression-and-equation_0.jpg
"J = ( \gamma D ^ { - 1 } + B ( D ) ) E + ( \gamma X _ { 1 } \prime D ^ { - 1 } + \gamma _ { 1 2 } X _ { 2 } \prime D ^ { - 1 } ) ( L J _ { 0 } \delta _ { 0 } - S q _ { 0 } H _ { 0 } ) +" ,d06dfe01-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\phi ( 0 ) = 0 ," ,d06dfe33-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_9.jpg
"| | \tilde { x } _ m - x | | \le | | x _ { m + p } - x | |" ,d06dfe67-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"v = b \sin \gamma" ,d0740f5c-224b-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_7.jpg
"\sin \frac { 1 } { 2 } \beta = \sqrt { \frac { ( m o + m k - o k ) ( m k + o k - m o ) } { 4 m o . o k } }" ,d09278e4-01bf-f7a0-fb77-3c61040f304f__mathematical-expression-and-equation_4.jpg
"\bar { a } = \bar { a } _ \rho = ( \ddot { r } - r \dot { \phi } ^ 2 ) \bar { \rho }" ,d0d2f2d0-3d93-11e4-bdb5-005056825209__mathematical-expression-and-equation_0.jpg
"\Omega _ 0 ^ 2 = \frac { k } { m }" ,d0e95a20-4874-4775-b88b-1bc1b6bc640d__mathematical-expression-and-equation_1.jpg
"v _ p ( x _ i ) \ge \delta > 0" ,d1decbdc-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x _ 9 = h ( x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ { 1 1 } , x _ { 1 2 } ) , x" ,d1decc31-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"I = - 4 \log D + 1 0 , 5" ,d1f28655-10f2-44ac-b636-2a6be095fc64__mathematical-expression-and-equation_0.jpg
"P = \frac { 1 } { 3 } \cdot y \cdot \epsilon" ,d22328a0-7eb5-11e8-bb44-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"E [ w ] = F _ w ( w ^ c ) E [ w | w < w ^ c ] + ( 1 - F _ w ( w ^ c ) ) w ^ c ." ,d26e5546-5c58-4300-832c-276e7daa76d9__mathematical-expression-and-equation_0.jpg
"M _ { c _ 1 } ^ { p + q } = M _ { c _ 1 } ^ p + M _ { c _ 1 } ^ q = + 3 5 9 0 - 9 6 . 2 = + 3 4 9 3 . 8 \text { k g m }" ,d2dcdbb0-7eb5-11e8-bb44-5ef3fc9ae867__mathematical-expression-and-equation_12.jpg
"y = \sqrt { a - b x + c x ^ 2 }" ,d2f8f06d-233f-4b3e-91dd-380d89942e19__mathematical-expression-and-equation_3.jpg
"( x ) = - \frac { 2 } { 3 } f _ { n - 1 } ^ { - 1 } F _ { n - 1 } \prime \prime f _ { n - 1 } ^ { - 1 } F \prime \prime ( x ) + [ I - \frac { 1 } { 2 } f _ { n - 1 } ^ { - 1 } F _ { n - 1 } \prime \prime ( x - x _ { n - 1 } ) ] f _ { n - 1 } ^ { - 1 }" ,d34c3fc4-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_16.jpg
"R \prime _ 1 \le R \prime _ 2" ,d3fffe05-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"v ( z _ 0 ) + \frac { 1 } { \pi i } \int _ C \frac { n t ( z _ 0 ) z _ 0 ^ { n - 1 } } { z ^ n - z _ 0 ^ n } v ( z ) \frac { d z } { t ( z ) } = t ( z _ 0 ) ( \frac { Q _ 0 - i \Gamma _ 0 } { \pi } \frac { 1 } { z _ 0 } +" ,d4b1e9ba-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\int _ c \frac { \overline { z - z _ 0 } } { z \exp ( 2 k \pi i / n ) - z _ 0 }" ,d4b1e9be-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"u \in \mathcal { V } \implies \alpha | | u | | ^ 2 \le [ u , u ] _ A \le C _ 0 | | u | | ^ 2" ,d4b1e9dd-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"2 1 x ^ 2 - 4 x y + 1 2 y ^ 2 - 4 2 x - 4 8 y = 0" ,d4cfb27e-6229-4bb7-a444-b197c5516d40__mathematical-expression-and-equation_12.jpg
"i = 1 , \dots , p \} =" ,d5642207-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_18.jpg
"\frac { V } { D } \rightarrow \frac { 3 V } { \frac { D } { 2 } } \rightarrow \frac { 5 V } { \frac { D } { 3 } } \rightarrow \dots = \frac { V } { D } \rightarrow \frac { 6 V } { D } \rightarrow \frac { 1 5 V } { D } \rightarrow" ,d5e0eac2-868c-11e7-bb2d-005056a54372__mathematical-expression-and-equation_4.jpg
"D ^ \alpha = \frac { \partial ^ { | \alpha | } } { \partial x ^ { \alpha _ 1 } \partial y ^ { \alpha _ 2 } }" ,d613e98f-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_5.jpg
"( \begin{array} { c c c c } n ^ { ( 1 ) } _ { 1 } , & n ^ { ( 2 ) } _ { 1 } , & \dots , & n ^ { ( l ) } _ { 1 } \\ \vdots \\ n ^ { ( 1 ) } _ { n } , & n ^ { ( 2 ) } _ { n } , & \dots , & n ^ { ( l ) } _ { n } \end{array} ) ;" ,d613eaea-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"K _ { 3 } ( N , d ) \le \frac { \Gamma ( N + \frac { 1 } { d } + 1 ) } { \Gamma ( N + 1 ) }" ,d613eb2b-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_8.jpg
"P _ 1 = \frac { s + a _ 2 ( 1 + \frac { Q _ 1 } { Q _ 2 } ) } { a _ 1 + s + a _ 2 }" ,d6281e4d-a986-11e0-a5e1-0050569d679d__mathematical-expression-and-equation_1.jpg
"Y _ { \alpha _ 2 } = \frac { \hat { \theta } _ { \alpha _ 2 } - \theta } { \theta } \sqrt { [ ( k + 1 ) n ] }" ,d77501d5-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { 1 } { 2 } | | v - u | | ^ 2 _ 1 = \mathcal { L } _ 1 ( v ) + \mathcal { S } _ 1 ( \lambda )" ,d8269d09-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"l ( x ) = \{ \begin{array} { c c } 0 & ( x \le 0 ) \\ 1 & ( x > 0 ) \end{array}" ,d8de5478-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\beta _ 0 = \frac { 1 } { 2 } - \frac { 1 } { 2 } \theta + \delta" ,d8de55f1-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_15.jpg
"| \epsilon , - \eta | = | - \epsilon , \eta | = | \eta , \epsilon" ,d8fd8a20-1e5b-11e5-b642-005056827e51__mathematical-expression-and-equation_8.jpg
"a \prime = 0 . 0 0 2 \pm 0 . 0 3 8" ,d9537f98-d2d0-43c9-b60c-d9b85801b751__mathematical-expression-and-equation_4.jpg
"\alpha \prime \doteq \frac { s } { a \prime }" ,d9653b20-0c73-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_9.jpg
"\parallel x ^ * - x _ n \parallel > \frac { \zeta _ n } { 1 + \eta _ n } ( n \in \mathbb { N } )" ,d9960b62-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d _ { i + 1 } = \frac { b _ { i + 1 } - a _ { i + 1 } d _ i } { c _ { i + 1 } - D ^ { ( i ) } a _ { i + 1 } } , d _ 1 = \frac { b _ 1 } { c _ 1 }" ,d9960c1f-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\xi \prime _ { i j } = \eta _ { i j }" ,d9960c3b-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"I = I _ 0 + I _ 1 \cos ( \phi + \phi )" ,da12b737-1195-456b-b983-a8f1a3f39970__mathematical-expression-and-equation_15.jpg
"G a m m a \subset k ^ { - 1 } G \forall k \equiv 1 + \epsilon > 1" ,da4ab6fa-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_14.jpg
"\pi i \tau = a ," ,daaebc90-1e5b-11e5-b642-005056827e51__mathematical-expression-and-equation_10.jpg
"\log f ( \omega ) - \log \prime f ( \prime \omega ) = \Omega _ 0 \omega - \prime \Omega _ 0 \prime \omega" ,db01aae3-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_9.jpg
"( B \wedge C ) \vee ( \bar { B } \wedge \bar { C } )" ,db0c6c47-3cfa-11e1-1119-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\log \Gamma ( a ) = ( a - \frac { 1 } { 2 } ) \log a - a + B + \omega ( a ) ;" ,dbe7f91c-2c93-485d-8d1d-e7bbf0ba767b__mathematical-expression-and-equation_5.jpg
"\epsilon _ T = ( 5 , 6 2 5 - 0 , 0 9 7 8 1 \cdot T ) \cdot 1 0 ^ { - 6 }" ,dc7cb2cc-4648-4c89-8d48-c0c5e4073f6b__mathematical-expression-and-equation_1.jpg
"( \alpha \beta ) ^ { 3 3 } = \alpha _ { 1 1 } \beta _ { 2 2 } + \alpha _ { 2 2 } \beta _ { 1 1 } - 2 \alpha _ { 1 2 } \beta _ { 1 2 }" ,dc9e9e41-4de8-4c39-9389-3f6d8088bf45__mathematical-expression-and-equation_8.jpg
"\forall F _ N ( x , \omega ) \in L _ 2 ( G \times \Omega )" ,dd27be63-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"| | \mathbf { n } . \mathbf { v } _ h | | ^ 2 _ { 0 , \Gamma _ 1 } + | | \mathbf { n } \wedge \mathbf { v } _ h | | ^ 2 _ { 0 , \Gamma _ 2 } \le" ,dd27bed3-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\lambda = \lambda ( r , s ) = \frac { r + s } { 2 } - c ( h ( \frac { r + s } { 2 } ) )" ,dd27bee5-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\parallel M v \parallel \le \alpha \parallel B \parallel ^ { - 1 } K ( \lambda ) ^ { 3 / 2 }" ,dd27beee-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"+ \sum _ { j = t + 1 } ^ M \sum _ { i = t + 1 } ^ M \alpha _ i ^ k \alpha _ j ^ k ( \ln \alpha _ i - \ln \alpha _ j ) ( \alpha _ j ^ k - \alpha _ i ^ k ) \} \le 0" ,ddddc8b9-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"+ ( j \prime ( u _ 1 ) , v - u _ 1 ) _ 0 \ge 0" ,ddddc8d8-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\sqrt { \frac { \Delta } { \pi } } K ( a , b , c ; \sigma , \tau ; 1 ) = - \log \Delta ( \sigma , \tau | w _ 1 , w _ 2 )" ,de1221aa-a89c-11e1-1726-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\delta _ v \mathcal { H } ( [ N ^ * , \mathbf { v } ^ * ] ; \lambda ^ * ) ( \mathbf { v } - \mathbf { v } ^ * ) \ge 0 \forall \mathbf { v } \in K _ \epsilon" ,de93f939-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\text { f o r } p ( x ) = J _ 1 ( x )" ,de93f975-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"j = 1 , \dots , n ." ,de93f989-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_22.jpg
"[ u ( x , t ) = Q ( x , t ) - f ( t )" ,de93f9b4-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_15.jpg
"c = 2 n" ,de97f97f-312a-4ae9-b8d5-b8ee54be0394__mathematical-expression-and-equation_17.jpg
"\varpi ( a ) = \sum _ { r = 0 } ^ { \infty } [ ( a + r + \frac { 1 } { 2 } ) \log \frac { a + r + 1 } { a + r } - 1 ]" ,debfc77f-a89c-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\omega _ { N \prime } = 0 ^ \circ . 0 0 2 2 0 6 4 1 3 - 0 ^ \circ . 0 0 0 0 0 0 0 0 4 7 T _ s" ,df637fa3-2e61-4d8d-a355-a73163d5174e__mathematical-expression-and-equation_2.jpg
"d J = i \frac { d s } { r ^ 2 }" ,dfe53eb0-4421-11e4-af1d-001018b5eb5c__mathematical-expression-and-equation_8.jpg
"\frac { ( [ T ] + l ) ^ 2 } { T ^ 2 } - 1 \le \frac { [ T ] ^ 2 + 2 [ T ] n + n ^ 2 } { [ T ] ^ 2 } - 1" ,dfff6f14-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"= \frac { \pi } { \rho } [ n ^ 4 - ( n + 1 ) ^ 4 + ( n + 1 ) ^ 4 - \lambda ^ 2 + 2 \lambda ^ 2 - 2 n ^ 2 \lambda ] =" ,dfff6f20-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_7.jpg
"p \prime ( \rho ) \le C _ 4 \rho ^ { \varkappa - 1 }" ,dfff7044-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_1.jpg
"F ( x ) = x ^ n + a _ 1 x ^ { n - 1 } + a _ 2 x ^ { n - 2 } + \dots + a _ n ." ,e052af5d-f0d7-4493-bec7-fcf81f71381b__mathematical-expression-and-equation_10.jpg
"\{ \bar { \epsilon } \} = \{ 0 , 0 , 0 , 0 , 0 , \beta _ { 5 5 } \} ^ T" ,e0766701-bc87-4e00-8c24-663d0e0e5c8f__mathematical-expression-and-equation_6.jpg
"H = 2 a - \frac { 1 } { 2 } \rho _ 0 \cos ^ 2 \alpha - \frac { 1 \cdot 1 } { 2 \cdot 4 } \frac { \rho _ 0 ^ 2 } { a } \cos ^ 4 \alpha - \dots - R ." ,e08f7b14-475c-464c-9f83-511d82d7ae7e__mathematical-expression-and-equation_6.jpg
"\eta ( b ) = \eta _ 0" ,e0b68ab0-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\kappa = \frac { N } { 2 } ( 1 + | d - 1 | )" ,e0b68ae4-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"S _ n ( f ) = \sum _ { j = 1 } ^ { n } \frac { f \circ T ^ j } { \sqrt { n } }" ,e0b68b20-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lim _ { \lambda \rightarrow \lambda _ { c r ^ + } } w ( x , 0 , \lambda ) = w ( x , 0 , \lambda _ { c r } ) = 0 ;" ,e16e1b1e-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_5.jpg
"x _ 3 ^ 2 - \rho x _ 1 x _ 2 = 0" ,e230a912-5924-4b75-8494-68091dec1ec9__mathematical-expression-and-equation_4.jpg
"M _ 1 = M _ { m a x } . c ," ,e2d87490-e953-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg
"O P = - ( \xi \cos \alpha _ i + \eta \sin \alpha _ i )" ,e3d36061-40e3-11e1-2755-001143e3f55c__mathematical-expression-and-equation_3.jpg
"F _ 3 ( x , y , t ) = \sum _ { n = 1 } ^ { \infty } ( \sum _ { m = 1 } ^ { \infty } D _ { m n } \sin m x e ^ { - m ^ 2 t } ) \sin n y e ^ { - n ^ 2 t }" ,e402f7a9-ee02-4cb1-9d5a-d869e22a4e2e__mathematical-expression-and-equation_3.jpg
"\frac { 1 } { 2 } \cdot 2 - 2 \cdot 5 = 1 - 1 . 2 5" ,e423d526-e2ff-11e6-83b0-001999480be2__mathematical-expression-and-equation_0.jpg
"p = 7 5 0 + 5 \lambda = 7 5 0 + 5 \cdot 1 . 8 2 = 7 5 9 . 1 \doteq 7 5 9 \text { k g / c m } ^ 2" ,e4b94280-e953-11e2-9439-005056825209__mathematical-expression-and-equation_16.jpg
"x ^ { 2 m - 3 } a _ { s _ 1 s _ 2 } + b _ { s _ 1 s _ 2 } x ^ { 2 m - 4 } a _ { s _ 1 s _ 3 } + b _ { s _ 1 s _ 3 } , \dots x ^ { m - 1 } a _ { s _ 1 s _ m }" ,e4f9d2ca-224d-4dbd-a39c-0da5d1fe9495__mathematical-expression-and-equation_13.jpg
"3 n ^ 2 - 2 n ," ,e4ff5cd2-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_9.jpg
"= \mp 3 2 2 . 7 k g [ c m ^ { 2 } ] ," ,e500abc0-e953-11e2-9439-005056825209__mathematical-expression-and-equation_8.jpg
"\lg \frac { V * k } { v } \ge 1 , 6 5" ,e641f15a-bc37-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"n = 6 0 0 l / m i n" ,e641f176-bc37-11e1-1418-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\Theta ^ { ( 0 ) } + ( \Theta ^ { ( 0 ) } - \bar { c } _ j ) . E [ \xi _ j ] \frac { 1 } { \tau ^ { ( 0 ) } } = \frac { z ^ { ( 0 ) } } { \tau ^ { ( 0 ) } }" ,e6477bb7-ac0a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"f ( x ) = M _ x \phi ( x ( \tau ) )" ,e723aa98-ac0a-11e1-1360-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { f ( b ) } { f ( a ) } = \frac { \phi ( b ) } { \phi ( a ) } = \frac { \psi ( b ) } { \psi ( a ) } = c" ,e745caff-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"y = \pm \frac { \mu ( \nu ^ 2 + 1 ) } { \nu ( \mu ^ 2 + 1 ) } i x ," ,e745cb1a-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
"b _ 1 ^ 2 = \frac { a ^ 2 b ^ 2 } { a ^ 2 \sin ^ 2 \beta + b ^ 2 \cos ^ 2 \beta } ," ,e765af49-e8ef-11ea-86d3-00155d012102__mathematical-expression-and-equation_1.jpg
"A - ( 0 , 0 0 4 2 e ^ { \frac { 1 , 4 L } { s } } | 0 , 0 2 8 ) . h _ 2" ,e7909273-bc37-11e1-4047-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\beta _ n = - \frac { 1 } { 2 } \frac { \lambda ^ 2 ( \lambda + 1 ) ( \lambda + 2 ) } { m ( m - 1 ) ( m + \lambda ) ( m + \lambda + 1 ) } , a = \lambda + 1 , b = - \frac { 1 } { 2 } \lambda ^ 2" ,e7c97030-5a87-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_6.jpg
"\frac { Z \cdot 1 0 ^ n } { N } = A + \frac { N - Z } { N }" ,e7f8d990-3fdc-11e7-b3c8-005056825209__mathematical-expression-and-equation_3.jpg
"N ^ { u ^ \gamma } _ c = - \frac { 1 } { 4 } s ( 1 + s ) ( 1 - s )" ,e7fe0e04-174f-429d-8fb5-82b1a833bb1d__mathematical-expression-and-equation_2.jpg
"p _ { i j } = \frac { p _ { 1 j } p _ { i 1 } } { p _ { 1 1 } }" ,e7ff158b-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\tau _ N ( n ) < i + 1" ,e7ff1670-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_11.jpg
"Z _ 6 \prime = Z _ 3 ^ 1 , \dots" ,e7ff16f2-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"v = \lambda _ 0 \varkappa _ 0 + \dots + \lambda _ n \varkappa _ n ," ,e7ff1740-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ { 1 1 } ( k ) = v _ 1 ( k ) + v _ 2 ( k ) = x _ { 1 2 } ( k )" ,e7ff180f-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\overline { u ^ 2 ( r ) } = c _ 2 - \frac { \epsilon } { v } r ^ 2" ,e83a3f92-bc37-11e1-4047-001143e3f55c__mathematical-expression-and-equation_4.jpg
"B \frac { \pi } { 2 } + a _ 1 \frac { 2 } { 3 } = - \frac { M } { ( \frac { l } { 2 } ) ^ 2 }" ,e83a401f-bc37-11e1-4047-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { 1 } { 1 + t } \le \sum _ { k = 1 } ^ { g ^ { + } - 2 } \frac { \exp \{ \frac { 0 , 9 9 } { g } \lg \frac { ( k + t ) ( k + 1 + t ) } { 1 + t } \} } { ( k + t ) ( k + 1 + t ) }" ,e8ae93a5-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_1.jpg
"b _ { \omega \mu \lambda } = \frac { \partial } { \partial \xi ^ \omega } b _ { \mu \lambda } - \genfrac \{ \} { 0 p t } { 2 } { \alpha } { \mu \omega } b _ { \alpha \lambda } - \genfrac \{ \} { 0 p t } { 2 } { \alpha } { \lambda \omega } b _ { \mu \alpha } ." ,e8ae93b4-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_3.jpg
"- ( \frac { 1 } { l } \Delta T ) ]" ,e8dd67aa-ac0a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_7.jpg
"J = \frac { 2 } { 5 } M r ^ { 2 }" ,e8f5bd70-dade-11e2-9439-005056825209__mathematical-expression-and-equation_7.jpg
"M \dot { z } = N \dot { q }" ,e91d2faa-8e88-4ec9-9da2-fb9729f6b836__mathematical-expression-and-equation_3.jpg
"\cos a = \cos b \cos c + \sin b \sin c \cos \alpha * )" ,e99988f0-3e1b-11e4-b6b9-001018b5eb5c__mathematical-expression-and-equation_8.jpg
"z \prime \zeta \prime = - \frac { a ^ 2 } { 2 }" ,e99d2802-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
"u _ 0 = \frac { U _ 0 } { r } \sqrt { r ^ 2 - x ^ 2 } ," ,e9a5b62c-bc37-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"v \in \mathcal { N } _ \text { f . p a s t }" ,e9b2e049-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_15.jpg
"e _ \alpha e _ \beta \neq e _ \beta e _ \alpha ." ,e9fdcf5a-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\{ a _ i \} \subseteq \{ x _ i \} ; \{ b _ i \} \subseteq \{ y _ i \}" ,e9fdcff3-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\beta ( \alpha ^ 2 + \gamma ^ 2 ) = \frac { b } { 4 } ," ,ea35e615-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\{ v _ B \} = R _ A = q _ A s _ A" ,ea4661e0-354a-11e3-b79f-5ef3fc9bb22f__mathematical-expression-and-equation_4.jpg
"A { \prime } ^ { - 1 } y = 0" ,ea77df49-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"B ( r ) = - r + C _ 2 r ^ 2 + C _ 3 r ^ 3 + \dots" ,eaa9eee4-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_3.jpg
"q _ { j + r - 1 } q _ { j + r - 2 } \dots q _ j \le t < q _ { j + r }" ,eaa9ef33-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_11.jpg
"C _ t = 0 . 1 6 7" ,eabcc61f-a89c-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"v = \sqrt { \frac { 4 } { \pi } ( k _ 1 - k _ 2 ) }" ,eacd6acb-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathcal { M } ( v ) = m _ { v _ 1 } m _ { v _ 2 } \dots m _ { v _ p }" ,eb5dd538-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"[ \overline { \omega } _ 1 \overline { \omega } _ 2 ] = \{ \rho _ 1 \rho _ 2 a + ( - \rho _ 1 ^ 2 + \rho _ 2 ^ 2 ) b - \rho _ 1 \rho _ 2 c \} [ \omega _ 1 \omega _ 2 ] \neq 0" ,eb5dd542-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"s ^ 2 = \sum _ { k = 1 } ^ { m } D W" ,eb5dd679-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"x y = x _ m y + ( x - x _ m ) y = \Sigma x ( t _ i ) y ( t _ i ) + \Theta \epsilon | y | =" ,eb5dd6a1-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\overline { c _ 1 c _ 2 } = c _ 1" ,eb66c4fc-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_1.jpg
"c _ L = c _ { L 0 } \times \frac { L } { L _ u } = 5 9 2 0 \times \frac { L } { L _ u }" ,ebc284b8-d253-44a4-88bc-eb857d90c6e1__mathematical-expression-and-equation_4.jpg
"n \equiv c _ 2 e ^ { - \frac { 1 } { 2 } c _ 1 ( a - u ) ^ 2 }" ,ebcab92f-bc37-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\tilde { k } _ B = \mp \frac { M _ B } { h W _ y } \dots . . ( 3 8 9 )" ,ebe49640-e953-11e2-9439-005056825209__mathematical-expression-and-equation_10.jpg
"F = [ - 1 ]" ,ec018b63-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"R _ 2 = R _ 3 = 0" ,ec018bd4-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_9.jpg
"h _ 7 < \beta < H" ,ec20d83c-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_11.jpg
"1 2 \% + 4 \%" ,ec3537c0-8e76-11df-afc6-0030487be43a__mathematical-expression-and-equation_5.jpg
"\int \frac { x d x } { x ^ 2 - a ^ 2 } = \frac { 1 } { 2 } \int \frac { 2 x d x } { x ^ 2 - a ^ 2 } = \frac { 1 } { 2 } l ( x ^ 2 - a ^ 2 ) + C" ,ec389084-20a0-4b7e-b7e5-6f8662b9b244__mathematical-expression-and-equation_5.jpg
"1 - 2 F _ r ^ { - 2 / 3 } ( X _ { \beta \prime } - 1 ) - \sqrt { F _ r ^ { - 4 / 3 } ( X _ { \beta \prime } ^ 2 - 1 ) - 2 F _ r ^ { 2 / 3 } + 2 F _ { r D V } ^ { 2 / 3 } + F _ { r D V } ^ { - 4 / 3 } } = 0" ,ec8d6cc9-bc37-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"a = E \sqrt { \frac { C } { A } }" ,ec93d2a0-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { a } { r } > \frac { k } { m } \implies \Delta ( a , r , k , m ) > \Delta ( a + 1 , r , k + 1 , m )" ,ecce2a03-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\chi = \sigma _ 1 \sigma _ 2 \sigma _ 3 + s _ 1 s _ 2 s _ 3" ,ecce2a30-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ { i + 1 } = A x _ i + B u _ i" ,ecce2b19-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"[ \begin{array} { c } z ^ { - 1 } - z ^ { - 2 } + z ^ { - 3 } ( 1 - z ^ { - 1 } ) ^ { 2 } t \\ 1 + z ^ { - 2 } - z ^ { - 3 } + z ^ { - 2 } ( 1 - z ^ { - 1 } ) ^ { 2 } t \end{array} ]" ,ecce2bee-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_15.jpg
"A _ j ^ { ( k ) } = a _ { t _ { k - j - 1 } - t _ { k - j } } ( \begin{array} { c } ( k - j ) s + t _ { j } \\ ( k - j - 1 ) s + t _ { j + 1 } \end{array} ) , t _ 0 = t - ( k - 1 )" ,ece734b3-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg
"N = H + H _ { 0 }" ,ece7351c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\int _ { x _ { 2 k } ^ { ( ) ) } } ^ { x _ { 2 k + 1 } ^ { ( 1 ) } } P ( y ) d y < - \frac { 1 } { 2 } \gamma _ 1 k ^ { \frac { r + 1 } { 2 } }" ,ece735ce-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x _ 1 x _ 2 = \frac { r } { p } = - \frac { q ^ 2 } { p ^ 2 } \frac { \sin ^ 2 \frac { \phi } { 2 } \cos ^ 2 \frac { \phi } { 2 } } { \cos ^ 2 \phi } ," ,ed2f00f3-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_5.jpg
"v _ r = \frac { 1 } { T } \frac { \partial \phi } { \partial r } = \frac { Q } { 2 \pi T } \frac { \partial } { \partial r } \ln \sqrt { \frac { r ^ 2 } { r ^ 2 + l ^ 2 - 2 r l \cos \theta } } =" ,ed526bc9-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_6.jpg
"[ m ^ 3 . s ^ { - 1 } ]" ,ed526c1e-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_18.jpg
"\partial b = 4" ,ed9d6188-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_15.jpg
"C = C ( \mathcal { H } , s , D )" ,ed9d6289-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\bigcup H _ i = X" ,edb4e528-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"T _ 1 ; 0 < \sigma < \sigma _ 0 , s \le \tau \le \epsilon" ,edb4e602-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg
"2 [ 1 - \Phi ( \frac { 1 } { \lambda _ \epsilon } ) ] > 1 - \epsilon ." ,edb4e656-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\mathbf { F } _ { \Theta R } - \mathbf { F } _ { \Theta \Theta } \mathbf { \Theta } = 0" ,ee62aca4-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"G = \{ h \} + \{ \mathfrak { G } \setminus ( h ) \}" ,ee861730-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"d a _ 2 + a _ 2 ( \omega _ { 2 2 } - 2 \omega _ { 1 1 } ) = 0" ,ee861799-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\int _ 0 ^ { T _ 0 ^ * } ( \frac { \partial f } { \partial \dot { x } } ) ^ * d s < 0 , \text { s i g n } \epsilon . M \prime ( \omega _ 0 ^ * ) < 0" ,ee861829-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { d x } { d \tau } = - D A _ k ^ * ( t ) x" ,ee8618d8-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"4 + 4 + 1 =" ,ee9623e1-224b-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_43.jpg
"\partial f / \partial \delta \prime _ { i n } = ( \sin \delta \prime _ { i n } \sin T \prime _ { i n } \sin \delta \prime _ { k n } + \cos \delta \prime _ { i n } \cos \delta \prime _ { k n } \sin T \prime _ { k n } ) x \prime _ { i k } +" ,ee9e3615-285b-481a-99ac-83e974c34521__mathematical-expression-and-equation_13.jpg
"k _ 6 = 0 , 4 9 5 5 k _ 2 + 0 , 5 8 6 3 k _ z - 0 , 0 8 4 3 I _ { p n } + 0 , 0 0 0 5 W _ { k _ z } - 0 , 1 0 1 4" ,eee5b4ca-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"0 . 0 , 1 . 0 , 2 . 0 , 3 . 0 , 4 . 0 , 5 . 0 m" ,ef0324bc-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
"f ( x ) = \sum _ { n = - \infty } ^ { \infty } a _ n x ^ n" ,ef0324e8-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"B = \{ ( ( [ \alpha _ 1 , A _ 1 ] , [ \alpha _ 2 , A _ 2 ] ) , ( [ \alpha _ 3 , A _ 2 ] , [ \alpha _ 4 , A _ 1 ] ) ) | \alpha _ 1 , \alpha _ 2 , \alpha _ 3 , \alpha _ 4 \in V _ \lambda" ,ef286ef0-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\beta _ v < \beta _ v ^ * \text { f o r } v > 0" ,ef286f20-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"s \in [ 0 , t ]" ,ef286f84-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_15.jpg
"\omega _ p = 2 , 6 1 6 1 / s" ,ef4fc9f8-98e0-4460-9684-bedb6cbf4118__mathematical-expression-and-equation_8.jpg
"d = \frac { \frac { 1 } { 2 } \sqrt { 2 } } { \sqrt { 2 } - 1 } = \frac { 1 } { 2 } \sqrt { 2 } ( \sqrt { 2 } + 1 ) = 1 + \frac { 1 } { 2 } \sqrt { 2 } = 1 . 7 0 7 1 1 \dots" ,ef509743-3a61-488d-8d12-571901ed0946__mathematical-expression-and-equation_0.jpg
"H _ { p _ 0 } \cap \{ H _ p \} _ { p \in \Pi _ 0 } = G" ,ef5610bc-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"| \frac { U ( x ) \phi \prime ( x ) } { U \prime ( x ) } | \le \frac { | U ^ { 2 } ( b _ 3 ) \phi \prime ( b _ 3 ) | } { U ( x ) U \prime ( x ) } + \epsilon" ,ef5612c9-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { S a P } { S e \Pi }" ,efcbbca2-e055-11ea-b978-00155d012102__mathematical-expression-and-equation_2.jpg
"a ( r ) = \text { c o n s t a n t } = a" ,efed1cf3-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_1.jpg
"= ( A _ { \alpha , \beta } - A _ { \gamma , \delta } ) ^ { - 1 } \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { m } ( p ^ { \alpha } ( x _ i , y _ j ) q ^ { \beta - \alpha } ( x _ i , y _ j ) - p ^ { \gamma } ( x _ i , y _ j ) q ^ { \delta - \gamma } ( x _ i , y _ j ) )" ,efed1db0-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_7.jpg
"| \phi | = A ^ m , m > 0" ,efed1de9-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_3.jpg
"W ^ * ( s , \zeta ) = \bigcap _ { n = 1 } ^ \infty W ^ * ( n , s , \zeta )" ,f02b1421-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\mathbf { w } _ { \mathcal { S } } ( \hat { \xi } _ a , \hat { \xi } _ b , \epsilon ) \equiv \mathbf { u } _ { \mathcal { S } } ( \hat { \eta } ( a ) , \hat { \eta } ( b _ 0 ) ) + \tau \int _ { 0 } ^ { 1 } [ \frac { \mathbf { D u } _ { \mathcal { S } } } { \mathbf { D c } _ { \bar { \nu } } } \frac { \partial \sigma } { \partial b } ] _ { \theta } d \theta +" ,f02b155d-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( A ) _ 0 = A _ 0" ,f02b1581-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_15.jpg
"\theta _ n [ \sqrt { m _ 1 m _ 2 } , \sqrt { p _ 1 p _ 2 } ] \le \sqrt { \theta _ n ( m _ 1 , p _ 1 ) \theta _ n ( m _ 2 , p _ 2 ) } ," ,f02b15d2-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"+ \frac { i } { e c } \lim . \sum _ { m = 0 } ^ { n - 1 } \sum _ { \mu = 0 } ^ { n - 1 } ( - 1 ) ^ { m + \mu } \psi _ 1 ( m , \mu ) ." ,f0c405f8-3342-4ac9-b368-b44c8c269544__mathematical-expression-and-equation_6.jpg
"f = a _ 1 x _ 1 ^ 2 + a _ 2 x _ 2 ^ 2 + a _ 3 x _ 3 ^ 2 ," ,f0da2f00-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\tilde { G } _ 2 ^ { ( p ) } = \{ C , g _ i ^ { ( \alpha ) } ( i = m + 1 , \dots , r ; \alpha = 1 , 2 , \dots ) \} / C" ,f0fd3117-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\omega _ { 0 0 } + \omega _ { 3 3 } = - \omega _ { 1 1 } - \omega _ { 2 2 } = 0" ,f0fd31d1-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\frac { t _ 2 + c t _ 1 } { t \prime _ 2 + c \prime t \prime _ 1 } = \frac { t _ 1 + c t _ 2 } { t \prime _ 1 + c \prime t \prime _ 2 } ( = j )" ,f0fd3212-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\mathrm { c l } t _ 1 \ge r + 1 ," ,f0fd327f-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_10.jpg
"u ( x , 0 ) = \phi ( x )" ,f0fd338c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\sin \frac { \alpha } { 2 } \cos ^ 2 \frac { \alpha } { 2 } = \sin 3 0 ^ \circ \cos ^ 2 3 0 ^ \circ" ,f178b9c2-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\Phi ( x y ) = \Phi ( x ) + \Phi ( y )" ,f17fcc65-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"U _ T = \{ a _ 1 , a _ 2 , a _ 3 , a _ 4 \}" ,f17fcc98-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"= \frac { 1 } { g } + ( b - 0 . 0 0 3 6 6 a + c t \prime ) \frac { 1 } { K _ 1 }" ,f18fcbc0-c2a2-4ee4-9e77-d34a8e950173__mathematical-expression-and-equation_7.jpg
"\frac { \Delta ^ 2 u _ { i k } } { h ^ 2 }" ,f1cd530a-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { \Delta q _ { i k } } { h } = \frac { \Delta p _ { i k } } { l }" ,f1cd530c-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x ^ 3 \equiv z" ,f1cd536f-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_8.jpg
"P ( \alpha _ 1 \frac { d y } { d \tau } - \alpha _ 2 \frac { d x } { d \tau } - \alpha _ 0 \frac { d t } { d \tau } ) = 0" ,f1cd5385-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\omega y \prime \prime - \omega \prime y \prime + ( \omega \prime \prime + 2 A \omega ) y = 0" ,f1cd5482-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\tilde { \mathcal { D } } : v ^ * \mapsto \frac { \partial v ^ * } { \partial t } + A v ^ *" ,f247d5c7-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"| \bar { \Phi } ( \lambda , \mu _ { i + 1 } , k , C ) - \bar { \Phi } ( \lambda , \mu _ i , k , C ) | =" ,f247d6c7-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"m = \frac { S _ 0 } { S }" ,f257d1b2-bc37-11e1-1360-001143e3f55c__mathematical-expression-and-equation_3.jpg
"y = x \cdot \frac { q } { Q }" ,f26a8c00-dade-11e2-9439-005056825209__mathematical-expression-and-equation_2.jpg
"[ A _ 1 + ( 4 + h ) ^ { - 1 } ( a _ 0 ^ 0 + a _ 2 ^ 2 - 2 a _ 1 ^ 1 + \frac { \partial \log \beta } { \partial u } ) A _ 0 , A _ 2 +" ,f2a16b7a-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x = \sqrt { - 1 }" ,f2ac0936-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_8.jpg
"( a _ k - u ) ( a _ k - K u ) = a _ k ^ 2 - ( u + K u ) a _ k + u . K u ," ,f2ac0952-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\frac { \partial } { \partial x } ( \Delta H _ 2 ) = - \frac { W } { \mu \sqrt { \pi a t } }" ,f3381f1a-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_3.jpg
"= | \int ^ t \{ [ f ( x ( \sigma , \lambda ) , \dot { x } ( \sigma , \lambda ) , \sigma , \lambda ) - \dot { x } ( \sigma , \lambda ) \Phi _ x ( x ( \sigma , \lambda ) , \sigma , \lambda ) ] ." ,f36e0a8b-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_18.jpg
"i = 1 , 2 , \dots , n - 1 ; k = 0 , 1 , \dots , i" ,f36e0bf2-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_18.jpg
"\times \exp \{ - \frac { 1 } { 2 } \parallel \mathbf { P } ^ { \theta } ( \eta ( \theta ) - \eta ) \parallel ^ { 2 } \}" ,f3dea332-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { d \tilde { x } } { d t } + \tilde { \theta } A \tilde { x } = \tilde { \theta } \tilde { f } , \tilde { x } = x _ 0" ,f3dea403-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_12.jpg
"f ( x ) = [ f ( \frac { x } { 2 } ) ] ^ 2 ," ,f3f06fe1-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_1.jpg
"L _ 1 = L _ 2" ,f3f07089-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_4.jpg
"a _ y = \frac { a } { 1 } + e" ,f415394f-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\frac { f ( x + t _ n h + t _ n g ) - f ( x + t _ n h ) } { t _ n } \in \overline { c o } \{ \frac { \partial ^ * } { \partial g } f ( x + t _ n h + \Theta t _ n g ) : 0 \le \Theta \le 1 \} \rightarrow \frac { \partial ^ * } { \partial g } f ( x )" ,f43f1706-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"d \sigma _ 3 = \frac { 1 } { 2 } \sqrt { \frac { ( \lambda _ 3 - \lambda _ 1 ) ( \lambda _ 3 - \lambda _ 2 ) } { ( a + \lambda _ 3 ) ( b + \lambda _ 3 ) ( c + \lambda _ 3 ) } } d \lambda _ 3 ," ,f466f5f0-9319-11e2-9142-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"T ^ 2 : T \prime { ^ 2 } = \frac { a ^ 3 } { 1 + \frac { m } { M } } : \frac { a \prime { ^ 3 } } { 1 + \frac { m \prime } { M } }" ,f497abc5-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"< \sqrt { ( n ) } d ( 2 \sqrt { ( } d ) ( \omega ^ \alpha [ a ] ) ^ { 1 / 2 } + \bar { K } \prime ( \omega ^ \alpha [ a ] ) ^ { 1 / 4 }" ,f4affccc-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_13.jpg
"h ( n + 1 ) - h ( n ) > \delta" ,f4affce7-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"l a l + \Delta l" ,f4ea6250-40bf-11e4-bdb5-005056825209__mathematical-expression-and-equation_4.jpg
"\int _ 0 ^ 1 ( 1 - \xi ) [ \xi ^ \alpha ( 1 - \xi ) ^ \beta ] d \xi = \frac { 1 } { 4 } \int _ { - 1 } ^ 1 ( 1 + u ) [ ( \frac { 1 - u } { 2 } ) ^ \alpha ( \frac { 1 + u } { 2 } ) ^ \beta ] d u =" ,f4f44fcc-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_4.jpg
"c = \frac { ( 1 5 5 + \sqrt { 1 5 } ) } { 2 4 0 0 }" ,f4f44fce-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_3.jpg
"E . \beta = \frac { 1 } { L } \sum _ { O } ^ { L } x \frac { d s } { E J } - C = A" ,f507c8a0-73f4-11e4-9605-005056825209__mathematical-expression-and-equation_0.jpg
"^ 0 H [ 2 3 ] = [ 2 \prime 3 \prime ] - \frac { 1 } { 2 } ( \gamma \prime _ 1 - \gamma _ 1 ) [ 1 \prime 2 \prime ]" ,f50e74fe-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\Delta = | \begin{array} { c c c c } a & b & c & d \\ c & d & a & b \\ d & c & b & a \\ b & a & d & c \end{array} |" ,f5448f68-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"V = [ \frac { \pi \alpha ^ 2 } { 2 } + \frac { \pi \beta ^ 2 } { 2 } + \frac { \pi v ^ 2 } { 6 } ] v ," ,f5748f5f-3336-11ec-af5b-001b63bd97ba__mathematical-expression-and-equation_4.jpg
"S = \sum _ { i = 1 } ^ { N } a _ i Z _ i" ,f57966dc-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"s ( t ) = e ^ { j ( \omega t + \phi _ k + \phi _ l ) }" ,f57967b3-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\dot { x } ( t ) = A x ( t ) + B u ( t )" ,f5796895-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"A [ \begin{array} { c } y ( t ) \\ s ( t ) \end{array} ] = H s ( t - 1 ) + b u ( t - T _ u ) + k _ x + c e ( t )" ,f57968e3-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"A = D _ 1 ( 0 , 0 ) = 0" ,f5e12dd6-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_7.jpg
"H A _ 2 = \pi _ { 2 2 } A \prime _ 2" ,f5e12eb6-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\delta ( \{ n ; \frac { \epsilon _ n ( t _ 0 ) } { q _ n } < \alpha \} ) = \alpha" ,f5e12ec8-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"+ K \int _ 0 ^ t \parallel x ^ { ( 1 ) } ( \tau ) - x ^ { ( 2 ) } ( \tau ) - y ^ { ( 1 ) } ( \tau ) + y ^ { ( 2 ) } ( \tau ) \parallel _ q d \tau +" ,f5e12fcd-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\psi ( \delta , \alpha ( d ) , \epsilon ) \le \psi _ 1 ( \delta , \epsilon ) \psi _ 2 ( d , \epsilon )" ,f5e12fd0-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"= \frac { 1 } { 2 c d } [ c ^ 2 + d ^ 2 - \frac { ( a c - b d ) ( b c - a d ) } { a b - c d } ]" ,f5f2f724-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"v = \frac { d s ( t ) } { d t } = v ( t )" ,f6462d16-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg
"P _ { \eta | \xi } [ D ( \xi , \delta _ 1 , \delta _ 2 ) ] \ge p ( \delta _ 1 , \delta _ 2 )" ,f6462e73-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"c ( k ) = \sigma ^ 2 \delta _ { 0 , k } + \sigma _ V ^ 2 \sum _ { j = 0 } ^ { p } \phi _ j \phi _ { j + k }" ,f6462ec6-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x ^ { ( h + k ) } ( t _ 0 ) \in T _ h ( t _ 0 )" ,f6c2b4a6-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_0.jpg
"D _ b = \frac { 1 } { L } \sum _ { 0 } ^ { L } M ^ { \circ } x \frac { d s } { J } = \frac { 1 } { 1 2 } \cdot 2 2 7 4 1 . 5 5 = 1 8 9 5 . 1 3" ,f6e89690-73f4-11e4-9605-005056825209__mathematical-expression-and-equation_3.jpg
"= \sum _ { u , v } \sum _ { x , y } T _ { h _ 1 } \delta ( u , v ) \overline { T _ { h _ 2 } \delta ( x , y ) } S ( u + x , v - y ) =" ,f7122f19-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg
"E [ \hat { D } _ { M N } ( \omega ) ] = D _ { M N } ( \omega ) + c _ 1 | s _ 1 | ^ 2 + c _ 2 | s _ 2 | ^ 2 - \frac { 2 } { L } c +" ,f7122fd8-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg
"| l _ { p + 1 } - 2 l _ p | \le 1" ,f7123089-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_20.jpg
"M _ { a , a \prime } + M _ { a \prime , a } + M _ { b , b \prime } + M _ { b \prime , b } = - V \cdot h = - 1 7 . 2 8" ,f71aa310-73f4-11e4-9605-005056825209__mathematical-expression-and-equation_10.jpg
"n _ 2 = n _ 1 - \frac { s \cdot n _ 1 } { 1 0 0 } = n _ 1 ( 1 - \frac { s } { 1 0 0 } ) = \frac { 6 0 \cdot f _ 1 } { p } ( 1 - \frac { s } { 1 0 0 } ) ." ,f723be10-c41c-11e3-93a3-005056825209__mathematical-expression-and-equation_4.jpg
"\sqrt { 3 } = 3 [ 1 - \frac { 1 \cdot 3 } { 3 \cdot 2 4 } + \frac { 1 \cdot 4 \cdot 3 ^ 2 } { 3 \cdot 6 \cdot 2 4 ^ 2 } - \frac { 1 . 4 \cdot 7 \cdot 3 ^ 3 } { 3 \cdot 6 \cdot 9 \cdot 2 4 ^ 3 } + \dots ]" ,f72a2550-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_10.jpg
"2 G m = 2 A j v + 4 C w + 2 B t" ,f74b23ce-1510-4a73-894e-e49f37100738__mathematical-expression-and-equation_19.jpg
"S = \frac { C w ^ 2 L } { 2 g ( H + \frac { S } { 2 } ) } + C = \frac { N C w ^ 2 L } { 2 g ( H + \frac { S } { 2 } ) }" ,f78ab005-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"[ \Theta ^ 0 ( z ) ] _ { z = 0 }" ,f78ab12c-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_13.jpg
"f ( x ) : F ( x )" ,f79a2530-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg
"\sum _ { 2 ^ { m _ j + n _ j } \le \sqrt { x } }" ,f7a46146-570a-11e1-1090-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\frac { p } { \sigma } = \frac { p _ 0 } { \sigma _ 0 } ( 1 + \gamma t ) ," ,f80861f0-dade-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg
"z = \frac { 1 } { r } \cdot z \prime + p ." ,f815af95-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\sin ( \alpha + 2 \phi ) - 2 \cos \phi \sin ( \alpha + \phi ) = - \sin \phi ." ,f815afac-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"0 < \zeta < \zeta _ 1" ,f85fb3c5-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"C H _ 4 + C l _ 2 = H C l + C H _ 3 C l" ,f8642c93-eef3-4a5b-8629-e0ce2f34f511__mathematical-expression-and-equation_7.jpg
"\nabla \tilde { \beta } _ { i s } = g _ { i } \nabla \beta _ { i s }" ,f87a010f-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_22.jpg
"W ^ V \in \Delta ( \rho _ { U V } ( a ) ; \tau _ V ) \}" ,f87a0287-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\text { V a l } _ x ( w _ { ( i ) } ) = \{ \begin{array} { c c } A _ { \text { L } } ( A _ { i } ) & \text { i f } P _ { i } = \text { L A } ( \text { i . e . } A _ { i } \text { i s a l o g i c a l a x i o m } ) \\ \text { X } ( A _ { i } ) & \text { i f } P _ { i } = \text { S A } ( \text { i . e . } A _ { i } \text { i s a s p e c i a l a x i o m } ) \\ r _ { i } ^ { \text { s e m } } ( \text { V a l } _ { x } ( w _ { ( i _ { 1 } ) } ) , \dots , \text { V a l } _ { x } ( w _ { ( i _ { n } ) } ) ) & \text { i f } A _ { i } = r _ { i } ^ { \text { s y n } } ( A _ { ( i _ { 1 } ) } , \dots , A _ { ( i _ { n } ) } ) \end{array}" ,f8a68add-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"| Q _ x ( \tau ) | \le \sum _ { k = 1 } ^ { \tau } | x ^ { * k } ( \tau ) | \le \sum _ { k = 1 } ^ { \tau } \parallel x ^ { * k } \parallel \le \sum _ { k = 1 } ^ { \tau } \parallel x \parallel ^ k , h e n c e" ,f8a68aee-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"H _ y ^ 2 = 1" ,f8a68b20-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"f \prime \prime \prime _ { x ^ 3 } ( x , y ) , f \prime \prime \prime _ { x ^ 2 y } ( x , y ) , f \prime \prime \prime _ { x y ^ 2 } ( x , y ) , f \prime \prime \prime _ { y ^ 3 } ( x , y )" ,f8b0fbc0-5a87-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_4.jpg
"\overline { P K } = \frac { 2 b _ 1 ^ 2 } { a }" ,f93938b6-b55a-4975-8c08-2402b73a6975__mathematical-expression-and-equation_7.jpg
"+ \Omega _ { v + 1 } ^ v ( \phi _ v ^ { s 1 } \phi _ 2 ^ { \beta ( v + 1 ) } - \phi _ v ^ { s ( v + 1 ) } \phi _ 2 ^ { \beta 1 } ) + \dots + \Omega _ m ^ v ( \phi _ v ^ { s 1 } \phi _ 2 ^ { \beta m } - \phi _ v ^ { s m } \phi _ 2 ^ { \beta 1 } )" ,f956305e-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_13.jpg
"[ x , y ] \in E ( X )" ,f95631ae-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { d \zeta } { d z } = - \alpha _ 1 z ^ { - 2 } - 2 \alpha _ 2 z ^ { - 3 } - 3 \alpha _ 3 z ^ { - 4 } - \dots" ,f98cc0b2-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_12.jpg
"v _ 1 = \frac { 1 } { 2 } \sqrt { ( - B ) }" ,fa312749-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_21.jpg
"s u p _ { y \in \mathcal { R } } | g \prime ( y ) | < K _ 5" ,fa42fd0c-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\int _ { - \infty } ^ { T } e ^ { \lambda t } [ ( \dot { X } _ t - f X _ t - b ( \alpha ) - U _ t ) \prime \ell ( \dot { X } _ t - f X _ t - b ( \alpha ) - U _ t ) - \dot { X } _ t \prime \ell \dot { X } _ t ] d t ," ,fa42fd55-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { d ^ 2 y } { d x ^ 2 } = 0" ,fa50d3bd-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"a = \mathcal { R } ( T _ \alpha ) = P ( \xi > T _ \alpha )" ,fa57bd3c-0b6f-4b78-a823-a252adc3d6ad__mathematical-expression-and-equation_4.jpg
"B D ( t ) = B A ( t - d )" ,faca76b0-797a-4001-86ce-bf97c9f0fbc8__mathematical-expression-and-equation_0.jpg
"f _ \mu ( x + 1 ) = f _ \mu ( x ) + 1" ,fb0eb512-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_0.jpg
"v _ 1 \phi + \alpha \delta A _ 3 + \alpha \phi B _ 3 = \phi b _ 3" ,fb0eb534-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\tau = \Omega _ F ( \sigma )" ,fb0eb54d-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_12.jpg
"M _ r ( f ) = \{ x \in \mathcal { O } | f ( x ) = r \}" ,fb0eb762-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_3.jpg
"s ^ 2 + \lambda s + K A _ 0 = 0" ,fb0f9cd6-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_10.jpg
"n _ 7 \prime = n _ 8 \prime = 2 m + 4 \mu + 2 \epsilon - 4" ,fb4e6c6b-50bc-11e1-1457-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\psi _ { 1 2 } = s _ { 3 4 } \cos \beta _ { 1 2 } , \psi _ { 2 1 } = s _ { 3 4 } \cos \beta _ { 2 1 } , \dots" ,fb4e6d4f-50bc-11e1-1457-001143e3f55c__mathematical-expression-and-equation_4.jpg
"K _ c = \frac { c } { a b }" ,fbdd185e-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p = u + 2 F \prime ( 2 v - \alpha ) ," ,fbdd18f4-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_24.jpg
"\sigma \prime _ a = \frac { c \sin \beta } { \sin \frac { \gamma - \beta } { 2 } }" ,fbdd19a2-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ 2 = - k v _ 2 \omega _ 0 \mathrm { s n } ( \omega _ 0 \lambda t )" ,fbe38f33-ac0a-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"j = 1 , 2 , \dots , \mu" ,fbe38f9a-ac0a-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\prime ( t ) = - \int _ { t + r } ^ { a + r } y \prime ( s ) B ( s ) d s + \int _ { a } ^ { b } y \prime ( s ) ( G ( s , t ) - G ( s , a ) ) d s + \Bmatrix \gamma \prime , & t < a \\ 0 , & t = a \Bmatrix -" ,fbe6ec81-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\int _ { - r } ^ 0 [ d _ \theta P ( t , \theta ) ] x ( t + \theta ) = \int _ { t - r } ^ t [ d _ s P ( t , s - t ) ] x ( s ) =" ,fbe6ec89-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"T f ( x , t ) = \frac { 2 } { \sqrt { \pi } } k ( G ( \alpha _ { x , t } ( t ) ) - G ( \alpha _ { x , t } ( a ) ) ) + T f _ 1 ( x , t )" ,fbe6ecbf-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"G ( x , x ) = + \infty" ,fbe6ed9b-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg
"d \omega _ 3 ^ 4 = - \omega _ 1 ^ 3 \wedge \omega _ 1 ^ 4 - \omega _ 2 ^ 3 \wedge \omega _ 2 ^ 4" ,fbe6ee46-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_14.jpg
"H = - \frac { 1 } { 2 } E" ,fbe6ef09-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\pi _ 9 = \frac { g \eta } { \Delta p U }" ,fca96b41-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\pi _ i = p _ i \{ 1 - \frac { 1 } { 2 } ( 1 - p _ i ) [ ( 1 - 2 p _ i ) v _ i \prime D ^ { - 1 } v _ i" ,fcbefa58-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\mathcal { A } ^ T = \{ f _ \alpha \circ T \} _ { \alpha \in I }" ,fcc40737-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x \cup y = g _ 2 ^ * ( x , y )" ,fcc40740-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"s = \frac { 3 P 3 } { 2 }" ,fce611ae-995b-11e8-a805-00155d012102__mathematical-expression-and-equation_0.jpg
"+ r + A \prime \log \rho \prime + A \prime \prime \log \rho \prime \prime + \dots + A ^ { ( k ) } \log \rho ^ { ( k ) } ," ,fd6681d4-ba24-4f22-b1a3-3f125a7dd4da__mathematical-expression-and-equation_3.jpg
"1 - \gamma ^ 2 = 0" ,fd79b087-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( x ) = 8 x ^ 3 + 1 0 x" ,fd79b1a1-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_12.jpg
"+ d _ { \rho + 1 } b _ { \rho + 1 } ( x + 1 ) R _ { \rho } ( x ) + d ^ { 2 } _ { \rho + 1 } A _ { \rho + 1 } ( x ) ," ,fd79b21a-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\lim _ { i \rightarrow \infty } \frac { \parallel x _ { i + 1 } - x ^ * \parallel } { \parallel x _ i - x ^ * \parallel } = 0" ,fd92ecd5-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"Q \sum _ { i = 1 } ^ { n } \frac { \partial ^ 2 u } { \partial x _ i ^ 2 } = \sum _ { i } \frac { \partial } { \partial y _ i } [ Q h _ i ^ 2 \frac { \partial v } { \partial y _ i } ]" ,fdacec60-5a87-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"+ \Delta c . \log g . \frac { c ^ { x - 1 } } { D _ x } . \sum _ { n = 1 } n . c ^ n . D _ { x + n } - \Delta c . \log g . x . c ^ { x - 1 } . a" ,fe4823de-40e3-11e1-1278-001143e3f55c__mathematical-expression-and-equation_14.jpg
"r ( 1 + \frac { \sqrt { 3 } } { 3 } )" ,fe4824f5-40e3-11e1-1278-001143e3f55c__mathematical-expression-and-equation_1.jpg
"c _ { 0 } = 0 . 5 7 7 2 1 5 6 6" ,fe4825c5-40e3-11e1-1278-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\sigma ( z + \omega _ 1 ) = \frac { 2 \omega _ 1 } { \pi } e ^ 2 \eta _ 1 \omega _ 1 v ^ 2 + 2 \eta _ 1 z + \frac { \eta _ 1 \omega _ 1 } { 2 }" ,fe6878ac-de12-4723-9046-431aedd617e9__mathematical-expression-and-equation_6.jpg
"\delta ^ 0 = \operatorname { a r g m i n } J ( \delta ) , J ( \delta ) = \operatorname { t r } E [ ( \delta ( \xi - \bar { \xi } ) + \bar { x } - x ) ( \delta ( \xi - \bar { \xi } ) + \bar { x } - x ) ^ T ]" ,fe69c48f-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\Lambda = [ \begin{array} { c c } 0 . 0 1 & 0 . 0 \\ 0 . 0 & 0 . 0 1 \end{array} ]" ,fe69c4a5-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"[ G \prime : G ] \le n" ,fe781f11-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_1.jpg
"H _ \epsilon ( A ) = \frac { L ( b - a ) } { \epsilon } - \frac { 1 } { 2 } \sum _ { i = 1 } ^ { N - 1 } \mathrm { l d } ( 1 + \frac { x _ { i + 1 } - x _ i } { 2 \epsilon } ) + O ( N )" ,fe781fb1-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_6.jpg
"+ \rho ( A + 2 d ) f ( A + 2 d ) + \dots + \rho ( B ) f ( B )" ,ff09781d-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { \partial C _ 1 } { \partial x } ( \infty , T ) = 0" ,ff35956f-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"g _ n ( \theta ( t ) ) \le ( 1 - r t ) g _ n ( \theta _ 0 ) + r t g _ n ( \theta _ n ) = r t g _ n ( \theta _ n ) ." ,ff49c3a2-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_6.jpg
"R ( g \prime \theta , \widehat { g \prime \theta } ) = E [ ( \widehat { g \prime \theta } - g \prime \theta ) ^ 2 ] = g \prime L \Sigma _ 0 L \prime g + ( g \prime ( I - L Q _ 0 ) \theta - g \prime I ) ^ 2" ,ff49c4c2-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"[ V _ 1 , V _ 2 ] = - \frac { 2 } { r } V _ 3" ,ff505744-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_8.jpg
"g \prime ( c ) \in f ^ { - 1 } ( f ^ { l + 1 } ( a ) ) = f ^ { - 1 } ( g ^ { l + 1 } ( a ) )" ,ff5057cf-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"y _ k = \frac { y _ 1 + y _ 2 } { 2 } = \frac { \epsilon N _ 2 \pm a } { p }" ,ff7a5240-1fac-11e4-a8ab-001018b5eb5c__mathematical-expression-and-equation_0.jpg
"r = \frac { a b } { d } \sqrt { 2 }" ,ffa9617c-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"y _ i = 1 )" ,ffa96386-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_16.jpg
"\bar { Q } ^ m = \sum _ { s = 1 } ^ m \chi Q _ s ( ( s - 1 ) h , s h )" ,ffd11d82-bb01-4848-afda-1845049e7150__mathematical-expression-and-equation_1.jpg
"P = V ( f . X + H ) + 0 , 0 2 . v ^ 2 . X" ,uuid:00d7e0e0-27d3-11e7-a38c-005056827e51__mathematical-expression-and-equation_7.jpg
"( \rho + \frac { 1 } { 2 } s ) \sin \gamma" ,uuid:268ef900-0d35-11e5-b309-005056825209__mathematical-expression-and-equation_13.jpg
"d _ 4 = | \begin{array} { c c c } a _ { 0 } & a _ { 1 } & 0 \\ b _ { 1 } & b _ { 2 } & a _ { 1 } \\ b _ { 0 } & b _ { 1 } & a _ { 0 } \end{array} | = 0" ,uuid:4c710b57-6a62-4be8-9a77-8f6e5cd06e84__mathematical-expression-and-equation_1.jpg
"3 ( H _ { 2 2 } C _ { 1 2 } O _ { 1 1 } C a O ) = C _ { 1 2 } H _ { 2 2 } O _ { 1 1 } \cdot 3 C a O + 2 C _ { 1 2 } H _ { 2 2 } O _ { 1 1 }" ,uuid:d3013a40-5281-11e5-b7d6-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"| A + C R B | = | A \prime + C \prime R \prime B \prime |" ,0024ba4b-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_4.jpg
"= - \tilde { B } Y - \tilde { A } _ { 1 } X + ( \tilde { B } A - \tilde { A } _ { 1 } B ) X _ { 1 } Y" ,0024ba4d-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_10.jpg
"| | \widehat { \underline { P } } _ { n } - \widehat { \underline { P } } | | _ { \mathcal { H } } ^ { \infty } < \delta" ,0024bb73-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_0.jpg
"| \mu _ { 6 } - \mu _ { \text { o p t } } | \le 2 \epsilon" ,0024bb7d-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_2.jpg
"f ^ { l o w } \le g \le f ^ { u p }" ,00283fac-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_5.jpg
"U = R _ { 1 } M _ { 1 } + R _ { 2 } M _ { 2 } ." ,00611914-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"y = z ( s ) + t \cdot e _ { 3 } ( s )" ,00ff8e9b-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\bar { \alpha } _ { n } ( X ) \equiv \alpha ( X ) \& \exists ( X _ { 1 } , \dots , X _ { n } ) ^ { \neq } ( \phi _ { 3 } ( X , X _ { 1 } ) \& \dots \& \phi _ { 3 } ( X , X _ { n } ) ) )" ,00ff8f1f-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { d } { d t } ( \gamma \sigma _ { 1 } ( \Delta ^ { N } , \Delta ^ { N } ) + \gamma | \Delta _ { t } ^ { N } | ^ { 2 } + 2 \langle \Delta ^ { N } , \Delta _ { t } ^ { N } \rangle )" ,0101fa74-ac0b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_8.jpg
"v ( K \cup L ) \le v ( K ) + v ( L )" ,0101fb09-ac0b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\lim _ { n \rightarrow \infty } M _ { n , T _ { L } } = \chi _ { 0 } ," ,0101fb76-ac0b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"u = \frac { \omega } { ( \beta - \alpha ) ^ { 4 } } \{ \frac { 4 ( \beta ^ { 3 } - \alpha ^ { 3 } ) } { 1 + q } ( \beta ^ { q + 1 } - \alpha ^ { q + 1 } ) - \frac { 6 ( \beta ^ { 2 } - \alpha ^ { 2 } ) } { 2 + q } ( \beta ^ { q + 2 } - \alpha ^ { q + 2 } ) \}" ,0101fb7e-ac0b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"C _ { 0 } = 1 = C _ { 1 } = C _ { 2 } , C _ { 3 } = 2 , C _ { 4 } = 4 , C _ { 5 } = 1 4 , C _ { 6 } = 3 8" ,0199724d-40e4-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\phi \equiv \frac { A ^ { 2 } } { a ^ { 2 } } + \frac { B ^ { 2 } } { b ^ { 2 } } - 1 = 0" ,01d6d7a0-95d4-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_4.jpg
"A _ { b } = [ \begin{array} { c } 0 _ { ( n - 1 ) \times 1 } \\ 0 \end{array} ]" ,01d7e967-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_15.jpg
"Y ( K ) = Y ^ { [ 0 ] } ( K ) = y ^ { [ 0 ] } ( k ) = y ( k ) ," ,01d92506-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"k = \lim f _ { n } ( a )" ,01d9265a-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_12.jpg
"( \pi _ { 2 } + \frac { 3 } { 1 - 2 \epsilon _ { 2 } } ) . ( 2 - 3 \epsilon _ { 2 } )" ,022d9b60-40e4-11e1-1331-001143e3f55c__mathematical-expression-and-equation_11.jpg
"A ( u v ) = \frac { b _ { 1 } } { u ( u + 1 ) } - \frac { b _ { 2 } } { u ( u + 1 ) ( u + 2 ) } + \dots" ,022d9b7a-40e4-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
"T _ { i } 3 = \bar { D } _ { i } Z _ { i 2 1 }" ,02b32d38-ac0b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg
"C ( s ) = [ I - F ( s I - A ) ^ { - 1 } B ] ^ { - 1 } G" ,02b32e96-ac0b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_1.jpg
"B ( \tau ) = \int _ { \Omega } G ^ { 2 } d \xi \le c \int _ { \Omega } | D _ { \xi } G | ^ { 2 } d \xi" ,02b469c6-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x b x ^ { = } = a" ,02b46a23-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_2.jpg
"( T ^ { * } ) ^ { * } = T" ,02b46aa6-570b-11e1-4758-001143e3f55c__mathematical-expression-and-equation_0.jpg
"n < 1" ,02c23a5d-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"V = - \frac { A _ { 0 2 k + \nu } } { A _ { 1 k } }" ,03752bd0-9944-11de-8a2c-0030487be43a__mathematical-expression-and-equation_0.jpg
"( W u ) ( y ) = \int _ { 0 } ^ { b } T ( b - s ) B u ( s , y ) d s" ,03904764-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\parallel U ( t ) - W ( t ) \parallel _ { X } \le [ \int _ { \tau } ^ { t } k _ { 2 } ^ { a } ( t - \sigma ) d \sigma ] ^ { 1 / a }" ,03921f86-570b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"N ( \alpha p _ { \mu n } ^ { 2 } + \beta p _ { \nu n } ^ { 2 } + \gamma p _ { s n } ^ { 2 } ) = I ," ,03e825c7-7112-44fb-8991-e633ccd2a1eb__mathematical-expression-and-equation_2.jpg
"| F _ { i } ( u _ { n } ) ( t , x ) - F _ { i } ( u ) ( t , x ) | ^ { 2 } \le 3 ( 4 p _ { i } ^ { 2 } ( v r _ { 0 } ) ) | g _ { i } ( t , x ) | ^ { 2 } +" ,046d3d65-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_6.jpg
"= - \frac { X _ { i } } { f _ { a } ^ { + } ( \mathbf { x } ) } { } ^ { b } \mathbf { X } ^ { ( n + 1 ) } \mathbf { W } \mathbf { Q } ^ { ( a ) } \mathbf { e } ^ { ( a ) \prime } \ge 0" ,046d3e3d-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"S = k o n s t . + \int \frac { d r } { r - a } \cdot \frac { a ^ { 2 } r ^ { 2 } - b ^ { 2 } ( 1 - \frac { a } { r } ) - N } { \sqrt { N } }" ,04a8116c-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\frac { 1 } { n ^ { 2 } y } \cot ( \theta - 1 ) y = \frac { 1 } { 2 }" ,04a8122b-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"v _ { 0 } f _ { 0 } + v _ { 1 } f _ { 1 } + \dots + v _ { h } f _ { h } + \dots + v _ { d _ { 1 } } f _ { d _ { 1 } } +" ,054798a2-570b-11e1-2069-001143e3f55c__mathematical-expression-and-equation_5.jpg
"x . y ( x . z y ) \bumpeq z" ,05479936-570b-11e1-2069-001143e3f55c__mathematical-expression-and-equation_18.jpg
"r \in ( 0 , 1 ]" ,0547995a-570b-11e1-2069-001143e3f55c__mathematical-expression-and-equation_14.jpg
"\frac { 2 } { p _ { j } \sqrt { ( \frac { 1 } { p _ { j } } + \frac { 1 } { p _ { j 2 } } ) ( \frac { 1 } { p _ { j } } + \frac { 1 } { p _ { j 4 } } ) } }" ,0549b8a4-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg
"U S _ { f } / u _ { * c r }" ,05559234-bc38-11e1-1154-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\Delta = \pm \sqrt { \frac { D } { 4 a ^ { 2 } } }" ,05e42ec0-860b-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"A B _ { x } = + p _ { x } = a O + O b = - x _ { 1 } + x _ { 2 } = x _ { 2 } - x _ { 1 }" ,05fbf5b0-3a1a-11e9-9fd6-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"\Delta _ { 0 } X _ { ( p ) } , \Delta _ { 0 } Y _ { ( p ) } , \Delta _ { 0 } X _ { ( p - 2 ) } , \Delta _ { 0 } Y _ { ( p - 2 ) } , \Delta _ { 0 } Z _ { ( p - 2 ) } , \dots" ,0620b97c-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_9.jpg
"i f ( | S - s | , 0 ) \in \mathcal { L } ." ,0620bacb-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\lim _ { | a | \rightarrow 1 } A [ \log | f - f ( a ) | , D ( a , \rho ) ] = - \infty" ,0620baf8-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\lim _ { R \rightarrow 1 } \Phi ( R ) = 1 - \epsilon \le \Phi ( R ) \le 1" ,0620bafa-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\cos H + \cos D = \sin S" ,06a30627-bf88-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\lambda _ { m l } = \frac { 1 } { q ( t ^ { m } ) } \Psi _ { t m }" ,06fb132f-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\sum ( k ^ { 2 } - j ^ { 2 } T ^ { 2 } ) a _ { k j } ( v _ { n } ) a _ { k j } ( w ) + \int _ { Q } g ( \cdot , v _ { n } ) w = 0" ,06fb1359-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_12.jpg
"Q \prime _ { 0 } + A ^ { T } Q _ { 0 } + Q _ { 0 } A + Q _ { 0 } B _ { 0 } Q _ { 0 } - C _ { 0 } = 0" ,06fb1476-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\wedge \omega ^ { 1 } + ( d c - d a + 4 b \omega _ { 1 } ^ { 2 } ) \wedge \omega ^ { 2 } \} = 0" ,06fb14f2-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_18.jpg
"L x = ( 1 - \lambda ) G x + \lambda F x" ,06fb1546-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_11.jpg
"l _ { p , \infty } ( \lambda _ { k } ( S ) ) \le c _ { p } l _ { p , \infty } ( x _ { k } ( S ) )" ,06fb1580-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathcal { S } = ( \{ S _ { \lambda } | \lambda \in \Lambda \}" ,06fb15d1-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { d ^ { 2 } J } { d z ^ { 2 } } - z \frac { d J } { d z } + n J = \int _ { ( C ) } \frac { d } { d t } ( e ^ { z t - \frac { 1 } { 2 } t ^ { 2 } } t ^ { - n } ) d t" ,07017acc-f13a-4cd2-af43-817a1aa68b18__mathematical-expression-and-equation_4.jpg
"\Sigma \Delta x _ { k } y _ { k + 1 } = 0 \dots ( 1 1 B )" ,07a5fc30-3a1a-11e9-9fd6-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"W - W _ { n } \subset \bigcup \{ T _ { i } : i = 1 , 2 , \dots , n \}" ,07df0b7e-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg
"= \{ \frac { 1 } { 2 } a _ { 3 } ( b _ { 1 } - b _ { 5 } ) - a _ { 2 } ( b _ { 2 } + b _ { 4 } ) \} \omega ^ { 1 } \wedge \omega ^ { 2 } ," ,07df0ba5-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\bar { i } = \frac { 1 } { N } \sum _ { j = 1 } ^ { l } n _ { j } \cdot i _ { j } = 6 . 1 8 6 2 : 5 0 4 = 0 . 0 1 2 2 7 \text { c u . m . }" ,084f8da0-af2a-11ea-998c-005056827e51__mathematical-expression-and-equation_3.jpg
"f ( t ) \le v _ { m + 1 } - m ^ { 2 }" ,08bd5cc4-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x _ { 1 } ( x ) = \dots = x _ { m } ( x ) = 0" ,08bd5f3a-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"F = \frac { c } { v } ( \frac { \omega _ { s 1 } } { \omega _ { s 2 } } - 1 ) = \frac { \mathbf { v } ( \mathbf { a } _ { i 2 } - \mathbf { a } _ { i 1 } ) } { 1 - \mathbf { v } \mathbf { a } _ { i 2 } / c }" ,0919a495-1978-4a9f-b98c-e9298e7d45b3__mathematical-expression-and-equation_0.jpg
"C _ { i } ^ { ( r ) } = \sum _ { j = 1 } ^ { r - i + 1 } \frac { ( i + j - 1 ) ! } { ( j - 1 ) ! } q _ { ( j ) } ^ { \sigma } \frac { \partial } { \partial q _ { ( i + j - 1 ) } ^ { \sigma } }" ,099bb16b-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\stackrel { * } { F } \stackrel { * } { G } = \int _ { \xi } ^ { x } F ( x , z ) G ( z , \xi ) d z" ,099cff1c-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"z = 0 . 0 0 3 2 m ." ,09eaa680-ef95-11ea-be7b-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"K = ( R ^ { 2 } + r ^ { 2 } + R r ) \frac { \pi v } { 3 }" ,09fb27e9-a8de-42cf-8af7-288ddbe0b054__mathematical-expression-and-equation_1.jpg
"V = \frac { 4 , 1 2 5 z } { \frac { x z } { 3 6 6 , 5 } } = \frac { 3 7 8 } { x }" ,0a028a68-6c45-11e5-a4fc-001b21d0d3a4__mathematical-expression-and-equation_0.jpg
"\frac { 1 } { 1 + z } + \frac { 1 } { 1 - z } - \frac { 1 } { 1 + \frac { 4 } { 5 } z } ." ,0a742368-40e4-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\epsilon = i n f \{ \parallel \frac { x } { \parallel x \parallel _ { 2 } } - \frac { y } { \parallel y \parallel _ { 2 } } \parallel _ { 2 } ; y \in \mathrm { o p t } ( A , \nu ) \}" ,0a7a7615-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\mathbf { v } ( P \cup Q ) \supset \mathbf { v } ( P )" ,0ac3ff93-5333-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { q } { q } = \frac { r - \rho } { \sigma } - \frac { \xi } { \gamma ^ { 2 } } r + q" ,0af10245-27b0-42cb-ac62-8b9be0a61404__mathematical-expression-and-equation_3.jpg
"t = \frac { k _ { t } - k _ { o } } { k _ { o } i }" ,0be6f011-c6ef-11ec-bd89-005056a54372__mathematical-expression-and-equation_2.jpg
"\Delta I _ { 0 } = \frac { 1 } { 2 } ( \Delta I _ { - 1 / 2 } + \Delta I _ { 1 / 2 } ) = + 0 . 0 0 7 5 1 0 6 5 4 6 1 | \underline { 5 }" ,0beac03a-c6ef-11ec-bd89-005056a54372__mathematical-expression-and-equation_7.jpg
"i _ { a } = A _ { 1 } e _ { g } + A _ { 2 } e _ { g } ^ { 2 } + A _ { 3 } e _ { g } ^ { 3 } + A _ { 4 } e _ { g } ^ { 4 } + A _ { 5 } e _ { g } ^ { 5 } + \dots ," ,0c1f148f-40e4-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"= \frac { d } { d s } [ y ( s ) + p y ( s - \tau _ { 0 } ) ] \frac { d s } { d t } + Q ( t ) ( \sum _ { i = 1 } ^ { n } a _ { i } y ( s - \tau _ { i } ) )" ,0c39da2c-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { \delta } { P } = \delta \frac { 1 } { P _ { k } } + \frac { e \pi ^ { 2 } } { 8 } \cdot \frac { 1 } { P _ { k } }" ,0c708e55-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"L \frac { d i } { d t } + \frac { 1 } { C } \int i d \tau = u ( t )" ,0c708fc8-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lim _ { n = \infty } \frac { a _ { n } } { b _ { n } } = 0" ,0ce39c7d-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"< - \frac { 1 } { 8 } \epsilon < - 2 \gamma \phi ( h _ { 0 } ) < h \prime \prime \gamma \frac { \phi ( h _ { 0 } ) } { h _ { 0 } }" ,0ce39d09-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"r = \frac { 2 a \cos \phi } { 1 - \alpha \sin \phi } ." ,0ce39e02-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d = \frac { m \lambda } { 2 \sin \phi _ { m } } ." ,0ce39e0f-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"g _ { 7 } = ( S _ { F } ^ { 0 } ) _ { x \ell } u _ { x } + ( S _ { T } ^ { 0 } ) _ { x \ell } \theta" ,0d1d827d-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_6.jpg
"W = \{ u \in C | u = u ^ { \lambda , \sigma }" ,0d1d82b4-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg
"r \in \mathbb { R }" ,0d1d835d-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_6.jpg
"x _ { 1 } = x _ { 2 } = 0 \}" ,0d1d849f-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\mathbf { K } = \frac { d ^ { 2 } \mathbf { r } } { d s ^ { 2 } } = \frac { 1 } { n } [ \nabla n - \mathbf { s } ( \mathbf { s } . \nabla n ) ]" ,0d8d2469-38c1-4b27-809f-d089b89e7a34__mathematical-expression-and-equation_3.jpg
"\overline { S S _ { 1 } } \cdot \frac { w } { c ^ { 2 } } \cos \phi ." ,0d993134-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"e \prime < \frac { 1 } { 2 }" ,0d9931c1-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\Theta _ { 1 } - \eta _ { 1 } ) + \lambda _ { i } ( \Theta _ { i } - \eta _ { i } ) = 0" ,0d9931fc-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- \frac { 2 } { n } \sum _ { k = 1 } ^ { n - 1 } ( - 1 ) ^ { k + 1 } \sum _ { l = 1 } ^ { m } \frac { r ( \bar { p } _ { l } ^ { k } ) } { r \prime ( \bar { p } _ { l } ^ { k } ) - s \prime ( \bar { p } _ { l } ^ { k } ) \bar { z } _ { k } } c ^ { \bar { p } _ { l } ^ { k } }" ,0e027943-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\pi - \pi \prime = 3 5 8 1 . 3 2 \prime \prime \log \mathcal { D } = 4 . 9 6 1 5 9" ,0e1ee3a4-b78b-4a54-9199-55c62fe723fa__mathematical-expression-and-equation_5.jpg
"r \neq 1" ,0e46611e-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_5.jpg
"r n + r \cos v = 0" ,0e975e30-404d-11e7-a7ae-001018b5eb5c__mathematical-expression-and-equation_8.jpg
"I = \{ t _ { 1 } , t _ { 2 } , \dots , t _ { n } \}" ,0ecd6a0a-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"P _ { n , k } = ( - 1 ) ^ { n } ( \frac { 1 } { 4 } ) ^ { k } \frac { 1 } { p _ { k - n } p _ { k + n } }" ,0ee333a6-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_5.jpg
"V ^ { \mathcal { B V } } _ { \eta , \delta } ( F \circ \Phi ) _ { A } ( E ) \le V ^ { \mathcal { B V } } _ { \eta ^ { \bullet } , \delta ^ { \bullet } } F _ { A ^ { \bullet } } ( E ^ { \bullet } )" ,0ee4afe3-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"C _ { 2 } ( N , p ) ( \int _ { 0 } ^ { \infty } t ^ { 2 p - 1 } F ( t , k ) d t ) ^ { \frac { 1 } { p - 1 } } \le \frac { 1 } { 2 } k \text { f o r a l l } k \in I ." ,0ee4b0bb-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\omega _ { 2 \psi } = \frac { R _ { R } } { \psi _ { R x } } ( i _ { S y F } - \Gamma _ { F } \psi _ { R x } ) = \frac { R _ { R } } { \psi _ { R x } } i _ { S y F } - \frac { 1 } { T _ { F } } ," ,0f28d874-8dcc-4764-b0b1-f5eb20ce29fb__mathematical-expression-and-equation_2.jpg
"3 . 0 , 2 5 + 4 3 4 , 7 . 0 , 0 5 + 2 1 9 . 0 , 1 0 = 1 3 0 \text { k g }" ,0f69639c-5308-11ea-8ddc-00155d012102__mathematical-expression-and-equation_7.jpg
"\lambda = k . c _ { v } . \eta = k . c _ { p } . \eta / \kappa" ,0f6d5b47-5308-11ea-8ddc-00155d012102__mathematical-expression-and-equation_3.jpg
"\frac { ( \rho + r ) ( \dot { \phi } + \dot { \psi } ) } { \sqrt { ( \dot { \rho } + \dot { r } ) ^ { 2 } + ( \rho + r ) ^ { 2 } ( \dot { \phi } + \dot { \psi } ) ^ { 2 } } } = \frac { \rho \dot { \phi } } { \sqrt { \dot { \rho } ^ { 2 } + \rho ^ { 2 } \dot { \phi } ^ { 2 } } } - \frac { \dot { \rho } \rho \dot { \phi } } { ( \dot { \rho } ^ { 2 } + \rho ^ { 2 } \dot { \phi } ^ { 2 } ) ^ { 3 / 2 } } \dot { r } +" ,0f9f60ce-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\overline { Q } _ { 2 6 } = ( Q _ { 1 1 } - Q _ { 1 2 } - 2 \cdot Q _ { 6 6 } ) \cdot \cos \theta \sin ^ { 3 } \theta" ,0fd02341-3c59-11e1-1331-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\phi = \phi _ { m } = 7 3 ^ { \circ } 4 5 \prime" ,1069664d-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_15.jpg
"P ( s ) \delta _ { \xi } = P ( \xi ) \delta _ { \xi }" ,10696799-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_2.jpg
"R _ { a } = ( V _ { n } - U _ { n } \sqrt { V - 1 } ) _ { r = a }" ,1116d3b1-0d12-4430-8381-cd7f733eef18__mathematical-expression-and-equation_0.jpg
"A _ { 2 } = 0" ,1138ecd7-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"X _ { 1 } Y _ { 1 } + \dots + X _ { p } Y _ { p }" ,11826463-901e-11ed-868a-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\overline { N } _ { 1 , S } = \overline { N } _ { 1 , 0 } , \overline { N } _ { 2 , S } = \overline { N } _ { 2 , 0 } ." ,11f9f266-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\{ A [ 2 G \frac { d ^ { 2 } } { d r ^ { 2 } } J _ { 0 } ( h r ) - \frac { \lambda } { \lambda + 2 G } p ^ { 2 } \rho J _ { 0 } ( h r ) ] + 2 B G \gamma \frac { d } { d r } J _ { 1 } ( \kappa r ) \} _ { r = R } = 0" ,11f9f383-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"h = \frac { S } { \sigma } b = \frac { 1 3 . 6 } { 0 . 0 0 1 2 9 } 0 . 7 6 = 8 0 0 0 m" ,11fd5950-73f7-11e4-9c7b-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg
"= \sum _ { j = 0 } ^ { d _ { t } - 1 } e ^ { \frac { 2 \pi i } { d _ { t } } j \cdot b } = \{ \begin{array} { c c } 0 & \text { i f } d _ { t } \nmid b \\ d _ { t } & \text { i f } d _ { t } | b \end{array}" ,126ab61c-40e4-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { \partial ^ { 2 } x ^ { a } } { \partial \xi ^ { I ^ { 2 } } } = - R _ { 1 } \frac { \partial ^ { 2 } X ^ { a } } { \partial \xi ^ { I ^ { 2 } } } , ( a = 1 , 2 , 3 )" ,126ab62d-40e4-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"G H J + G H J \prime = \frac { \gamma } { 3 6 0 } \cdot S" ,1333f4dc-bdf8-11e6-b796-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"[ \omega _ { 0 0 } - \omega _ { 1 1 } - \omega _ { 2 2 } + \omega _ { 3 3 } \omega _ { 1 } ] - 2 [ \omega _ { 2 1 } - \omega _ { 3 } \omega _ { 2 } ] = 0" ,133b2708-40e4-11e1-3052-001143e3f55c__mathematical-expression-and-equation_3.jpg
"b ( s _ { 4 } \prime s _ { 3 } \prime \prime + s _ { 3 } \prime s _ { 4 } \prime \prime ) = b s _ { 7 }" ,133b272f-40e4-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\alpha t + \beta u + \gamma v = 0" ,138159d9-9e40-4c81-a4fc-6b318b5f6580__mathematical-expression-and-equation_4.jpg
"\psi = \frac { 2 ( 1 + \alpha ) } { \sqrt { ( 4 - \xi ^ { 2 } ) } } \exp ( \sqrt { 3 } . \arcsin ( \frac { \xi } { 2 } ) ) - \alpha ." ,13883274-3c62-11e1-5298-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\int _ { 0 } ^ { t } ( \sum _ { k } D _ { k j } + v _ { j j } ) d t = x _ { j } + y _ { j }" ,13883369-3c62-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\beta _ { 1 , 2 } = \pm k _ { 1 } \alpha" ,1388348e-3c62-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg
"z _ { 0 } = 0 , 0 ^ { 3 } 1 6 8 . 3 4 9 0 . 1 , 1 0 4 = 0 , 6 4 7" ,140d6d00-ee50-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_27.jpg
"[ a b ] x + [ b b ] y + [ b c ] z + [ b d ] t + [ b l ] = 0" ,140f850d-8096-7a3c-4c29-b48df4fd8972__mathematical-expression-and-equation_28.jpg
"+ \frac { 1 } { R ^ { 2 } } ( a _ { 2 } u _ { 2 } ( x , y ) + b _ { 2 } v _ { 2 } ( x , y ) ) + \dots" ,14485700-5d32-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"= 2 + ( \frac { y } { l } ) ^ { 2 } [ ( 1 - \cos \frac { \gamma l v } { R } ) ^ { 2 } + \sin ^ { 2 } \frac { \gamma l v } { R } ] - \frac { 2 y } { l } ( 1 - \cos \frac { \gamma l v } { R } ) + \dots =" ,1467222a-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_3.jpg
"F = z . \frac { v } { 2 } = z _ { 1 } . \frac { v _ { 1 } } { 2 }" ,149b96e0-5839-11e6-b155-001018b5eb5c__mathematical-expression-and-equation_3.jpg
"X = L _ { 1 } + x" ,152542e0-ac34-7682-4133-b43492bf9a7b__mathematical-expression-and-equation_9.jpg
"- C _ { s } ( \bar { \kappa } _ { 3 } - \kappa _ { 3 } ) \frac { h } { b } b \phi _ { 0 }" ,153e6e68-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\Vmatrix G R - B X ; & - B R - G X \\ B R + G X ; & G R - B X \Vmatrix = J" ,153e6ed9-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_5.jpg
"E _ { i + 1 } = \mu E _ { i }" ,153e6fa4-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_11.jpg
"f _ { 1 \mu } ( t ) = \frac { c _ { 1 \mu } } { ( \mu - 1 ) ! } t ^ { \mu - 1 } e ^ { p _ { 1 } t }" ,153e70f4-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\xi = X - X _ { 0 } ; \eta = y - Y _ { 0 } \dots" ,1558f4d1-6924-4b3d-8439-01796c82a5d1__mathematical-expression-and-equation_5.jpg
"- \frac { l } { 2 } \le x \le \frac { l } { 2 }" ,1623c61b-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\psi _ { n } = \psi _ { n } ^ { ( 1 ) } + \psi _ { n } ^ { ( 2 ) } = B _ { n } ^ { ( 1 ) } Q _ { n } ( q ) P _ { n } ( p ) + B _ { n } ^ { ( 2 ) } P _ { n } ( q ) P _ { n } ( p )" ,1623c824-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_10.jpg
"x = \Gamma _ { p } R _ { 1 }" ,1623c844-3c62-11e1-1457-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\dot { X } = F ( X )" ,17085b2e-3c62-11e1-5015-001143e3f55c__mathematical-expression-and-equation_4.jpg
"y - n = \frac { d \sin \alpha } { \sin \theta }" ,1715b35b-901e-11ed-868a-001b63bd97ba__mathematical-expression-and-equation_7.jpg
"M _ { a } \zeta _ { n } = n M _ { a } z" ,17ebdac6-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_2.jpg
"S _ { 0 } = \frac { 1 } { 4 } C \prime v _ { 0 } \xi" ,17ebdae4-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_3.jpg
"[ \begin{array} { c } f _ { 2 } \\ f _ { 3 } \\ f _ { 4 } \\ f _ { n } \end{array} ] = - [ \begin{array} { c c c } h _ { 1 2 } & h _ { 1 3 } & h _ { 1 n } \\ h _ { 2 2 } & h _ { 2 3 } & h _ { 2 n } \\ h _ { 3 2 } & h _ { 3 3 } & h _ { 3 n } \\ h _ { ( n - 1 ) , 2 } & h _ { ( n - 1 ) , 3 } & h _ { ( n - 1 ) , n } \end{array} ] ^ { - 1 } [ \begin{array} { c } h _ { 1 1 } \\ h _ { 2 1 } \\ h _ { 3 1 } \\ h _ { ( n - 1 ) , 1 } \end{array} ]" ,18c34f80-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"f ( R ) = 2 \frac { R } { R _ { 0 } ^ { 2 } }" ,18c34fcc-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( 2 x + 1 ) y \prime \prime + ( 4 x - 2 ) y \prime - 8 y = ( 6 x ^ { 2 } + x - 3 ) e ^ { x } ," ,1996d440-0a0b-11e3-9439-005056825209__mathematical-expression-and-equation_11.jpg
"i _ { n } = \frac { L _ { s } + L _ { p k } } { L _ { s } + L _ { p } } \frac { \phi _ { M } } { \sigma L _ { p k } }" ,19993da6-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_0.jpg
"j _ { 1 } = ( 1 - \sigma \beta ) j _ { n k }" ,19993da7-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x ^ { - p } \int _ { 0 } ^ { x } y ^ { p - 1 } e ^ { - y } d y = f ^ { * } ( p , x )" ,19993e27-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\epsilon ( A \cos \omega t ) = \sum _ { v = 0 , 2 , 3 , \dots } m _ { v } \cos v \omega t" ,1a69fb95-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg
"+ 4 \alpha ^ { 2 } ( a ^ { 2 } + b ^ { 2 } ) ( \cosh ^ { 2 } a \delta \cos ^ { 2 } b \delta +" ,1a69fbd2-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_13.jpg
"N _ { r } = \int _ { - h _ { 2 } } ^ { 0 } \sigma _ { r _ { 2 } } d z + \int _ { 0 } ^ { h _ { 1 } } \sigma _ { r _ { 1 } } d z = s _ { 1 } [ \frac { d u _ { 0 } } { d r } + \frac { 1 } { 2 } ( \frac { d w } { d r } ) ^ { 2 } ] + s _ { 2 } \frac { u _ { 0 } } { r } - s _ { 3 } \frac { d ^ { 2 } w } { d r ^ { 2 } } -" ,1a69fc8b-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"K = \frac { r . 1 , 0 p ^ { t - m } } { 1 , 0 p ^ { t } - 1 }" ,1b378587-369b-478e-964d-0c25bcda245b__mathematical-expression-and-equation_0.jpg
"( 4 - \pi ) \xi _ { S } ^ { 3 } - \frac { 3 ( 4 a x + b ^ { 2 } ) } { 4 x ^ { 2 } + b ^ { 2 } } \xi _ { S } ^ { 2 } + \frac { 3 a } { 2 x } - \frac { 1 } { 2 } = 0" ,1b3ded58-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"- \frac { 2 \pi } { t } \sum _ { i = 0 } ^ { \infty } \frac { ( - 1 ) ^ { i } ( 2 i - 1 ) ! ! } { ( 2 i + 2 ) ! ! } ( \frac { 1 + s ^ { 2 } } { t ^ { 2 } } ) ^ { i } P _ { i } ^ { ( 1 , - \frac { 1 } { 2 } ) } ( \frac { s ^ { 2 } - 1 } { s ^ { 2 } + 1 } )" ,1b3ded8a-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
"A _ { 1 } \equiv 0 , 2 6 5 \Sigma _ { I I } + 0 , 1 0 3 \Sigma _ { I I I } + 0 , 6 5 2 A _ { 3 }" ,1b42974a-cc0f-4e89-b984-f72566c8b410__mathematical-expression-and-equation_7.jpg
"\lambda = \frac { l _ { 1 } - l } { l }" ,1b853f20-e07c-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg
"\frac { n ^ { 2 } - 1 } { n ^ { 2 } } = 0 . 4 3 8 ." ,1be174a0-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_0.jpg
"j = 1 , 2" ,1be98b2a-216a-46a4-9f31-743d49a3a06b__mathematical-expression-and-equation_2.jpg
"8 7 = 1 5 { , } 4 0 \%" ,1bffc099-eab4-445d-b021-7e7e6e399808__mathematical-expression-and-equation_0.jpg
"i = A T ^ { 2 } e ^ { - \frac { b } { T } }" ,1c186cb0-1b94-11e4-8e0d-005056827e51__mathematical-expression-and-equation_0.jpg
"+ ( \frac { 1 } { 6 } I ^ { 3 } _ { a + b - c } - \frac { 1 } { 2 } I _ { a + b - c } I I _ { a + b - c } + \frac { 1 } { 3 } I I I _ { a + b - c } ) \delta _ { i j } ," ,1c1d4f5c-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_15.jpg
"E _ { v } ( \mathbf { x } ) = \int _ { 0 } ^ { x } d E _ { v } ( \mathbf { x } ) = \int _ { 0 } ^ { x _ { 2 } } \tau _ { 2 } d \tau _ { 2 } + \int _ { 0 } ^ { x _ { 1 } } g ( \tau _ { 1 } ) d \tau _ { 1 }" ,1c1d5020-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_2.jpg
"X _ { n } ( r ) = \Phi ( r ) + \phi ( r )" ,1c1d5181-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\tilde { \phi } ( p ) = \frac { 2 b _ { 2 } + b _ { 1 } p + b _ { 0 } p ^ { 2 } } { ( 1 + p ) ^ { 3 } }" ,1c1d5199-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"C _ { 6 } H _ { 4 } < { N O _ { 2 } \atop N H _ { 2 } }" ,1ce2239d-cb97-42d8-8c3c-a8992290d442__mathematical-expression-and-equation_18.jpg
"i = 0 ; 1 ; 2 ; 3 ; 4 ; 5 + L" ,1dd05695-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_39.jpg
"M _ { y 4 } = 0 . 2 6 5" ,1dd057a0-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_15.jpg
"y \in P , \rho ( x , y ) < \delta \implies | \frac { 1 } { f ( x ) } - \frac { 1 } { f ( y ) } | = \frac { | f ( x ) - f ( y ) | } { | f ( x ) \cdot f ( y ) | } < \frac { \epsilon \cdot \alpha ^ { 2 } } { \alpha ^ { 2 } } = \epsilon ." ,1e0fff1b-4772-4bff-9f57-ecadc03a1531__mathematical-expression-and-equation_3.jpg
"\epsilon = \beta + n" ,1e3faff0-ef94-11ea-b427-005056825209__mathematical-expression-and-equation_0.jpg
"\alpha = K r ^ { n } \frac { r - 1 } { r ^ { n } - 1 } = K \cdot \frac { 1 } { a _ { \overline { n | } } }" ,1e586e80-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"+ \frac { 1 - 3 ( \frac { b _ { 1 2 } } { a _ { 1 } + a _ { 2 } } ) ^ { 2 } } { ( 2 k \frac { a _ { 1 } + a _ { 2 } } { 2 } ) ^ { 2 } [ 1 + ( \frac { b _ { 1 2 } } { a _ { 1 } + a _ { 2 } } ) ^ { 2 } ] ^ { 2 } } ]" ,1f799bf8-3c62-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { \partial t } { \partial y } = - \frac { \partial F \prime } { \partial y } \cdot x - \frac { \partial \Phi \prime } { \partial y } \cdot \frac { x ^ { 2 } } { 2 }" ,1f7d81d7-5cf2-11e8-a84a-001999480be2__mathematical-expression-and-equation_1.jpg
"B _ { r k } ^ { e } ( \phi , \psi , \xi ) =" ,2051aa70-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_10.jpg
"r _ { B } ^ { \prime } = r _ { B } + x" ,2051aa8b-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { d U } { d T } \doteq - 2 \cdot 1 0 ^ { - 3 } + [ 2 , 8 ( 1 0 ^ { - 4 } - 1 0 ^ { - 3 } ) + R _ { s } ] \cdot ( 1 0 ^ { - 7 } - 1 0 ^ { - 6 } )" ,2052fede-dbc4-4cb1-bba1-4d8a7746e5cb__mathematical-expression-and-equation_13.jpg
"+ \frac { 1 } { 4 } X _ { 4 \prime 5 \prime } ) - I _ { 6 } \frac { 1 } { X _ { 3 , 1 0 } } \times" ,213248d3-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_1.jpg
"q \frac { q ^ { n } - 1 } { q - 1 } = Q _ { n }" ,229520a0-0a78-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_6.jpg
"0 . 0 0 0 0 0 6 \times \frac { 1 } { 1 9 3 1 . 5 } \times 1 . 5 9 4 8 ( 6 , 2 9 6 \times 2 0 . 5 + 3 , 2 7 2 \times 2 \times 2 0 . 6 7 )" ,22d30a60-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_14.jpg
"F e ^ { + + } + M n \rightleftharpoons F e ^ { + } + M n ^ { + + }" ,233cd510-84af-11e4-a354-005056825209__mathematical-expression-and-equation_2.jpg
"v _ { e } ( = 1 - v _ { f } ) , \mu _ { e } , \rho _ { e } , \mu _ { f } ^ { * } , \rho _ { f } ^ { * } , \eta , \eta _ { 0 } , \kappa , \omega , K" ,23c01eab-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"V _ { k } ( \zeta ^ { b } ) = \int _ { S } X _ { i } ( \mathbf { x } ) U _ { i k } ( \mathbf { x } - \zeta ^ { b } ) d S _ { x }" ,23c01f9e-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"T _ { n n } ^ { * } = \sum _ { i , j = 1 } ^ { 2 } t _ { i j } ^ { * } n _ { i } ( \xi ) n _ { j } ( x )" ,249e480b-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { \frac { \omega _ { 1 } } { p _ { b } v } + \omega ^ { r } } { \frac { \omega _ { 1 } } { p _ { b } v } } = \frac { \omega _ { 1 } + p _ { b } v \omega ^ { r } } { \omega _ { 1 } } = ( 2 - s _ { v } )" ,249e490b-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p _ { t } i _ { b } = \frac { 1 } { 3 L _ { S \sigma } } ( 2 h _ { 2 } - h _ { 1 } + \sqrt { ( \frac { 3 } { 2 } ) } p _ { t } \psi _ { M \alpha } - \frac { 3 } { \sqrt { 2 } } p _ { t } \psi _ { M \beta } )" ,249e4984-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\phi _ { 1 } = \dot { \epsilon } _ { M } / \{ \sigma _ { M } ( 1 - 3 \chi ) + 2 \tau _ { L } ^ { 2 } [ \frac { \sigma _ { S } ^ { 2 } - 3 \chi ( 2 - 3 \chi ) \sigma _ { M } } { ( 1 - 3 \chi + 3 \chi ^ { 2 } - 3 \chi ^ { 3 } ) \sigma _ { C } \sigma _ { T } ( \sigma _ { C } - \sigma _ { T } ) } -" ,249e49f3-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\Delta = ( \lambda ^ { 2 } - \alpha _ { 1 } ) ( \lambda ^ { 2 } - 2 \beta ) ( \lambda ^ { 2 } - \alpha _ { 3 } ) - \beta ^ { 2 } ( \lambda ^ { 2 } - \alpha _ { 1 } ) - \beta ^ { 2 } ( \lambda ^ { 2 } - \alpha _ { 3 } ) = 0" ,249e4a60-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_22.jpg
"[ ( A _ { 1 } \pm r _ { 1 } ) + ( A _ { 2 } \pm r _ { 2 } ) ] ," ,25e2015e-e3ab-11e6-b9b6-001999480be2__mathematical-expression-and-equation_4.jpg
"\int _ { a } ^ { \infty } f ( x ) d x = \lim _ { x = \infty } [ F ( x ) - F ( a ) ] = \lim _ { x = \infty } F ( x ) - F ( a ) ," ,25f264b0-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_4.jpg
"S ^ { i } _ { ( r s ) } = 0" ,276bb841-3e4f-449d-8f2b-8847bad0098e__mathematical-expression-and-equation_6.jpg
"\frac { 1 } { m _ { 1 } m _ { 4 } } \frac { d x _ { 2 3 } } { d t } , \frac { 1 } { m _ { 2 } m _ { 4 } } \frac { d x _ { 3 1 } } { d t } , \frac { 1 } { m _ { 3 } m _ { 4 } } \frac { d x _ { 1 2 } } { d t } , \frac { 1 } { m _ { 2 } m _ { 3 } } \frac { d x _ { 1 4 } } { d t } , \frac { 1 } { m _ { 3 } m _ { 1 } } \frac { d x _ { 2 4 } } { d t } , \frac { 1 } { m _ { 1 } m _ { 2 } } \frac { d x _ { 1 2 } } { d t }" ,27a055e2-02cc-4ad0-8b0c-aa88395b4e1e__mathematical-expression-and-equation_11.jpg
"\sum _ { i } a _ { i k } ^ { 2 } = 1" ,27c88220-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"2 7 0 0 = \frac { 1 . 5 0 } { 0 . 0 0 0 6 }" ,28baa582-6761-11e9-bca3-001999480be2__mathematical-expression-and-equation_14.jpg
"a + b + c = 1" ,2949edaf-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"R 6 8 8 = \frac { H _ { D } 6 8 8 } { H _ { D } 6 3 0 + \overline { H } _ { D } 6 5 7 }" ,29b7a183-4ce4-11e1-1726-001143e3f55c__mathematical-expression-and-equation_0.jpg
"C l _ { 2 } + H _ { 2 } O + H _ { 2 } S O _ { 3 } = 2 H C l + H _ { 2 } S O _ { 4 }" ,2a8e37e0-376c-4de3-8f2c-fcd1a7ea9559__mathematical-expression-and-equation_5.jpg
"\sqrt { a } = \sqrt { \sqrt { a } } , \sqrt { a } = \sqrt { \sqrt { a } } , \sqrt { a } = \sqrt { \sqrt { a } }" ,2bea2807-4b41-401e-835e-469b9213fe48__mathematical-expression-and-equation_4.jpg
"1 4 \frac { 3 } { 4 } + 1 \frac { 1 } { 4 } + 1 \frac { 1 } { 4 } = 1 7 \frac { 1 } { 4 }" ,2bf5673c-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg
"1 3 \frac { 1 } { 2 } + \frac { 1 } { 2 } + 1 \frac { 1 } { 4 } = 1 5 \frac { 1 } { 4 }" ,2bf69fea-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg
"\frac { f ( x ) h ( x ) } { \phi \prime ( x ) f ( \phi ) } - h ( \phi ) \le 0" ,2c1e7d28-df3d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"Q ^ { n } _ { m } = 2 ^ { - n + 1 } \sum _ { r = 0 } ^ { \frac { 1 } { 2 } m n } \mathfrak { N } \prime _ { m n - r } Q _ { m n - r } , n \text { g e r a d e }" ,2cdceb57-df3d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\frac { \partial \sigma } { \partial v } = \cos \lambda" ,2d671acf-ed86-4edd-9509-9bcffc749c80__mathematical-expression-and-equation_3.jpg
"\mu = \sqrt { \frac { \pi } { 2 } }" ,2e3bee70-ee52-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_16.jpg
"1 0 ^ { \frac { 1 } { 1 6 } } = \sqrt { 1 . 3 3 3 5 2 1 } = 1 . 1 5 4 7 8 2" ,2e44c0a0-2eee-11e5-b57a-005056825209__mathematical-expression-and-equation_0.jpg
"d : \alpha = 0 . 9 2 s c m ^ { - 1 } ( r _ { m } = 1 . 5 s c m ^ { - 1 } )" ,2e54f660-4ce4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\Delta _ { m } = \sum _ { \alpha \ge \beta \ge 0 } z ( m - \alpha n - \beta , n ) - \frac { 1 } { 2 } E ( \frac { m - 1 } { n + 1 } ) E ( \frac { m - 1 } { n + 1 } + 1 )" ,2eadb511-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_6.jpg
"D _ { m } ^ { p + q } = \frac { R r } { d _ { m } }" ,2ec83581-48e8-440b-a8a2-d849ff9530bf__mathematical-expression-and-equation_2.jpg
"x ^ { 2 } = 2 5 ." ,2ecc5430-14e4-11e5-9192-001018b5eb5c__mathematical-expression-and-equation_33.jpg
"\int \frac { d x } { 1 - \cos x } = - \cot \frac { x } { 2 } + C" ,2ee7ef00-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_8.jpg
"a ^ { 2 } = b ^ { 2 } + c ^ { 2 } - 2 b c \cos \alpha \dots" ,2f308d32-af44-4564-958a-8303616d1203__mathematical-expression-and-equation_11.jpg
"A : ( A - E ) \dots b" ,2f8d1f20-2eee-11e5-b57a-005056825209__mathematical-expression-and-equation_14.jpg
"\iint _ { \Omega } f ( x , y ) d x d y = \lim _ { \omega } \iint _ { \Omega - \omega } f ( x , y ) d x d y" ,304edeb0-5d32-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"\frac { 2 } { 3 } , \frac { 4 } { 5 } , \frac { 6 } { 7 } , \frac { 5 } { 1 4 } , \frac { 1 1 } { 1 5 }" ,3061abe3-91a3-4a3b-8472-0367a6622fd5__mathematical-expression-and-equation_5.jpg
"l _ { F } F = ( b _ { A } - \frac { 1 } { 3 } l _ { A } ) F _ { A } + ( b _ { B } - \frac { 1 } { 3 } l _ { B } ) F _ { B }" ,30da51a1-7580-4af1-a594-cead5bb5993b__mathematical-expression-and-equation_2.jpg
"\rho _ { 3 } = 0 , 5 7 7 1 9 \sqrt { \frac { [ | \epsilon | ] ^ { 3 } } { n } } ( 1 \pm \frac { 0 , 4 9 7 2 0 } { \sqrt { n } } )" ,3143d740-ee52-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"( a _ { k } - u _ { p } ) ( u _ { k } - k u _ { p } )" ,3161fd26-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_3.jpg
"b ^ { 2 } = \frac { 1 - \cos \omega _ { 1 } - \cos \omega _ { 2 } + \cos \omega _ { 3 } } { 3 - \cos \omega _ { 1 } - \cos \omega _ { 2 } - \cos \omega _ { 3 } } ," ,31b73743-dc04-11e7-bc7e-00155d012102__mathematical-expression-and-equation_8.jpg
"( \alpha _ { 2 2 } - \omega ^ { 2 } ) b \equiv - e \cdot c \omega" ,324ab146-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_6.jpg
"q = \frac { \mu } { 2 } ( v - k ) ^ { 2 } \sqrt { 2 g c } \int \frac { z ^ { 2 } d z } { \sqrt { z ^ { 2 } + 1 } }" ,3274e3aa-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_18.jpg
"+ \frac { 1 } { 2 } \sum m [ ( \frac { d \xi _ { k } } { d t } ) ^ { 2 } + ( \frac { d \eta _ { k } } { d t } ) ^ { 2 } + ( \frac { d \zeta _ { k } } { d t } ) ^ { 2 } ]" ,3274e3ab-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"b \doteq b _ { 1 } \doteq b _ { 2 } \doteq b _ { 3 }" ,3274e3ad-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_12.jpg
"v = m 4 K + v 2 i K \prime - u" ,32792ea9-bc81-43fb-a786-e7f6ea1dc1e4__mathematical-expression-and-equation_4.jpg
"N - M - 2 m _ { s } \le m _ { s } \le \frac { 1 } { 2 } ( N - 3 m _ { s } )" ,33204f77-df3d-11e1-1431-001143e3f55c__mathematical-expression-and-equation_6.jpg
"p ^ { 2 } : q ^ { 2 } = a ^ { 2 } : x ^ { 2 } = b ^ { 2 } : y ^ { 2 } = c ^ { 2 } : z ^ { 2 } \text { o d }" ,33badfe0-c575-11e7-80e7-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg
"c _ { 2 1 } b _ { 1 1 } + c _ { 2 2 } b _ { 2 1 } = a _ { 2 1 }" ,3450870a-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"- \phi ^ { \prime 2 } [ ( q ( \phi ) - \bar { q } ( \phi ) ) + ( \bar { q } ( \phi ) - \bar { q } ( \bar { \phi } ) ) ] \le | q ( t ) - \bar { q } ( t ) | +" ,345087fe-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\partial M = \partial ( R ^ { m } - \overline { M } )" ,34508879-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"( f \in \mathcal { A } , \parallel f _ { 0 } - f \parallel _ { \mathcal { } } { B } < \epsilon ) \implies f \in M _ { k }" ,34fd1ace-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1" ,3569ab40-bb47-41e5-a81d-ec4e96e049ad__mathematical-expression-and-equation_4.jpg
"0 \le x \le 1" ,35a8c55b-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ \frac { 2 c f x } { e } - \frac { f f x x } { e e }" ,35a8eda7-fcdb-43cc-b828-1bd03d3164b0__mathematical-expression-and-equation_0.jpg
"S = \frac { 1 } { 2 } b \cdot \gamma \cdot h ^ { 2 } \cdot \text { t g } ^ { 2 } ( 4 5 - \frac { \phi } { 2 } )" ,363baca0-e718-11e5-8d5f-005056827e51__mathematical-expression-and-equation_0.jpg
"B ) \sum \phi _ { i } ^ { i } B ^ { i } = S ( B ) = 1 - s _ { 1 } B - \dots - s _ { q + T - 1 } B ^ { q + T - 1 }" ,36546d61-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_14.jpg
"l = [ \frac { n } { 2 } ] - 2" ,36546df2-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"d \omega _ { 1 } ^ { 2 } = - \omega _ { 1 } ^ { 3 } \wedge \omega _ { 2 } ^ { 3 }" ,36546df9-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_19.jpg
"x \le \bar { c } \le \bar { d } \le y , x \le \bar { \bar { c } } \le \bar { \bar { d } } \le y , x \le \bar { z } \le y , x \le \bar { \bar { z } } \le y ." ,36546e49-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_16.jpg
"\sum _ { n = 1 } ^ { \infty } a _ { n + 1 } . \ln \frac { k . ( a _ { n } - a _ { n + 1 } ) } { a _ { n + 1 } - a _ { n + 2 } } = \sum _ { n = 1 } ^ { \infty } a _ { n + 1 } . \ln \frac { k . b _ { n } } { b _ { n + 1 } } =" ,36546ec2-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\omega _ { i } ^ { j } + \omega _ { j } ^ { i } = 0" ,36546ed9-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"V _ { k j i i } = ( V _ { k } V _ { j i i } ) ^ { N } ( i , j , k = 1 , 2 )" ,36ff537d-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"U ^ { \alpha } _ { i } = S _ { i } ( R ^ { \alpha } _ { i } - T ^ { \alpha } _ { i } ) - S ^ { \alpha } _ { i } ( R _ { i } - T _ { i } )" ,36ff5452-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\lambda > \frac { p + 1 } { T } + \omega ." ,36ff548d-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\bar { y } = e ^ { - \int \bar { p } d \bar { x } } . \bar { \eta }" ,3712df9a-cfbe-4d13-9907-53ded46ac495__mathematical-expression-and-equation_2.jpg
"V ^ { ( o ) } ( t , S , n , x , \delta , p ) = \sup _ { \pi } E _ { t } [ U ( W ^ { \pi } _ { t , S , n , x } ( T ) + \frac { \delta } { p } C ( S ( T ) ) ) ]" ,375f43fc-ab9c-4b79-8c61-ca1fc55bc516__mathematical-expression-and-equation_1.jpg
"s \equiv 0 ( \operatorname { m o d . } 4 )" ,3760bca4-3a5a-4e3c-8ba0-2f4657000d24__mathematical-expression-and-equation_1.jpg
"u _ { 1 } + u _ { 2 } = \pm \frac { \omega _ { 3 } } { 2 } , u _ { 1 } + u _ { 2 } = \pm \frac { \omega _ { 3 } } { 2 } + \omega" ,3764000e-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_8.jpg
"\frac { d ^ { n } _ { - } y } { d x ^ { n } } = f ^ { u } _ { - } ( x )" ,3792d828-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_8.jpg
"\pi = w + \Omega" ,3792ff3f-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_11.jpg
"\pm \Delta V _ { 1 } = \alpha + \beta" ,379fa8e0-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_5.jpg
"= \frac { 1 } { i \lambda - i \omega _ { j } } \sum _ { k = 0 } ^ { r _ { j } - 1 } \frac { 1 } { 2 \pi i } \oint _ { K _ { j } } ( z - i \omega _ { j } ) ^ { - r _ { j } + k } \Gamma _ { j } ( z ) d z \frac { e ^ { i \lambda t } } { ( i \lambda - i \omega _ { j } ) ^ { k } } =" ,37a928d8-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"h ( 0 ) = 0 , h ( 1 ) = 1 ." ,37a9292f-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"( p _ { 1 } p _ { 1 } \prime m _ { 0 } m ^ { * } _ { 1 } ) = ( P P \prime S ^ { * } A _ { 1 } ^ { * } )" ,37df2316-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"+ 2 \pi a R \int _ { v _ { 1 } } ^ { v _ { 2 } } d v \dots" ,3801ed63-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_10.jpg
"h ( x ) = 0 \text { l o r s q u e } x \in X - ( A _ { 1 } \cup \bigcup _ { n > n _ { 0 } } \bigcup _ { i = 1 } ^ { m _ { n } } K _ { i } ^ { n } ) ;" ,3855e3ef-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\sum _ { n = 1 } ^ { \infty } \frac { w ^ { n } \sigma } { \sin n \sigma \pi }" ,3882dd44-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"C _ { 2 2 } = ( a e - 4 b d + 3 c ^ { 2 } ) x ^ { 2 } + \dots" ,389a5c8a-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg
"D _ { 0 } P ( D _ { 0 } ) = s _ { 1 } ^ { 2 } \sum _ { m = 1 } ^ { \infty } ( \frac { D _ { 0 } } { m } ) \frac { 1 } { m } = s _ { 1 } ^ { 2 } P ( D _ { 0 } )" ,38b6497a-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_3.jpg
"1 , | \begin{array} { c c } 1 , & n \\ x + a _ { 1 } , & ( n - 1 ) a _ { a } \end{array} |" ,38de91e4-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_15.jpg
"Z = - \frac { \partial P } { \partial z }" ,38efa908-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_8.jpg
"R b = 8 5" ,3995ad01-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_6.jpg
"V _ { \lambda } ( s + \eta , \psi ( s + \eta ) ) - V _ { \lambda } ( s , \psi ( s ) ) \le ( e ^ { - \lambda \eta } - 1 ) V _ { \lambda } ( s , \psi ( s ) )" ,39b0e05d-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\beta \prime - \beta = \rho \prime \prime \frac { w \prime } { \sqrt { 2 } } \sqrt { \mathrm { t g } \beta \prime }" ,39bbd20e-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_0.jpg
"\overline { 1 1 0 0 } : 5 \cdot \overline { 1 0 } \cdot \overline { 5 } \cdot 8 = 6 2 ^ { \circ } 4 3 \prime 5 0 \prime \prime" ,39beb8a0-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg
"\lambda A = - x" ,39e525c0-df28-11e1-1331-001143e3f55c__mathematical-expression-and-equation_17.jpg
"a = - 2 0" ,39f3d267-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_0.jpg
"E ( y , t ) \subset E ( 0 , \tilde { T } )" ,3a5e8568-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"u = \pm i" ,3a77f00f-df28-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { 1 } { 2 N } = \frac { 2 l } { c } ," ,3b7256c0-d035-11e3-93a3-005056825209__mathematical-expression-and-equation_0.jpg
"p x + q y = B" ,3bbd7a47-da8e-cb1e-9133-81df8bf7733e__mathematical-expression-and-equation_15.jpg
"s _ { r } = \sum _ { o } ^ { 6 } s p _ { s } ^ { r }" ,3bcb78ec-947e-43a7-914e-8d63635924fd__mathematical-expression-and-equation_0.jpg
"Y _ { P } = \frac { y _ { p } \cdot \hat { c } _ { 1 } + \hat { c } _ { 3 } } { y _ { p } \cdot \hat { c } _ { 2 } + 1 } , X _ { P } = \frac { x _ { p } \cdot D _ { h } / \cos ( \omega \cdot c ) } { y _ { p } \cdot \hat { c } _ { 2 } + 1 }" ,3c11aa60-cdca-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg
"( 1 - \frac { 1 } { 4 } \Omega ^ { 2 } - \frac { 1 } { 2 } \Omega ^ { 2 } A ) R _ { 2 } = 0" ,3c14889a-a074-401e-b9c6-e00cce2b1461__mathematical-expression-and-equation_4.jpg
"= \sqrt { 2 } U _ { n } \sin [ \omega ( k - \frac { 1 } { 2 } ) \Delta t + \alpha ] \cdot \frac { \sin \frac { \omega \Delta t } { 2 } } { \frac { \omega \Delta t } { 2 } }" ,3c52c16e-33c0-4df8-a290-182377244a1f__mathematical-expression-and-equation_5.jpg
"d \gamma = \frac { r _ { 1 } r _ { 2 } } { 2 \gamma } \frac { ( r _ { 2 } ^ { 2 } - r _ { 1 } ^ { 2 } ) ( N _ { 1 } - N _ { 2 } ) } { ( N _ { 1 } r _ { 2 } - N _ { 2 } r _ { 1 } ) ^ { 2 } } d N" ,3c550960-df3d-11e1-1431-001143e3f55c__mathematical-expression-and-equation_2.jpg
"V = \sum _ { \lambda = 0 } ^ { \infty } \frac { ( \alpha _ { \lambda } ^ { 2 } + \beta _ { \lambda } ^ { 2 } ) \alpha ^ { 2 } } { [ R ^ { 2 } + ( S \lambda \omega ) ^ { 2 } ] [ r ^ { 2 } + ( \frac { 1 } { c \lambda \omega } - s \lambda \omega ) ^ { 2 } ] }" ,3c55096d-df3d-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( u ^ { 4 } ) _ { 1 } = ( u ) _ { 1 } ^ { 4 } + 4 ( u ) _ { 1 } ( u ) _ { 3 }" ,3c5fc2a5-df28-11e1-1726-001143e3f55c__mathematical-expression-and-equation_8.jpg
"s _ { 1 } ^ { ( n ) } = \sum _ { v = 0 } ^ { n - 1 } j _ { v }" ,3c6810da-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"B Y = \rho m" ,3c762225-3195-46f9-aa31-fb0e77a64c03__mathematical-expression-and-equation_13.jpg
"y \prime \prime ( x ) = - y ( x )" ,3d165158-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\mp ( \phi _ { b } + \phi _ { b } ) , \pm \phi _ { b } , \pm \phi _ { b }" ,3d1f83b8-df3d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_5.jpg
"+ I _ { l } ( t , T ; p _ { 1 } , p _ { 2 } , \dots , p _ { l } | y _ { l + 1 } | )" ,3dc3cf9a-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\lim _ { y \rightarrow t ^ { + } } W ( t , [ t , y ] ) = \lim _ { y \rightarrow t ^ { + } } I + A ( y ) - A ( t ) = I + \Delta ^ { + } A ( t ) ," ,3dc3d07d-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\Delta = a _ { 1 } | \begin{array} { c c } 1 & b _ { 1 } \\ 1 & b _ { 2 } + b _ { 1 } ( 1 - \frac { a _ { 2 } } { a _ { 1 } } ) \\ 1 & b _ { 3 } + b _ { 1 } ( 1 - \frac { a _ { 3 } } { a _ { 1 } } ) \\ \dots \\ 1 & b _ { n } + b _ { 1 } ( 1 - \frac { a _ { n } } { a _ { 1 } } ) \end{array} |" ,3dc40f1e-df28-11e1-1154-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\psi ( a ) = a \prime , \psi ( b ) = b \prime" ,3e71e9e5-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\dot { x } = v" ,3e71eafa-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"- \zeta ( 3 ) + P _ { \rho } ( 3 ) + Q _ { \chi } ( 3 ) - R _ { \tau } ( 3 ) - S _ { \psi } ( 3 ) = V _ { 3 0 } \prime \prime U" ,3ea4c57a-df3d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\overline { a \alpha } = r" ,3ef3c997-eb8b-40bd-b477-5077437bd9fa__mathematical-expression-and-equation_9.jpg
"2 8 9 s _ { D } + 2 2 5 s _ { E } > 1 4 5 s _ { M D } + 8 1 s _ { M E }" ,3f0c0691-d3ba-4010-8990-71bc7458a1f0__mathematical-expression-and-equation_0.jpg
"\sum y _ { k - 1 } \mu ( M _ { k } ) - H = \epsilon > 0" ,3f277db9-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\sqrt { a b + 2 c ^ { 2 } + 2 c \sqrt { a b + c ^ { 2 } } }" ,3f3f5f76-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"\frac { 1 } { n } = a m ^ { 2 } + b ; \frac { 1 } { n } = a ( m - \frac { 1 } { 2 } ) ^ { 2 } + b ," ,3f4b6311-559e-4701-b416-92488e969370__mathematical-expression-and-equation_1.jpg
"x = u _ { e } ^ { T } \phi" ,3f86be27-5a1d-4327-a55c-b1713006f255__mathematical-expression-and-equation_7.jpg
"x ^ { 3 } ( \frac { p + k } { 2 } ) l = \frac { l x ^ { 2 } } { 2 } ( p + k ) - \frac { x ^ { 3 } } { 4 } . h ( p + k ) + \frac { x ^ { 4 } } { 4 } . l ( p + k ) - \frac { h x } { 2 } ( p + k ) + \frac { h k } { \epsilon l } - \frac { h k } { 1 6 l } . x ^ { 2 }" ,4030f61e-dbdb-11e6-95e2-001b63bd97ba__mathematical-expression-and-equation_13.jpg
"\frac { y ^ { \prime 2 } } { f } \le V ( x _ { 0 } ) + \int _ { x _ { 0 } } ^ { x } \frac { y ^ { \prime 2 } } { f } \cdot \frac { | f \prime | } { f } d t" ,4094a272-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( \mathcal { F } [ A _ { 1 } f , A _ { 2 } g ] , \phi ) = \sum _ { m = - \infty } ^ { \infty } \sum _ { n = - \infty } ^ { \infty } c _ { m , n } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } e ^ { i m x } e ^ { i n y } \phi ( x , y ) d x d y" ,414afbaf-408b-11e1-2238-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x _ { 1 } = \frac { a - V } { 3 2 0 } = 2 , 0 0 9 . 1 2 5 : 3 2 0 = 6 2 7 8" ,414cddf0-86a4-11e0-b8c5-0013d398622b__mathematical-expression-and-equation_4.jpg
"d _ { 0 } \le \min ( \frac { \lambda } { 2 ( v _ { 0 } + 1 ) } , \frac { \lambda } { 2 ( v _ { 0 } + 1 ) ( n ^ { 3 } K q + b n ^ { 2 } ( M _ { 1 } + M _ { 2 } + M _ { 3 } ) ) ^ { v _ { 0 } - 1 } }" ,41fe1d87-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { 1 } { 2 } \alpha \lambda ( \parallel y ( \eta ) \parallel ) ) ] . [ 1 - \sum _ { 1 } ^ { n } \psi ( t _ { k } ^ { 2 } , y ( t _ { k } ^ { 2 } ) ) \Delta _ { k } y ] ^ { + } \} < \eta" ,41fe1e97-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p \prime + p _ { 1 } = \frac { \partial V } { \partial x ^ { ( n - 1 ) } } , \\ p \prime _ { 1 } + p _ { 2 } = \frac { \partial V } { \partial x ^ { ( n - 2 ) } } , \\ \dots \\ p \prime _ { n - 2 } + p _ { n - 1 } = \frac { \partial V } { \partial x \prime } , \\ p \prime _ { n - 1 } = \frac { \partial V } { \partial x } ," ,42a4c342-ea23-4ee4-aeda-3776177a0607__mathematical-expression-and-equation_12.jpg
"\lim _ { n \rightarrow \infty } \sup [ f _ { n } ( t \prime \prime ) - f _ { n } ( t \prime ) ] = \lim _ { n \rightarrow \infty } \sup \frac { t \prime \prime - t \prime + h _ { n } ( t \prime \prime ) - h _ { n } ( t \prime ) } { 1 + h _ { n } ( 1 ) } \le" ,42a8f85e-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_0.jpg
"g ( s ) = \frac { 1 } { \Delta ^ { - } v ( t ) } \exp [ \frac { s - v ( t - ) } { \Delta ^ { - } v ( t ) } C _ { t } ^ { - } ] \Delta ^ { - } f ( t ) \text { f o r } s \in [ v ( t - ) , v ( t ) ) v" ,42a8f9a4-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"c o s ( 1 8 0 ^ { \circ } - \alpha ) = - c o s \alpha" ,43368c3b-18c2-4135-bf52-9b516fc72634__mathematical-expression-and-equation_11.jpg
"s \in [ c , d ] , f \in G _ { L } ( a , b )" ,4365dfef-f33d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"6 x ^ { 2 } - 1 5 y - 8 z ^ { 3 } - [ 4 x ^ { 2 } - 5 y - ( 3 x ^ { 2 } - 1 2 y ) - ( 9 x ^ { 2 }" ,43d27156-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_10.jpg
"3 \prime \prime - 4 \prime \prime - 8 \prime \prime" ,43d2e864-0d7f-11e3-3085-001143e3f55c__mathematical-expression-and-equation_1.jpg
"t _ { 0 } \in \mathbb { R } ^ { 1 } , x _ { 0 } \in \bar { C } ^ { n }" ,4419c6d9-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\delta _ { v } \approx \frac { d _ { v - 1 } d _ { v } } { d _ { v - 1 } - d _ { v } }" ,44282a85-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"p = \max ( p _ { 1 } , p _ { 2 } )" ,44282a92-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"= R _ { \xi } ( o ) - \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \tilde { h } ( r _ { 1 } ) \tilde { h } ( r _ { 2 } ) R _ { v } ( r _ { 2 } - r _ { 1 } ) d r _ { 2 1 } d r _ { 2 2 } d r _ { 1 1 } d r _ { 1 2 } +" ,443c0847-46a6-451c-849e-103d0d5699db__mathematical-expression-and-equation_7.jpg
"\sum _ { j = 1 } ^ { p } a _ { 2 q + 1 , j } \epsilon _ { 2 q + 1 , j } = \sum _ { r = 1 } ^ { m } ( 2 q p + r ) - \sum _ { r = m + 1 } ^ { 3 m - 2 } ( 2 q p + r ) +" ,44e14029-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"T = \sum _ { n = 1 } ^ { \infty } \mu _ { n } e _ { n } \otimes e _ { n + 1 } ," ,463fda98-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"V ( \sigma ( \gamma ) , \gamma ) \le V ( \sigma ( \alpha ) , \alpha ) - \int _ { \alpha } ^ { \gamma } c ( g ( s ( \theta ) , \theta ) ) d \theta < b ( \Omega ) - c ( \psi ( \zeta ) ) . T ( \zeta ) = 0 ," ,46490e9d-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\int _ { 0 } ^ { T } V _ { 1 } \prime \prime V _ { 2 } \prime d t = \int _ { 0 } ^ { T } [ B _ { 1 } x _ { 1 } e ^ { x _ { 1 } t } + B _ { 2 } x _ { 2 } e ^ { x _ { 2 } t } + B _ { 3 } x _ { 3 } e ^ { x _ { 3 } t } + B _ { 4 } x _ { 4 } e ^ { x _ { 4 } t } ]" ,46c92b15-d87a-4019-a4c6-6eff9f86d2a5__mathematical-expression-and-equation_9.jpg
"3 : 1 , 4 , 9" ,46fe53bd-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\int _ { X } a \cdot \theta _ { i } d \mu \le \int _ { X } f \theta _ { i } d \mu \le \int _ { X } b \theta _ { i } d \mu" ,4702b5bd-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"v = 2 . 4 2 5 \sqrt { R } \cdot \sqrt { J }" ,4755dd20-7822-11e7-ad78-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"E ^ { 3 } = \frac { F ^ { 2 } . v ^ { 2 } } { g . b ^ { 2 } } = \frac { b ^ { 2 } . a ^ { 2 } . k ^ { 2 } . R . J } { g . b ^ { 2 } } \doteq \frac { a ^ { 3 } . k ^ { 2 } . J } { g }" ,47573cf6-7822-11e7-ad78-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"\kappa _ { 1 } ^ { 4 } = 0" ,47ac1fe2-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\omega _ { 2 } ^ { 3 } = \omega ^ { 1 }" ,47ac200e-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"Q ( t , s ) = \{ \begin{array} { c } P ( t , s + ) \\ P ( t , 1 - ) \end{array}" ,47babb91-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\bar { \alpha } _ { i } = \alpha _ { i } - \alpha _ { i } \prime o n \bar { \Omega }" ,485928c7-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\ge ( ( p ^ { * } - p ) \sigma - \epsilon ) \zeta ^ { n } - \alpha C _ { \epsilon } \parallel h \parallel _ { Q } ^ { \frac { p } { ( p - q ) } } )" ,4877a2ca-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
"p = \frac { 1 } { 2 } ( p _ { 1 } + p _ { 2 } ) ," ,48b5c7f0-7a07-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"^ { i } \tilde { \tilde { F } } ( ^ { i } \mathbf { H } _ { k } ^ { 2 } \mathbf { m } ) - ^ { i } \tilde { \tilde { F } } ( ^ { i } \mathbf { H } _ { k } ^ { 1 } \mathbf { m } ) = ^ { i } D _ { F } ( ^ { i } \mathbf { H } _ { k } ( ^ { 2 } \mathbf { m } - ^ { 1 } \mathbf { m } ) ) + ^ { i } \mathbf { H } _ { k + 1 } ^ { r } ( ^ { 2 } \mathbf { x } _ { k + 1 } - ^ { 1 } \mathbf { x } _ { k + 1 } ) )" ,48c39b56-ec17-4d6a-99de-183f33ccf745__mathematical-expression-and-equation_7.jpg
"[ a b ] + [ b b ] + [ b c ] + [ b l ] + [ b s ] = 0" ,49658cc0-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_24.jpg
"N ^ { – } : N \prime = \emptyset ; I = \emptyset : \emptyset \prime" ,49740763-518b-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg
"| u ^ { ( k - i ) } ( t ) | \ge | u ^ { ( k - i ) } ( 2 ^ { - m + k + 1 } t ) | \ge" ,49b13f1b-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"B _ { 1 } ( t , s ) = U ( t ) S _ { 1 } V ( s )" ,49b14011-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\frac { \Delta h } { h } 1 5 - 2 0 \% ." ,4ad810bc-8368-47e5-8924-fe1f293d04c5__mathematical-expression-and-equation_2.jpg
"\dot { V } = - \lambda z ^ { T } Q Q ^ { T } z" ,4b40f63b-3552-4c56-88b1-f34be64f7b66__mathematical-expression-and-equation_1.jpg
"\mathbf { v } _ { r } = \frac { d \mathbf { r } } { d t } = \{ \frac { \partial H } { \partial n } \} _ { n } = \{ \frac { \partial H } { \partial n _ { L } } i _ { L } + \frac { \partial H } { \partial n _ { T } } i _ { T } \} _ { n }" ,4be82dec-10ac-4828-800d-8657e12177e6__mathematical-expression-and-equation_0.jpg
"p = - 2 , q = 3 , a = \sqrt { 1 6 } = 4 ." ,4cd27b34-2dac-11ec-b355-001b63bd97ba__mathematical-expression-and-equation_5.jpg
"3 : 1 , 5 , 6" ,4d29621d-b740-4bbd-acba-2c2483f2fb13__mathematical-expression-and-equation_8.jpg
"\frac { a } { b } = \frac { a : m } { b : m }" ,4df205e5-22be-11ec-b1c8-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"\frac { a } { e } : \frac { b } { f } = \frac { c } { g } : \frac { d } { h }" ,4df49d17-22be-11ec-b1c8-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"\psi ( \mathbf { p } ) = \sum _ { i = 0 } ^ { 2 } \tilde { F } _ { 1 } ( 7 0 + i . 2 , 5 , \mathbf { p } )" ,4e597959-3220-4964-8fb3-21145812301b__mathematical-expression-and-equation_0.jpg
"P = 2 \pi r v + \pi ( \rho _ { 1 } ^ { 2 } + \rho _ { 2 } ^ { 2 } )" ,4e8045a4-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"+ 2 . 5 8 ( c \times 0 . 7 0 4 9 P _ { 1 } + 0 . 0 2 7 8 t )" ,51a2c05c-dbdb-11e6-95e2-001b63bd97ba__mathematical-expression-and-equation_15.jpg
"\frac { d y } { d x } = \frac { \frac { d y } { d t } } { \frac { d x } { d t } }" ,51cc8c9c-0920-455c-b379-9e9d3bf33562__mathematical-expression-and-equation_0.jpg
"A E _ { i ( r - 1 ) } = \frac { \partial \psi } { \partial x _ { i ( r - 1 ) } } = \sum _ { j = 1 } ^ { q } \frac { \partial \psi } { \partial x _ { j } } \frac { \partial x _ { j } } { \partial x _ { i ( r - 1 ) } } = - \sum _ { j = 1 } ^ { q } ( t _ { j } - x _ { j } ) ( 1 - x _ { j } ) x _ { j } w _ { i j r }" ,51fccaaf-0894-43a1-84a0-d6f73fdbcbb8__mathematical-expression-and-equation_1.jpg
"+ A g C l + C _ { 2 } H _ { 5 } O H" ,52b3b470-029d-11e8-816d-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg
"B D = \frac { n \cdot p \cdot \alpha } { n \cdot \alpha } = p" ,52b4c371-59b9-11e8-b45f-001999480be2__mathematical-expression-and-equation_0.jpg
"0 . 3 9 - 0 . 3 6 = 0 . 0 3" ,52b4c382-59b9-11e8-b45f-001999480be2__mathematical-expression-and-equation_4.jpg
"x _ { m } - x _ { 1 } = m ( x _ { 2 } - x _ { 1 } )" ,5306a860-5d9e-11e6-95c7-005056825209__mathematical-expression-and-equation_12.jpg
"V _ { 3 } = \frac { M v _ { 3 } } { 1 0 0 }" ,537cb2e1-0d86-11e8-8ee8-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\rho _ { 2 } = \frac { 1 } { R _ { 2 } }" ,5519c6eb-4495-46f4-899a-194987f37dfd__mathematical-expression-and-equation_5.jpg
"\Gamma ( E ^ { * } ) = \frac { \overline { E } ^ { 2 } e ^ { - ( \nu - a ) t ^ { * } } } { \nu - a } + \frac { E ^ { * 2 } e ^ { - ( \nu + a ) t ^ { * } } } { \nu + a } - \frac { 2 E ^ { * } \overline { E } e ^ { - \nu t ^ { * } } } { \nu }" ,557698ed-951e-418a-88b9-b68ac53e4f75__mathematical-expression-and-equation_1.jpg
"X _ { 1 } - X _ { 3 } + X _ { 4 } - X _ { 5 } = 0" ,5645f11c-0550-dc24-6ddf-d737caee0a95__mathematical-expression-and-equation_14.jpg
"\log \mathrm { n a t } p = - \frac { l } { R T } + \mathrm { k o n s t } ." ,57ad34e0-d035-11e3-93a3-005056825209__mathematical-expression-and-equation_0.jpg
"C _ { 6 } H _ { 5 } . J O = C _ { 6 } H _ { 5 } . J O _ { 2 } + A g . O H = A g J O _ { 3 } + ( C _ { 6 } H _ { 5 } ) _ { 2 } . J ." ,580b3d9f-7eca-4017-8426-acfca32fa4d7__mathematical-expression-and-equation_5.jpg
"\omega _ { i } ^ { n + 1 } \equiv a _ { i j } \omega ^ { j } ( a _ { i j } = a _ { j i } )" ,589e53df-5882-4ff6-a404-3a8a047f3ea6__mathematical-expression-and-equation_8.jpg
"N = 6 6 4 \cdot 4 9 7" ,591f1179-3fb9-463b-9fff-bc9bc41a56ae__mathematical-expression-and-equation_2.jpg
"p O = p \frac { m } { \rho } = R T" ,59286dc0-d036-11e3-93a3-005056825209__mathematical-expression-and-equation_2.jpg
"c = V _ { K } ^ { - 1 }" ,5951c8aa-7cbf-4cd9-a6c5-55b264331208__mathematical-expression-and-equation_3.jpg
"2 w - 2 k - \delta - ( n - 2 k - k _ { 1 } + 4 ) \le n + k _ { 1 } - \delta - 4" ,59f0c3e9-4299-41ac-9a8b-229c7f13898d__mathematical-expression-and-equation_2.jpg
"\beta \prime = \frac { s \prime } { E \prime U \prime \prime } , \beta \prime \prime = \frac { s \prime \prime } { E \prime \prime U \prime \prime } , \beta \prime \prime \prime = \frac { s \prime \prime \prime } { E \prime \prime \prime U \prime \prime \prime }" ,59f189b2-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"u ^ { \prime 2 } + ( \frac { u ^ { 4 } + a ^ { 4 } } { 2 u ^ { 3 } } ) u \prime + \frac { a ^ { 4 } } { u ^ { 2 } } = 0 ," ,5a790a90-c04f-11e6-86b1-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"| \begin{array} { c c c } u _ { n } & ( \frac { 1 + \sqrt { 5 } } { 2 } ) ^ { n } & ( \frac { 1 - \sqrt { 5 } } { 2 } ) ^ { n } \\ 1 & \frac { 1 + \sqrt { 5 } } { 2 } & \frac { 1 - \sqrt { 5 } } { 2 } \\ 2 & \frac { 3 + \sqrt { 5 } } { 2 } & \frac { 3 - \sqrt { 5 } } { 2 } \end{array} | = 0" ,5b15b3f5-ae40-49f0-91d1-5202d28fe8b6__mathematical-expression-and-equation_1.jpg
"\frac { \partial i ( x , t ) } { \partial x } = \frac { \partial u ( x , t ) } { \partial t } \cdot c ( x )" ,5b5abc12-4d9e-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg
"x = 2 ^ { 2 } . x _ { 1 } = 1 6 ," ,5ba79b28-082e-9ae9-fb73-664362ed3bd7__mathematical-expression-and-equation_6.jpg
"m _ { C } = m C E F Q _ { m }" ,5db57c64-ba20-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\cos ^ { 2 } \beta = \frac { \overline { N _ { 1 } N ^ { 2 } } } { R _ { 1 } ^ { 2 } } = \frac { d ^ { 2 } \sin ^ { 2 } \omega } { a ^ { 2 } - d ^ { 2 } }" ,5de55ec5-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_3.jpg
"\Sigma \mathbf { y } = \mathbf { n } \cdot \mathbf { a } + \mathbf { b } \Sigma \mathbf { x }" ,5e56035c-8817-11e7-b67d-005056a54372__mathematical-expression-and-equation_0.jpg
"\frac { 2 } { \alpha _ { 1 } + \alpha _ { 2 } } \lim p ^ { \alpha _ { 6 } + \alpha _ { 3 } }" ,5e5696c8-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"x ^ { 2 } + y ^ { 2 } = \text { k o n s t . }" ,5e7ae85c-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_5.jpg
"H _ { r } = - \frac { M _ { r } } { h } = - \frac { p l ^ { 2 } } { 8 v } \cdot \frac { I } { \cos \tau }" ,5ea2b4a1-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"n = \frac { \sin i } { \sin r }" ,5f50e720-695e-11e8-943b-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"= \frac { 1 } { 2 } \int _ { V } E _ { i j k l } [ \epsilon _ { i j } \epsilon _ { k l } + ( \epsilon _ { k l } + \eta _ { k l } ) \eta _ { i j } + \epsilon _ { i j } \eta _ { k l } ] d V =" ,5fbe9849-e504-4a7d-a78b-28e44a4421c0__mathematical-expression-and-equation_10.jpg
"\log ( - 1 0 ^ { 7 } \cdot \chi _ { a } ) = 2 . 2 6 + 0 . 0 0 5 6 4 a" ,5fe36bff-ac13-4c0d-b036-fffdf152eef1__mathematical-expression-and-equation_1.jpg
"\mu _ { 2 } = 0 . 5 4 + 0 . 4 6 \frac { h _ { 2 } } { h _ { 1 } }" ,613ea82d-5cf1-11e8-a84a-001999480be2__mathematical-expression-and-equation_2.jpg
"V = \frac { \Delta c _ { r } \cdot 1 0 0 } { \beta }" ,6280ca52-a59a-446f-b6bc-e74eaea791fb__mathematical-expression-and-equation_0.jpg
"\tan \{ \frac { \pi } { 4 } - [ \gamma - \arcsin \frac { \tan \gamma } { \sqrt { \{ } 2 [ 2 ( 1 + \tan \gamma ) + \tan ^ { 2 } \gamma ] \} } ] \} = \frac { 1 - \epsilon _ { x } } { 1 + \epsilon _ { y } }" ,63416285-cc76-4567-b4bd-66a8c278888a__mathematical-expression-and-equation_5.jpg
"E + \Sigma T = R J ." ,63b29e8f-16b1-4d48-957a-67b4c19b2608__mathematical-expression-and-equation_2.jpg
"m _ { y } ^ { 2 } = \beta _ { 1 } ^ { 2 } m _ { 1 } ^ { 2 } + \beta _ { 2 } ^ { 2 } m _ { 2 } ^ { 2 } + \dots + \beta _ { n } ^ { 2 } m _ { n } ^ { 2 } = \frac { k ^ { 2 } } { p _ { n } }" ,63fd35e3-10d0-471a-9b17-3ef14aa1b897__mathematical-expression-and-equation_11.jpg
"c o \frac { 4 8 } { 1 0 } : \frac { 1 2 } { 1 0 } = \frac { 4 8 } { 1 0 } \times \frac { 1 0 } { 1 2 } = \frac { 4 8 0 } { 1 2 0 } = \frac { 4 8 } { 1 2 } = 4" ,6506032d-533b-4cdd-8af3-7b767a7c72f6__mathematical-expression-and-equation_2.jpg
"7 2 \times 1 = 8 \times 9" ,6513b035-a016-402e-a653-a0d156cef32d__mathematical-expression-and-equation_19.jpg
"= 2 . 5 ^ { 5 } - 3 . 5 ^ { 4 } + 1 . 5 ^ { 3 } - 4 . 5 ^ { 2 } + 1 . 5 + 2" ,66ba385f-1abb-4e30-92c4-5f73e89ecdee__mathematical-expression-and-equation_14.jpg
"\overline { 1 1 1 } = 0 , \overline { 2 1 2 } = 0" ,67ab1b60-a42e-4cae-81b2-a37ff8c4b632__mathematical-expression-and-equation_7.jpg
"\frac { p + q ) - f ( p ) } { q } = f \prime p + \phi ( p , q ) \text { o d e r , w e n n } y = f ( x ) , p = x , q = d x : \frac { d y } { d x } = f \prime x + \phi ( x , d x )" ,6801c529-b426-49b5-9710-49fcc272eaa2__mathematical-expression-and-equation_0.jpg
"\frac { v } { u + v } u _ { i } R T \ln \frac { P } { p \prime }" ,6a93a994-99b0-4d7f-990d-62bb2eac126d__mathematical-expression-and-equation_0.jpg
"\delta = \frac { 1 } { 2 } C \cdot E ^ { 2 } ," ,6b2f08a4-8549-40e7-b5b1-b0eab3c7a209__mathematical-expression-and-equation_0.jpg
"y \prime = \cos 2 x" ,6b5c7650-989e-11de-a593-0030487be43a__mathematical-expression-and-equation_18.jpg
"\binom { n } { 4 } = \frac { n ( n - 1 ) ( n - 2 ) ( n - 3 ) } { 1 \cdot 2 \cdot 3 \cdot 4 } = \frac { n ( n - 1 ) ( n - 2 ) ( n - 3 ) } { 4 ! }" ,6b76dc20-989e-11de-b5dc-0030487be43a__mathematical-expression-and-equation_8.jpg
"\frac { \partial } { \partial t } \mathbf { u } = \nabla ; \mathbf { v } - \nabla ; ( \mathbf { v } \cdot \nabla ; \mathbf { u } )" ,6b9826e9-e341-418b-8b17-af1ca3166f33__mathematical-expression-and-equation_5.jpg
"\frac { 7 } { 1 6 } = \frac { 2 1 } { 4 8 }" ,6d1cc91e-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"( 0 , 7 - ) 1 , 5 - 5 , 6 ( - 6 , 1 )" ,6d746983-0d7f-11e3-4047-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\% = \frac { 1 0 0 \times 5 0 0 } { 5 0 0 \times 2 5 } = 4 \%" ,6e06c320-f959-11e4-9f08-005056825209__mathematical-expression-and-equation_0.jpg
"3 ( n + 2 ) ( 2 n + 3 ) - 5 n + 4 ( n + 1 ) ^ { 2 } - ( 2 n + 2 ) = 2 n ^ { 2 } - 2 n" ,6f0b5454-7d9e-4d1a-af65-43bea1c455d5__mathematical-expression-and-equation_4.jpg
"p \wedge p , p \vee p , p \rightarrow p ," ,70062f75-37c6-44a1-af23-a06604b9c7b1__mathematical-expression-and-equation_11.jpg
"m = - c \ln n + c \frac { n } { n _ { 2 } } + c \ln n _ { 2 } - c = c [ \frac { n } { n _ { 2 } } + \ln ( \frac { n _ { 2 } } { n } ) - 1 ] \dots" ,7170c284-ed72-11e8-b65a-00155d012102__mathematical-expression-and-equation_3.jpg
"\lambda _ { 0 } = \frac { \pi \omega ^ { 2 } r ^ { 3 } l ^ { 2 } \sigma } { 2 . 1 0 ^ { 4 } d ^ { 2 } E _ { g } } [ ( \frac { \pi r } { h } - \frac { h } { \pi r } ) ( \alpha _ { 0 } - \frac { 2 ( 1 - \cos \alpha _ { 0 } ) } { \alpha _ { 0 } } ) ]" ,717137f2-ed72-11e8-b65a-00155d012102__mathematical-expression-and-equation_4.jpg
"\bar { x } = \phi ( x )" ,7178d1e4-77df-4d3a-bb13-7f084808bbd6__mathematical-expression-and-equation_8.jpg
"C _ { 1 5 } H _ { 2 3 } . O . C _ { 1 0 } H _ { 1 9 } ," ,71ace160-fa5c-11e7-9854-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"a _ { 1 } ^ { 2 } \cos ^ { 2 } \alpha + b _ { 1 } ^ { 2 } \cos ^ { 2 } ( \omega - \alpha ) ] y ^ { 2 } = a _ { 1 } ^ { 2 } b _ { 1 } ^ { 2 } \sin ^ { 2 } \omega" ,720c8ab8-224a-11ea-b704-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"A = \lim \{ \log \frac { x } { 1 - e ^ { - 2 x \pi } } + \int _ { 2 x \pi } ^ { \infty } \frac { e ^ { z ( 1 - v ) } - 1 } { e ^ { z } - 1 } d z \}" ,722d229d-9e77-492d-807a-b972a939c319__mathematical-expression-and-equation_3.jpg
"- \beta + \gamma + \alpha = \emptyset ," ,72d2a0a0-f6b6-4fde-b4d2-365594daeade__mathematical-expression-and-equation_0.jpg
"\dot { \mathbf { q } } = \mathbf { F } ( \mathbf { q } ) \mathbf { u } ," ,731de6e6-89f2-4b66-b504-350739ee29b5__mathematical-expression-and-equation_2.jpg
"y = { } _ { \beta } \{ \frac { x \prime \equiv d } { v } \} ^ { \beta \prime }" ,731fb0f4-b934-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"a ^ { 2 } \cdot \overline { M P } ^ { 2 } + ( a ^ { 2 } + e ^ { 2 } ) \overline { C P } ^ { 2 } = a ^ { 2 } ( a ^ { 2 } + e )" ,74508580-d210-11e2-b081-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"\beta \cdot 1 \cdot \frac { w ^ { 2 } } { 2 g } = h _ { d } \cdot 1 = H _ { d } ( \gamma _ { H g } - 1 )" ,74a26c70-5a1a-11e6-b155-001018b5eb5c__mathematical-expression-and-equation_2.jpg
"T = \frac { \lambda } { \omega }" ,74e6af90-e580-11e8-9984-005056825209__mathematical-expression-and-equation_9.jpg
"\frac { d x \sqrt { 3 } } { \sqrt { 1 + x ^ { 2 } + x ^ { 4 } } } = \frac { d y } { \sqrt { 1 - x ^ { 2 } + x ^ { 4 } } }" ,75994c88-476d-4d8d-9463-8bda7082f078__mathematical-expression-and-equation_0.jpg
"| \rho _ { w } ( x , t ) ( u _ { i } ( x , t ) - w _ { i } ( x , t ) + e ( x , t ) v _ { i } ( x , t ) ) v _ { i } ( x ) d S = 0" ,76166ebe-9aec-40b5-91ef-4b39d5ade9ab__mathematical-expression-and-equation_12.jpg
"\displaymath { q = 0 j e s t x _ { 0 } = 2 6 3 }" ,772be82c-6a05-bada-ae51-0fe7c818b666__mathematical-expression-and-equation_12.jpg
"= \frac { 1 3 0 \times 1 3 0 } { 1 2 - 2 2 } \cdot ( V" ,79647400-e953-11e2-9439-005056825209__mathematical-expression-and-equation_8.jpg
"p _ { n } = \frac { a _ { 1 } ( k ^ { n } - 1 ) } { k - 1 }" ,79885c7b-fd03-42ae-be98-97f12ee827a1__mathematical-expression-and-equation_1.jpg
"1 5 7 6 - 2 7 5" ,7a06f760-1e73-11e9-aca8-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"\frac { 7 : 1 \frac { 3 } { 4 } } { \frac { 7 } { 4 } : \frac { 7 } { 4 } = \frac { 7 } { 4 } \times \frac { 4 } { 7 } = \frac { 2 8 } { 7 } }" ,7a1e191a-e545-4ea6-96b9-e9fe2bda97d2__mathematical-expression-and-equation_2.jpg
"x ^ { 4 } + \frac { 3 } { 2 \cdot 7 } x , ^ { 3 } + \frac { 2 } { ( 2 \cdot 7 ) ^ { 2 } } x , ^ { 2 } + \frac { 6 } { ( 2 \cdot 7 ) ^ { 3 } } x , - \frac { 1 4 8 \cdot 6 } { ( 2 \cdot 7 ) ^ { 4 } } = 0" ,7aff88d8-b934-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"H = \frac { \rho \prime \prime } { g } V . 1 0 ^ { - 3 }" ,7b9c7578-f4a5-4fb6-8d55-faf8703b9221__mathematical-expression-and-equation_0.jpg
"O = 1 1 0 - \frac { 1 0 0 - 0 . 5 } { 2 } = 6 0 . 2 5 \mathrm { c m }" ,7c567d05-8916-bc71-c9ca-dae864599c4e__mathematical-expression-and-equation_1.jpg
"R \prime - \cot R = \frac { 2 \sin \frac { a } { 2 } \cos \frac { b + c } { 2 } } { k }" ,7c8889eb-100e-4090-bfff-bc69e25531cd__mathematical-expression-and-equation_11.jpg
"\frac { a \in \phi a a \in \psi } { \phi \cap \psi \neq \emptyset }" ,7cf08415-6928-4ea7-882d-4528c5e9930c__mathematical-expression-and-equation_3.jpg
"\pi = 3 . 1 4 1 5 9 2 6 5 3 6" ,7d234d3a-170b-4200-8b2c-421ea3924a3d__mathematical-expression-and-equation_13.jpg
"I = 3 \log 0 . 9 8 + 5 . 1" ,7d385cfc-282d-4613-bc19-7720f1cfcc7c__mathematical-expression-and-equation_1.jpg
"R r = P p + Q q" ,7e653310-0d86-11e8-8ee8-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"B _ { x } - C _ { x } - M _ { x } = - A _ { x } q _ { x } - \{ \frac { 1 - q _ { x } } { q _ { x } } \log ( 1 - q _ { x } ) \} ( B _ { x } - C _ { x } )" ,7f028452-cc77-4b0c-b9fa-a94e631c2707__mathematical-expression-and-equation_9.jpg
"K _ { 1 } ^ { \gamma , \sigma , \sigma _ { 0 } , \lambda } ( v ) \le c o n s t . ( 1 + v ^ { 2 } ) ^ { - \frac { \sigma } { 2 } } \exp ( - \lambda v ^ { 2 } ) \times" ,7f0ab50b-c9c0-4591-bc08-6b83f170d868__mathematical-expression-and-equation_8.jpg
"\mathfrak { S } = \frac { k } { 2 \mathfrak { A } \mathfrak { B } } , \mathfrak { A } = [ 3 + 2 \frac { b } { r } ( 2 + 2 \sec \frac { a } { 2 } + 5 \tan \frac { a } { 2 } ) ]" ,7f54a4ea-37aa-4bd6-8e04-57566866b3a7__mathematical-expression-and-equation_8.jpg
"[ \frac { u ^ { 2 } } { a ^ { 4 } } + \frac { v ^ { 2 } } { b ^ { 4 } } + \frac { w ^ { 2 } } { c ^ { 4 } } ] [ \cos \omega ^ { 2 } + \cos \pi ^ { 2 } ] - [ \frac { v } { b ^ { 2 } } \cos \pi - \frac { w } { c ^ { 2 } } \cos \omega ] ^ { 2 } = \frac { u ^ { 2 } } { a ^ { 4 } }" ,7fdb0802-53a9-449b-9a5c-d4954fc2d3a0__mathematical-expression-and-equation_6.jpg
"F ( x + 2 \pi ) - F ( x ) = \phi ( x )" ,80655160-e3d6-4c6b-a8ea-f79ce93455c1__mathematical-expression-and-equation_2.jpg
"S _ { 5 } = 5 0 , 3 1 1 + \frac { 5 + 5 } { 9 . 3 4 2 \cdot 7 . 8 6 9 } [ \frac { 1 5 1 0 \cdot 6 } { 4 } ( 6 1 . 6 5 - 1 8 . 3 2 5 - 8 . 3 2 5 ) - 2 1 2 . 1 3 2 4 ( 9 . 3 4 2" ,81519b53-afa8-4c1c-8cab-e5395fd3472d__mathematical-expression-and-equation_16.jpg
"[ i k . r ] = [ i k . ( r - 1 ) ] - \frac { [ r i . ( r - 1 ) ] } { [ r r . ( r - 1 ) ] } [ r k . ( r - 1 ) ]" ,81817a1a-e2e4-0667-e293-1102b62257e9__mathematical-expression-and-equation_5.jpg
"\frac { h } { l } \cdot \frac { c } { x } = \operatorname { t g } ( 0 0 1 : h h l" ,8185e3f0-0f1c-11de-8858-0030487be43a__mathematical-expression-and-equation_10.jpg
"v _ { 0 } ^ { 2 } . \frac { d ^ { 3 } W } { d s ^ { 2 } . d t } = \frac { 2 U _ { 1 } } { \tau }" ,81f6ff5d-59f2-4cfe-903d-aa89afef047b__mathematical-expression-and-equation_5.jpg
"e ^ { \frac { 2 K \pi l } { p } } = ( e ^ { \frac { K \pi i } { p } } ) ^ { 2 } = ( \cos \frac { K \pi } { p } + i \sin \frac { K \pi } { p } ) ^ { 2 } = \cos ^ { 2 } \frac { K \pi } { p } +" ,82856d60-eec1-11e6-8d33-005056825209__mathematical-expression-and-equation_7.jpg
"= ( A ^ { 2 } - B ^ { 2 } ) \cos ^ { 2 } \phi + B ^ { 2 }" ,82e8c5df-d311-4fe4-9ce5-d1e9174ffeb8__mathematical-expression-and-equation_3.jpg
"R _ { 1 } = Z ^ { - 1 } L" ,82ff032a-d71d-46a5-86f5-52fc3d7d1149__mathematical-expression-and-equation_4.jpg
"\psi _ { 2 } ( x ) = ( \frac { \psi \prime _ { 1 } , x } { 1 . 2 . \phi \prime x } ) ; ( \psi _ { 3 } ( x ) = ( \frac { \psi \prime _ { 2 } x } { 1 . 2 . 3 . \phi \prime \prime x } )" ,845e8017-bf5b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg
"R e g . M B V I , p . 6 7 5 n . 1 2 6 8 . - [ Z ] ." ,85106490-c357-11e0-8bdc-0030487be43a__mathematical-expression-and-equation_0.jpg
"A = 6 \cdot 2 0 \cdot 1 0 ^ { 2 3 } ," ,854fd580-5d99-11e6-9dd6-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"d A _ { 2 } = f \omega _ { 1 } A _ { 0 } + \omega _ { 2 } A _ { 1 } - c \omega _ { 2 } A _ { 2 } ;" ,856ff630-5484-45bb-9d84-1ac60c8975e6__mathematical-expression-and-equation_15.jpg
"\frac { v } { u } = \frac { \sin y } { \cos y - 1 } = - \cot \frac { y } { 2 } \text { d a h e r } V = \frac { \pi } { 2 } + \frac { y } { 2 }" ,87e32180-e348-11e8-9445-5ef3fc9bb22f__mathematical-expression-and-equation_21.jpg
"= \lambda _ { m } v _ { m } \frac { v _ { m } + v _ { m - 1 } - v _ { m } + v _ { m - 1 } } { ( v _ { m } - v _ { m - 1 } ) ( v _ { m } + v _ { m - 1 } ) } = \frac { 2 \lambda _ { m } v _ { m - 1 } v _ { m } } { ( v _ { m } - v _ { m - 1 } ) ( v _ { m } + v _ { m - 1 } ) }" ,88377de6-6c0f-4c36-8b4e-1e240dfd66f0__mathematical-expression-and-equation_3.jpg
"\hat { h } _ { m } = h _ { s } - \eta ." ,8879a770-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_2.jpg
"\frac { \partial \sigma _ { 1 } } { \partial \sigma _ { x } } = l _ { 1 } ^ { 2 } + 2 [ l _ { 1 } \frac { \partial l _ { 1 } } { \partial \sigma _ { x } } \sigma _ { x } + l _ { 2 } \frac { \partial l _ { 2 } } { \partial \sigma _ { x } } \sigma _ { y } + l _ { 3 } \frac { \partial l _ { 3 } } { \partial \sigma _ { x } } \sigma _ { z } +" ,8881cb40-4ffd-4353-bab7-80f001a58b02__mathematical-expression-and-equation_2.jpg
"\frac { 2 } { \sqrt { \pi } } \int _ { 0 } ^ { n h p } e ^ { - t ^ { 2 } } d t ;" ,89c7f09f-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_0.jpg
"- z R _ { n }" ,89c83f42-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_21.jpg
"c ^ { 2 } x ^ { 2 } = \eta ^ { 2 } [ x ^ { 2 } + c ^ { 2 } x ^ { 2 } + y ^ { 2 } + 2 c y z + c ^ { 2 } z ^ { 2 } ]" ,89c8b3f3-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_8.jpg
"\delta z = d z = \frac { d z } { d t } d t" ,89c90264-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_4.jpg
"\mathcal { L } \rho _ { n , 1 } = 1" ,8a5aec70-7aa3-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg
"\begin{array} { c c c c c c c } a & b & c & d & e & f & g \\ 0 & \frac { 1 } { 3 } & \frac { 1 } { 2 } & \frac { 2 } { 3 } & 1 & 2 & \infty \end{array}" ,8ad25960-3947-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"P _ { E } = p \cdot \Delta T / ( \vec { E } ^ { T } \cdot \vec { \Gamma } ^ { * } ) ( \vec { \Gamma } ^ { T } \cdot \vec { E } ^ { * } )" ,8b069a41-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\Sigma \Delta ^ { 2 } = ( M - M _ { 1 } ) ^ { 2 } + ( M - M _ { 2 } ) ^ { 2 } \dots ( M - M _ { N } ) ^ { 2 }" ,8b5166ba-a679-11e6-adc0-d485646517a0__mathematical-expression-and-equation_0.jpg
"A _ { 1 } = 9 3 7 + 5 0 7 + [ ( 4 0 8 0 + 2 2 0 6 ) ( 6 1 . 6 5 - 3 . 8 2 5 ) + 4 ( 4 9 0 0 + 2 6 5 0" ,8bea8d32-0b89-4489-92a2-8dc2df1ace7a__mathematical-expression-and-equation_9.jpg
"\theta \prime \prime = \psi + N \prime \prime" ,8c84de30-0b4e-11e4-a8ab-001018b5eb5c__mathematical-expression-and-equation_8.jpg
"| = a b \prime c \prime \prime + a \prime b \prime \prime c + a \prime \prime b c \prime - a \prime \prime b \prime c - a b \prime \prime c \prime - a \prime b c \prime \prime" ,8c9f9e50-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_9.jpg
"Y = b _ { 1 } + b _ { 2 } + b _ { 3 } = 0 . 0 0 8 9 u ^ { 3 } \log \text { n a t } \frac { 1 9 } { 1 9 - v } + 0 . 0 0 0 8 2 2 u ^ { 3 } ( v ^ { 2 } - 2 ) \\ Y = + 0 . 0 1 3 5 4 \log \text { n a t } \frac { 1 9 + \mathfrak { R } } { 1 4 } + 0 . 0 0 1 2 5 ( 2 5 - \mathfrak { R } ^ { 2 } )" ,8d0bb4c4-5ea3-4b39-b47f-0421296045a0__mathematical-expression-and-equation_11.jpg
"S _ { 1 } > S _ { 3 } > S _ { 5 } > S _ { 7 } \dots ," ,8d522570-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_20.jpg
"\frac { p \prime \prime } { q \prime \prime } = \frac { n p \prime + p } { n q \prime + q }" ,8d66e851-22b1-11ec-af09-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"T = 1 . 6 4 3" ,8e3e6ac9-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_5.jpg
"\frac { 1 } { p _ { y } } = [ \beta \beta ]" ,8e3e9229-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_9.jpg
"c = m \sqrt { \omega } [ ( 1 3 ) ( 0 2 ) ( 2 4 ) ( 4 0 ) ] ^ { \frac { 1 } { 4 } }" ,8e4270b9-9f68-4da3-bdba-909246eedaea__mathematical-expression-and-equation_14.jpg
"x \cos \phi + y \sin \phi - 2 r \sin \phi \cos \phi = 0" ,8e512500-7ad7-11e8-9690-005056827e51__mathematical-expression-and-equation_9.jpg
"a _ { i } = l _ { i } - X = l _ { i } - x + x - X = l _ { i } - x + F _ { 2 } ," ,8ecce6e0-ee57-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg
"H = \frac { a + n } { n } \cdot \frac { 1 } { 1 0 . 0 0 0 }" ,8f03e9ca-7da1-4cb8-9fa8-6d769b8420c8__mathematical-expression-and-equation_1.jpg
"\mu \mu ( = 0 . 0 0 1 \mu ) = 1 . 1 0 ^ { - 7 }" ,8f0b57d0-d5e1-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_5.jpg
"( \frac { d x \prime } { d x } ) _ { u }" ,8f494140-76ad-11e4-9605-005056825209__mathematical-expression-and-equation_7.jpg
"A l = A l _ { o } + d A l" ,8fb8d7db-b9f4-11e1-6101-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\dot { u } _ { 2 } = - \frac { 1 } { L } ( E u _ { o } - p ) \exp ( - t / T )" ,9033ad63-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"u = \frac { ( s - p ) ^ { 2 } } { 2 L s _ { 0 } } + \frac { s - p } { E }" ,9033ad8f-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_15.jpg
"- z \le u _ { 1 } \le + z" ,9033ada8-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"s \prime _ { 2 } = \min z \prime = s \prime _ { 2 }" ,9033adae-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ 2 ( u x - y z ) h + 2 ( u y - x z ) i + 2 ( u z + x y ) k" ,90612a28-cae8-45b3-9b19-303280e547c0__mathematical-expression-and-equation_14.jpg
"u = u _ { 1 } \pm u _ { 2 } \pm u _ { 3 }" ,917104d0-ee57-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg
"u = 3" ,91a06bf0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg
"\Delta = 1 / k _ { i } = c / ( n _ { i } \omega ) = ( 2 \pi ) ^ { - 1 } c / ( n _ { i } f )" ,91abf256-100f-4a1e-bf0a-5cd1e8cfe5a4__mathematical-expression-and-equation_7.jpg
"( 2 2 + 3 1 + 1 0 ) \text { d n í } = 6 3" ,91ee2570-1012-11e9-91df-005056825209__mathematical-expression-and-equation_0.jpg
"\frac { \delta ^ { 2 } n } { \delta r ^ { 2 } } + \frac { 2 } { r } \cdot \frac { \delta n } { \delta r } - \frac { n } { L _ { 2 } } = 0" ,923c4e35-b9f4-11e1-6101-001143e3f55c__mathematical-expression-and-equation_1.jpg
"= \delta - 0 . 6 \delta" ,923cc630-e953-11e2-9439-005056825209__mathematical-expression-and-equation_9.jpg
"u _ { z } = 0" ,92efa340-2578-45fd-aa43-dc63fcf5ae05__mathematical-expression-and-equation_8.jpg
"z _ { 2 } = ( R ^ { 2 } \cos ^ { 2 } \chi + 2 R H + H ^ { 2 } ) ^ { 1 / 2 } - ( R ^ { 2 } \cos ^ { 2 } \chi + 2 R h + h ^ { 2 } ) ^ { 1 / 2 } ." ,9346552a-024d-4f94-ad49-b6b941531d2a__mathematical-expression-and-equation_5.jpg
"A n \times n B = A D : A B" ,94ac9e8b-c2d6-11e7-bf53-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"( p \And q ) \rightarrow q" ,94e37e8a-b8ca-4417-9779-cfce3f4f0626__mathematical-expression-and-equation_14.jpg
"q \in \{ 0 , 1 , \dots \}" ,95547c27-bd12-4d2a-9c7e-b06c036af80b__mathematical-expression-and-equation_12.jpg
"w = \frac { d k } { d s } = \frac { 2 4 . y } { ( 1 + 4 x ) ^ { 3 } }" ,958321b3-2983-4410-b805-a3d8dea7b22c__mathematical-expression-and-equation_3.jpg
"= - \frac { \sigma _ { r } ( z ) } { \sigma ( z ) } [ 1 - \frac { \sigma _ { s } ^ { 2 } ( z ) } { \sigma _ { t } ^ { 2 } ( z ) } ]" ,958e5f52-06ec-441b-9a13-03a8f5422332__mathematical-expression-and-equation_0.jpg
"p _ { 1 } = \frac { a _ { 1 } } { v } , p _ { 2 } = \frac { a _ { 2 } } { v } , \dots p _ { n } = \frac { a _ { n } } { v } ." ,95cf74a0-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_1.jpg
"v = \frac { u } { x } \sqrt { A ^ { 2 } + B ^ { 2 } } ;" ,95ff6b0e-4334-11e1-1331-001143e3f55c__mathematical-expression-and-equation_3.jpg
"n _ { 2 } ^ { 2 } = n , \text { č i l i } n _ { 2 } = \sqrt { n } ;" ,9686c34e-4334-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { \partial ^ { 2 } \bar { e } _ { r r } } { \partial \theta ^ { 2 } } - 2 \frac { \partial ^ { 2 } ( r \bar { e } _ { r \theta } ) } { \partial r \partial \theta } + \frac { \partial ^ { 2 } ( r ^ { 2 } \bar { e } _ { \theta \theta } ) } { \partial r ^ { 2 } } - r \frac { \partial \bar { e } _ { r r } } { \partial r } + 2 \bar { e } _ { \theta \theta } - \frac { 2 } { r } \frac { \partial ( r ^ { 2 } \bar { e } _ { \theta \theta } ) } { \partial r } = 0" ,97198cfd-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\phi _ { 1 } = \phi _ { 2 } = \arctan \frac { v _ { 0 } ^ { 2 } } { g x } = \arctan \frac { 2 h } { x }" ,97e32dc0-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_12.jpg
"\Delta \Theta _ { i } \text { e t } S \prime \Delta \Theta _ { i }" ,98269950-3064-11e9-bda0-005056a2b051__mathematical-expression-and-equation_0.jpg
"\rho = - \frac { 3 e } { 4 \pi R ^ { 3 } } v" ,98a5f960-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_10.jpg
"l _ { 2 3 } = \frac { J _ { 2 0 } - J _ { 1 0 } } { \hbar \omega } a u = \frac { \gamma } { \beta }" ,98a5f966-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"+ \frac { 4 } { \pi ^ { 2 } } \frac { d _ { 1 } } { d _ { 2 } } \sum _ { k = 1 } ^ { \infty } \frac { \eta _ { 2 k - 1 } } { ( 2 k - 1 ) ^ { 3 } } t h ( 2 k - 1 ) \frac { \pi } { 2 } \frac { d _ { 2 } } { d _ { 1 } } ;" ,98a5fa9b-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"E = E \prime = \frac { 1 } { 2 } ( E + E \prime ) = J t" ,98c8f458-6b5d-4805-8c41-e7b8a2d0e03d__mathematical-expression-and-equation_0.jpg
"V \sqrt { | \dot { x } | } [ \frac { 1 } { \sqrt { | \dot { x } | } } ] \prime \prime + q ( x ) \dot { x } ^ { 2 } = Q ( T )" ,990d60fe-2ffe-4f04-82f4-175a5681f56d__mathematical-expression-and-equation_3.jpg
"w _ { i j } ^ { ( 3 ) } = \frac { 2 \pi } { \hbar } \sum _ { \sigma } \sum _ { \sigma \prime } ( \hbar \omega ( \sigma ) ) ( \hbar \omega ( \sigma \prime ) ) S _ { j i } ^ { ( 2 ) } ( \sigma ) S _ { j i } ( \sigma \prime )" ,9979c595-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg
"m \ddot { y } = e E" ,9979c6ad-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { 1 } { 2 } ) y y = [ ( 0 , - 1 ) + ( 1 , - 1 ) + ( 0 , 2 ) + ( 1 , 2 ) ]" ,99f4227c-6527-4112-a0a6-38fbb0d2f5e8__mathematical-expression-and-equation_5.jpg
"n \prime _ { i } = 2 m - 2 \mu - 2" ,9a13d593-7500-4120-9d11-89894ba79824__mathematical-expression-and-equation_17.jpg
"w = a _ { 0 } + a _ { 1 } z + a _ { 2 } z ^ { 2 } + \dots + a _ { n } z ^ { n } + \dots" ,9aa863b0-7d97-11e7-921c-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg
"\tau = \tau _ { 0 } \cos \phi + \beta \sin \phi" ,9b285ed0-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_5.jpg
"S \sim 1 0 \delta ^ { 2 } r _ { 0 } ^ { 2 }" ,9b285ed4-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"t _ { R } \prime e ^ { i \partial _ { R \prime } } . t _ { L } \prime e ^ { i \partial _ { L \prime } } - r _ { R } \prime e ^ { i \delta _ { R \prime } } . r _ { L } \prime e ^ { i \delta _ { L \prime } } = 1" ,9b285efd-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_12.jpg
"( l _ { 0 } w _ { I I } ) = 2 \rho w [ Z - m ]" ,9b58782f-1bb9-47e9-baa6-1ac5ab23ce1f__mathematical-expression-and-equation_6.jpg
"\frac { \omega _ { 3 } - \omega _ { 2 } } { \omega _ { 4 } - \omega _ { 2 } } = - \frac { z _ { 4 } } { z _ { 3 } } , \frac { \omega _ { 4 } - \omega } { \omega _ { 6 } - \omega } = - \frac { z _ { 6 } } { z _ { 5 } }" ,9b819780-0fca-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"\dots + [ \Delta i , q ^ { N ( f ) } _ { ( K - 1 ) } ] ^ { [ 0 , 1 ] } _ { [ ( K ) ] } ( 1 + i ) ^ { t + 1 - ( K ) } \} -" ,9e9bd451-0e5a-11eb-b87e-005056a54372__mathematical-expression-and-equation_3.jpg
"v = \sqrt { 2 \times 1 0 \times 4 5 } = \sqrt { 9 0 0 } = 3 0" ,9ec2c690-7806-11e5-a2d8-005056825209__mathematical-expression-and-equation_3.jpg
"\frac { ( n - n _ { 1 } ) \frac { S } { n } } { ( s - n _ { 2 } \delta ) t } > \frac { ( n - n _ { 1 } - n _ { 2 } ) \frac { S } { n } } { ( s - n _ { 3 } \delta ) t }" ,9f7cf4a0-e953-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg
"D = 0 , 1 4 + 2 \kappa _ { g l } t _ { g l } \mu _ { g l } = 0 , 1 4 + 2 \cdot 1 , 5 \cdot 0 , 0 1 5 \cdot 0 , 6 = 0 , 1 6 7 m" ,9fffccfe-b529-4466-aa0b-ba75aef74a9e__mathematical-expression-and-equation_5.jpg
"- \frac { 2 } { 3 } u _ { e } \Theta \frac { \partial n _ { e } } { \partial z } - \frac { 2 } { 3 } N _ { e } \Theta \frac { \partial u _ { e } } { \partial z } - n _ { e } \sum _ { k } \alpha _ { k 0 } q _ { 0 } U _ { k } - \Theta \frac { \delta N _ { e } } { \delta t }" ,a09e13ce-4334-11e1-1121-001143e3f55c__mathematical-expression-and-equation_6.jpg
"C _ { 6 } H _ { 5 } \cdot P ^ { I I I } = P ^ { I I I } \cdot C _ { 6 } H _ { 5 }" ,a0d76f44-e44a-4aaa-a6ee-9b8d76b16759__mathematical-expression-and-equation_8.jpg
"\langle u _ { n k } | \mathrm { g r a d } _ { k } H ( \mathbf { k } ) | u _ { n k } \rangle = \mathrm { g r a d } _ { k } \epsilon _ { n } ( \mathbf { k } )" ,a2363f9c-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"c = \frac { 1 } { x } \{ D ( v _ { 2 } - w _ { x } ) - D ( v _ { 1 } - w _ { x } ) + w _ { x } [ S ( v _ { 2 } - w _ { x } ) - S ( v _ { 1 } - w _ { x } ) ] \}" ,a2a081e0-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"\sinh x = \sqrt { \cosh ^ { 2 } x - 1 } ," ,a2d715c0-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"v _ { z i } = k _ { K } \cdot v \prime _ { z i }" ,a39ac456-8eef-48b1-809b-0b0a9deeaf1b__mathematical-expression-and-equation_4.jpg
"c _ { I } = 1 5 k N / m ^ { 2 }" ,a45fb544-b9f4-11e1-2544-001143e3f55c__mathematical-expression-and-equation_10.jpg
"= t x - \int \frac { a d t } { \sqrt { t ^ { 2 } - 1 } }" ,a51bfcb0-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 7 0 }" ,a5322f7e-5030-43d2-9e80-4dd05033639e__mathematical-expression-and-equation_12.jpg
"1 c m ^ { 3 } = 0 . 0 0 1 d m ^ { 3 }" ,a558aa20-dbae-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_10.jpg
"( a - f _ { 1 } ) ( b - f _ { 2 } ) = f _ { 1 } f _ { 2 }" ,a592f2a0-8655-11e3-8cd6-005056825209__mathematical-expression-and-equation_5.jpg
"= \int _ { a } a ^ { 2 } . \sinh ^ { 2 } u . d u ," ,a679df00-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_14.jpg
"\frac { d ^ { 4 } y } { d x ^ { 4 } } = - \frac { C b } { E _ { 1 } J _ { 1 } } \cdot y" ,a6ba1fe9-3240-4472-8e02-cc6dcaf65316__mathematical-expression-and-equation_1.jpg
"\frac { n _ { 1 } } { n _ { 2 } } \rho _ { 1 } V _ { 1 } = P _ { 1 } , \rho _ { 2 } V _ { 2 } = P _ { 2 } , \frac { n _ { 3 } } { n _ { 2 } } \rho _ { 3 } V _ { 3 } = P _ { 3 } \dots 8" ,a6e92ba7-335b-11e9-8d85-00155d012102__mathematical-expression-and-equation_13.jpg
"+ \kappa _ { e } \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { k + 1 } \frac { ( n + k ) ! } { ( k + 1 ) ! ( n - 1 ) ! } \lambda _ { 1 , n + k + 1 } \epsilon ^ { n + k + 1 } \alpha _ { e , n } ^ { ( 1 ) } +" ,a75bbbaf-292e-43b6-844d-80e63ae36524__mathematical-expression-and-equation_12.jpg
"2 \sqrt { g . b ( 1 - \cos \phi ) } = 2 \sin \frac { \phi } { 2 } . \sqrt { 2 g . b }" ,a7642cd4-cc6d-4550-865a-bf108183d1dd__mathematical-expression-and-equation_7.jpg
"P \frac { N - 1 } { D } = p _ { 1 } \frac { n _ { 1 } - 1 } { d _ { 1 } } + p _ { 2 } \frac { n _ { 2 } - 1 } { d _ { 2 } } + p _ { 3 } \frac { n _ { 3 } - 1 } { d _ { 3 } } \dots" ,a80fe189-63df-11e8-ae35-00155d012102__mathematical-expression-and-equation_0.jpg
"c _ { m } = c _ { m - 2 } + 4 \frac { u _ { m - 1 } g _ { m - 1 } } { p _ { m - 1 } }" ,a882a785-ae87-4d45-8ba4-52cdb63669c8__mathematical-expression-and-equation_2.jpg
"1 5 8 0 - 8 0 9" ,a90cf213-2e37-4669-84e8-0b57fc4274c2__mathematical-expression-and-equation_9.jpg
"\alpha _ { 1 } \doteq 2 8 ^ { \circ } 2 0 \prime" ,aacae850-d035-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_17.jpg
"\cos \eta _ { 2 } \pm \sqrt { \frac { 1 + c _ { 2 } } { 2 + a _ { 2 } + c _ { 2 } } } = \pm \sqrt { \frac { 1 + C m } { 2 + ( A + C ) m _ { 2 } } }" ,aaf257c1-7ea5-482c-86fb-e2d625fe4668__mathematical-expression-and-equation_3.jpg
"F _ { ( d ) } = k _ { ( d ) } \gamma _ { g } [ \frac { 1 } { r _ { c } } - \frac { 1 } { r _ { g } } \pm \frac { 3 \phi _ { p } } { 4 r _ { p } } ]" ,ab2aba9a-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( Z _ { i e } - 1 ) ( \sigma + 1 ) + \kappa F P _ { i e } = \frac { 1 } { \gamma _ { i } Z _ { i i } }" ,ab2abc25-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_7.jpg
"C D = \Delta E = O B" ,acef22b0-e3d1-11e3-bbd5-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg
"\theta _ { 3 } = \beta g a _ { 3 } ( \Delta T \prime + q _ { 3 } ) / I _ { 2 } \lambda \mu" ,ad88592e-4334-11e1-7459-001143e3f55c__mathematical-expression-and-equation_7.jpg
"U _ { E B } = \frac { k T } { e } \ln ( U _ { 0 } / \alpha I _ { 0 } ) - \ln R _ { s } ]" ,ad885a9c-4334-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\Delta g \prime = ( g - \gamma ) + \Delta g _ { t } = \Delta g _ { B + t } + 2 \pi f \delta H" ,adb8bc0f-367b-44a9-90e1-1a3a441cfb31__mathematical-expression-and-equation_2.jpg
"z = \frac { \phi } { \psi } = \frac { p } { P }" ,ade41470-35eb-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"+ 0 . 1 3 | + 0 . 5 3 | - 0 . 0 4 | + 0 . 3 4 | - 0 . 1 0 | + 0 . 5 2 | + 0 . 3 2 | + 0 . 1 0 | - 0 . 0 4 | + 0 . 5 4 | + 1 . 1 1 | +" ,adf9aa92-7a2a-4be3-a950-2b9e2c73915f__mathematical-expression-and-equation_0.jpg
"\begin{array} { c c } p + 1 & m \\ p & m _ { p } - m \\ p - 1 & \mu _ { p - 1 } \\ \vdots & \vdots \\ 1 & \mu _ { 1 } \\ 0 & \mu _ { 0 } \end{array} \begin{array} & + \Sigma ( \mu _ { p } - m _ { p } + m _ { p - 1 } ) \dots & ( \mu _ { 1 } - m _ { 1 } + m _ { 0 } ) \\ & m _ { p 1 } & m _ { 0 } \end{array}" ,ae03b230-ff5d-11e9-baca-005056825209__mathematical-expression-and-equation_1.jpg
"\frac { A - y _ { 1 } } { A - y _ { 2 } } = \frac { A - y _ { 2 } } { A - y _ { 3 } }" ,ae0e1560-cf87-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_4.jpg
"\frac { 0 , 0 0 1 2 9 3 2 } { 1 + 0 , 0 0 3 6 7 t } \frac { b } { 7 6 0 }" ,ae94fbb0-ee5d-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"h _ { 0 } + \frac { 1 } { h _ { 1 } + \frac { 1 } { h _ { 2 } + \dots } }" ,aebefd47-25f6-4ba5-8f60-d3156fb5cb4f__mathematical-expression-and-equation_1.jpg
"C _ { x } = c \cos \alpha" ,aec3d0d0-0a78-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"\mathfrak { S } I ( a + b ) = \frac { \mathfrak { B } _ { 1 } s _ { 1 } ^ { 2 } ( S - s _ { 1 } ) ^ { 2 } } { 3 H J S } = ( I l \prime )" ,af16f910-421d-11e3-ac54-005056825209__mathematical-expression-and-equation_1.jpg
"\sum _ { p ^ { m } = q } ^ { \infty } f ( \frac { x } { p ^ { m } } )" ,afab5759-587f-4fb2-8221-4d8d22524f09__mathematical-expression-and-equation_1.jpg
"\Delta v _ { \_ } = \pm 1 , 2 7" ,afc204bd-f1e8-45ef-97a8-0f65574184a0__mathematical-expression-and-equation_4.jpg
"G ( \rho _ { 1 } , \rho _ { 2 } , \Delta \rho , \phi _ { 1 } \phi _ { 2 } \Delta \phi ) = \frac { 1 } { s ( 1 ) s ( 2 ) } \int _ { \phi _ { 1 } } ^ { \phi _ { 1 } + \Delta \phi } d \phi \int _ { \phi _ { 2 } } ^ { \phi _ { 2 } + \Delta \phi } d \psi \int _ { \rho _ { 1 } } ^ { \rho _ { 1 } + \Delta \rho } r d r \int _ { \rho _ { 2 } } ^ { \rho _ { 2 } + \Delta \rho }" ,aff80336-61e5-46af-8145-85c502b00026__mathematical-expression-and-equation_2.jpg
"\Pi = \sum _ { i = 1 } ^ { m } ( \frac { 1 } { 2 } ( r _ { r } ^ { ( j ) } ) ^ { T } ( \mathbf { E } ^ { ( j ) } ) ^ { T } \mathbf { K } ^ { ( j ) } \mathbf { E } ^ { ( j ) } r _ { r } ^ { ( j ) } + \frac { 1 } { 2 } ( r _ { r } ^ { ( j ) } ) ^ { T } ( \mathbf { E } ^ { ( j ) } ) ^ { T } \mathbf { K } ^ { ( j ) } \mathbf { F } ^ { ( j ) } r _ { c } +" ,b0179d35-3ded-443d-977b-9d3fc597008e__mathematical-expression-and-equation_6.jpg
"\epsilon = \epsilon _ { 0 } + \dot { \epsilon } _ { s } + \epsilon _ { t } [ 1 - \exp ( - \frac { t } { \tau \prime } ) ]" ,b03f2523-f752-4fe7-bcdb-f7272fae1eef__mathematical-expression-and-equation_0.jpg
"F _ { y } = F _ { y k } + F _ { y l } + F _ { y m }" ,b0d11137-7c33-4f95-8671-98987db7a5db__mathematical-expression-and-equation_7.jpg
"C ( \bar { \epsilon } ^ { p } ) = \frac { d N _ { t } } { d \bar { \epsilon } ^ { p } }" ,b19900df-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\chi _ { z z } = \frac { [ N q ^ { 2 } / ( \epsilon _ { v a c } m ) ] } { \omega _ { 0 } ^ { 2 } - \omega ^ { 2 } - i \omega \Gamma }" ,b19901c8-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg
"A D = A M \tan y" ,b1b635f0-bc8f-11e2-9592-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg
"S = \sigma T ^ { \alpha - 1 }" ,b20f8a70-3f08-11e6-8746-005056825209__mathematical-expression-and-equation_7.jpg
"+ i R l m \Psi ( m , n , t ) - \alpha ^ { 2 } ( m , n ) \Theta ( m , n , t )" ,b267e8d9-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_15.jpg
"R _ { 1 } = \sqrt { K _ { 1 } \sqrt { \frac { 9 ( m ^ { 2 } K _ { 2 } - n ^ { 2 } K _ { 1 } ) } { \pi ^ { 2 } ( n ^ { 2 } K _ { 1 } ^ { 2 } - m ^ { 2 } K _ { 2 } ^ { 2 } ) } } } = 2 4 , 3 6 6 \dots \mathrm { c m }" ,b2aff5cd-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_4.jpg
"k = \frac { 3 } { \pi } K = 9 . 0 2 9 8 . . d m ^ { 3 } ." ,b2aff5d3-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"K = \frac { 1 } { 3 } ( 4 S - M ) v = 1 5 , 7 0 6 4 7 d m ^ { 3 } ." ,b2b01ceb-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_10.jpg
"\frac { d ^ { 2 } u } { d z \prime ^ { 2 } } - ( \frac { h ^ { 2 } p ^ { 2 } } { c ^ { 2 } } \cos ^ { 2 } z \prime - A ) u = 0" ,b2c50bf7-4d6a-470f-8fda-738c7a9dba98__mathematical-expression-and-equation_2.jpg
"\Delta ^ { 2 } y = \Delta y _ { k - 1 } - \Delta y _ { k }" ,b45a421c-e2fb-4561-b918-03209f485d39__mathematical-expression-and-equation_6.jpg
"A x ^ { 2 } + B x y + C y ^ { 2 } + ." ,b49e87a5-c04a-11e6-8cf4-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\sum _ { \substack { j \\ P _ { j } \in \mathcal { X } _ { l } ^ { k } } } x _ { j } ^ { k } = x _ { j } ^ { * k }" ,b5893fae-4ddb-4e94-b483-aa876d0182b6__mathematical-expression-and-equation_7.jpg
"O = 4 0 0 \text { k o r }" ,b63df2b0-e3d1-11e3-bbd5-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg
"J ( z ) \equiv F _ { 1 } ( z ) \exp [ \int q ( a _ { 1 } + b ) d z ]" ,b63e938b-dfe0-4e9b-82ba-c007c9ba1284__mathematical-expression-and-equation_0.jpg
"\epsilon _ { M } = \frac { 1 } { 3 } ( \dot { \epsilon } _ { 1 1 } + \dot { \epsilon } _ { 2 2 } + \dot { \epsilon } _ { 3 3 } )" ,b6c0b014-e63f-4ec7-870a-ac63862bb168__mathematical-expression-and-equation_3.jpg
"d ( \sigma _ { n + 1 } ^ { 1 } , \sigma _ { n + 1 } ^ { 2 } ) \le d ( \sigma _ { n } ^ { 1 } , \sigma _ { n } ^ { 2 } )" ,b6d6924b-26a8-4ec8-b0cb-041e077f9b97__mathematical-expression-and-equation_1.jpg
"f _ { D } = - r _ { D } i _ { D }" ,b6e537c2-48d3-425a-971a-95c328227e27__mathematical-expression-and-equation_9.jpg
"\frac { B } { \mu } [ 1 - \frac { p _ { 2 } } { p _ { 1 } } + \frac { 1 } { \kappa - 1 } ( 1 - [ \frac { p _ { 2 } } { p _ { 1 } } ] ^ { \frac { \kappa - 1 } { \kappa } } ) ]" ,b7051290-4421-11e4-af1d-001018b5eb5c__mathematical-expression-and-equation_3.jpg
"\frac { M } { J } \le \frac { k \prime \prime } { e \prime \prime }" ,b7073bd2-e228-11e2-a0b3-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"\sin \phi _ { 0 } = a _ { 1 } ^ { 0 } : M" ,b724e18c-e097-4682-9633-a5b359a25b1f__mathematical-expression-and-equation_3.jpg
"\frac { \frac { a } { x } + \frac { a } { a + b } } { \frac { a } { x } - \frac { b } { a + b } } = \frac { a + b } { b }" ,b76fb110-369c-41e5-ad27-b9c6b34f03af__mathematical-expression-and-equation_5.jpg
"H _ { 1 } = \frac { 2 I _ { 1 } } { r } ." ,b8441740-0c73-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg
"\delta = \log \mu - \log m = \frac { c } { a ^ { 2 } \gamma C } [ q \cos ( \gamma s - q t ) - \frac { b n u } { r } \sin ( \gamma s - q t ) ] + T - \log m" ,b89d17bd-d665-4633-ba86-0f50eeee616f__mathematical-expression-and-equation_7.jpg
"x + \frac { [ p a b ] } { [ p a a ] } y = \frac { [ p a o ] } { [ p a a ] }" ,b8f37228-7979-40e4-8845-6c09ffa9028d__mathematical-expression-and-equation_2.jpg
"p = \pi d \text { u n d } q = \frac { \pi d ^ { 2 } } { 4 }" ,b93c0130-e83e-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_1.jpg
"\bar { b } _ { 1 3 } = \bar { r } _ { 1 3 } \frac { \bar { \sigma } _ { 1 } } { \bar { \sigma } _ { 3 } }" ,b9784fd0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"\frac { m \prime n \prime _ { 1 } - n \prime m \prime _ { 1 } } { m \prime _ { 2 } n \prime _ { 3 } - n \prime _ { 2 } m \prime _ { 3 } } = \frac { m n _ { 1 } - n m _ { 1 } } { m _ { 2 } n _ { 3 } - n _ { 2 } m _ { 3 } }" ,b97e9218-3225-4485-b74b-33796dff9aef__mathematical-expression-and-equation_3.jpg
"\text { P o s t o } l = \frac { 1 } { \rho }" ,bbc8e16d-b34f-41f1-94d2-e64e6f8062f7__mathematical-expression-and-equation_24.jpg
"+ 2 \epsilon _ { 3 1 } ^ { 2 } [ ( \epsilon _ { 3 3 } + \epsilon _ { 1 1 } ) ^ { 2 } - \epsilon _ { 3 3 } \epsilon _ { 1 1 } - \epsilon _ { 2 2 } ^ { 2 } ] + 1 2 \epsilon _ { 1 2 } \epsilon _ { 2 3 } \epsilon _ { 3 1 } ( \epsilon _ { 1 1 } + \epsilon _ { 2 2 } + \epsilon _ { 3 3 } )" ,bbe84160-f903-42b1-82a0-0fd0b770f4fb__mathematical-expression-and-equation_8.jpg
"\tau _ { 2 } = \frac { s _ { 2 } } { 2 r } \sqrt { \frac { l } { g } }" ,bc1902d0-0bb5-11e5-b309-005056825209__mathematical-expression-and-equation_3.jpg
"1 9 1 8 / - 2 3" ,bc73f8ee-443e-11eb-836c-00505684fda5__mathematical-expression-and-equation_18.jpg
"\alpha _ { 3 } x + \beta _ { 3 } y + \gamma _ { 3 } z = 0" ,bf758ff5-e361-4a9b-9810-147cfbd5cb88__mathematical-expression-and-equation_5.jpg
"\sqrt { n } . \frac { \partial S _ { n } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) } { \partial \beta } = \frac { 1 } { \sqrt { n } } \sum _ { i = 1 } ^ { n } s \prime _ { \beta } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) . I ( s _ { i } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) \le s _ { [ h _ { n } ] } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) )" ,bfb5e7d7-6892-4d86-8f88-5b2f69ec7479__mathematical-expression-and-equation_1.jpg
"W ^ { n e w } = W ^ { c u r r e n t } + \gamma ( \frac { 1 } { M } - W ^ { c u r r e n t } )" ,c02541cb-238d-44b9-8d21-b04b60eb06b2__mathematical-expression-and-equation_0.jpg
"0 . 4 0 0 : 0 . 6 0 0 = 0 . 3 5 2 : x" ,c0e8c0eb-e257-11e6-9504-001999480be2__mathematical-expression-and-equation_0.jpg
"\Gamma ( 1 + \sigma ) \zeta ( 1 + \sigma ) = \frac { 1 } { \sigma } + a _ { 1 } \sigma + a _ { 2 } \sigma ^ { 2 } + \dots" ,c11cfebc-1776-4411-a15a-19246ab32267__mathematical-expression-and-equation_3.jpg
"( \frac { a + b } { 2 b } ) + ( \frac { a + b } { 2 b } ) + ( 1 - \frac { a } { b } ) + 1" ,c15da0f1-4be8-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"- \frac { 1 } { 2 ^ { 2 } } \log \frac { b \prime ^ { 2 } } { b \prime _ { 3 } } - \dots ]" ,c1d0bcb0-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg
"\int _ { a } ^ { b } f ( x ) d x - \tilde { L } _ { n } | \le \frac { 1 1 n h ^ { 5 } } { 7 2 0 } \tilde { B } _ { 4 } = \frac { 1 1 L ^ { 5 } } { 7 2 0 n ^ { 4 } } \tilde { B } _ { 4 } , `" ,c1eef158-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d _ { i _ { 1 } } ^ { 2 } + \frac { 1 } { h } d _ { i _ { 2 } } ^ { 2 } + d _ { i _ { 3 } } ^ { 2 }" ,c1eef1b7-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { d ^ { 2 } G } { d y ^ { 2 } } \ge 0" ,c29cc596-045d-4be6-9040-3362f3b499a4__mathematical-expression-and-equation_7.jpg
"Z _ { s } = - 7 \lambda _ { s } \mu _ { s } \nu _ { s }" ,c3575fa3-e0a4-4c48-8b89-7141b022f2f6__mathematical-expression-and-equation_12.jpg
"\parallel u _ { h } \parallel _ { V } \le r _ { 0 } : = \zeta ^ { - 1 } ( \parallel g \parallel _ { V \prime } + \parallel F ( 0 ) \parallel _ { V \prime } )" ,c36e174a-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\eta = \frac { \omega } { \Omega _ { 0 } } , Q ^ { 2 } = \frac { k / m } { \Omega _ { 0 } ^ { 2 } } , q ^ { 2 } = \frac { g / l } { \Omega _ { 0 } ^ { 2 } }" ,c3d23e28-5417-4f0f-a737-9b561396e321__mathematical-expression-and-equation_3.jpg
"\hat { e } _ { w } ( \xi ) = \rho + \sigma \hat { z } ( \xi )" ,c42ecedc-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg
"g ( \xi _ { 0 } , t ^ { * } ) - \bar { g } ( \xi _ { 0 } ) = C \cos ( \omega ^ { * } t ^ { * } + \phi ( \xi _ { 0 } ) )" ,c4922dac-0d12-4348-9cdc-a1300a8df2b5__mathematical-expression-and-equation_9.jpg
"\sum _ { i = 1 } ^ { M } \frac { 1 } { W _ { k } } p _ { i k } t _ { i }" ,c4ed6480-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"x = \lambda ( \nu \tilde { \omega } \theta )" ,c537f01c-11b4-47c7-a9b2-6cb450422bdb__mathematical-expression-and-equation_9.jpg
"\tilde { A } = C ^ { T } A C" ,c5b7b829-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { 1 } { 2 } | w | _ { 1 } ^ { 2 } \le \parallel \nabla w - \beta \parallel _ { 0 } ^ { 2 } + \parallel \beta \parallel _ { 0 } ^ { 2 }" ,c5b7b854-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\parallel ( I _ { M } \eta ) \prime \prime \parallel _ { 0 , \infty , I } \le C _ { 2 }" ,c5b7b9fc-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { 1 3 0 . 2 0 0 \times 1 0 0 } { 6 0 0 . 0 0 0 + 1 0 0 . 0 0 0 } = 1 8 . 6 0 \% , \text { t . j . } 6 \%" ,c5c5bd7c-20ed-11ea-8e31-005056a54372__mathematical-expression-and-equation_0.jpg
"^ { n } D _ { u } v = \frac { \Gamma ( n + 1 ) } { \Gamma ( 1 ) \Gamma ( n + 1 ) } { } ^ { 0 } D _ { u } { } ^ { n } D _ { v } + \frac { \Gamma ( n + 1 ) } { \Gamma ( 2 ) \Gamma ( n ) } D _ { u } ^ { n - 1 } D _ { v }" ,c6123e97-3542-48e5-8c18-880bec6f71e5__mathematical-expression-and-equation_16.jpg
"\frac { \partial \Theta _ { * } } { \Theta _ { * } } = \frac { \log \Theta _ { * } \prime } { M } - 1 \Theta _ { * } { } ^ { 2 0 9 ) }" ,c62a6860-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"A = [ \begin{array} { c c } \alpha + \beta \delta & \beta \gamma \\ \delta & \gamma \end{array} ]" ,c681721f-e09b-11e1-1121-001143e3f55c__mathematical-expression-and-equation_1.jpg
"F . - i A" ,c6b58dff-8b76-43ec-81c0-c01d34a98241__mathematical-expression-and-equation_2.jpg
"Q + P \dddot { x } + M x ^ { 2 } + \dots + C x ^ { m - 2 } + B x ^ { m - 1 } + A x ^ { m }" ,c764d5f2-0844-696d-8412-87bf73fafc71__mathematical-expression-and-equation_11.jpg
"( 7 2 _ { 2 } - 7 3 . )" ,c78e0232-5417-4f0a-8d8c-95279914c707__mathematical-expression-and-equation_0.jpg
"v = \frac { I } { 4 k ( I + k ) } [ \mu ^ { 3 } + \mu ^ { 2 } + ( 4 k - 5 ) \mu + 3 ( 1 - 4 k ^ { 2 } ) ] ," ,c9270436-9d51-4277-af23-fbfb9e805d17__mathematical-expression-and-equation_7.jpg
"- 1 < \operatorname { R e } p < \frac { 3 } { 2 }" ,c95520c3-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\lim _ { x \rightarrow \infty } \frac { e ^ { - \sqrt { p x } } } { 2 \sqrt { p } } \int _ { 0 } ^ { x } p ( s ) e ^ { \sqrt { p s } } d s = 0" ,c95520d0-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { d u } { d \phi } = 2 N u + 2 f ( \phi )" ,c9552170-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"M _ { 3 } = s _ { 3 } \frac { J } { e } = 6 0 \times 1 . 7 5 h ^ { 3 } = 1 0 5 h ^ { 3 }" ,cc1c9b40-00cb-11eb-b636-005056825209__mathematical-expression-and-equation_4.jpg
"\ddot { x } = - \frac { \kappa ^ { 2 } } { k r ^ { 3 } } x" ,cc2caa17-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d c _ { i } ( = - \frac { 1 } { r _ { i } ^ { 2 } } d r _ { i } )" ,cc2caafb-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\lambda = \frac { \rho - \rho _ { + } } { \rho _ { + } }" ,cc2cab75-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"E O ^ { a } \leftrightarrow ( K _ { 1 } ^ { a } + K _ { 2 } ^ { a } + K _ { 3 } ^ { a } + \dots )" ,cc67c9cc-48e1-11e1-1232-001143e3f55c__mathematical-expression-and-equation_2.jpg
"1 1 , 3 9 6 2 \doteq 1 2 8" ,cd978668-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_13.jpg
"x _ { 0 } = y _ { 0 } = 0" ,ce766530-3d93-11e4-bdb5-005056825209__mathematical-expression-and-equation_9.jpg
"A _ { 1 } [ s h \beta \sin \beta + H ( c h \beta \sin \beta - s h \beta \cos \beta ) ] +" ,cf00ffd7-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\bar { \mathbf { U } } ( k - s ; 1 ) = - \bar { \mathbf { Z } } ( k - s ) \bar { \mathbf { I } } _ { v } ( k - s ; 1 )" ,cf00fff1-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"b = 0 , 0 8 8 ," ,cf010053-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { 2 } { 3 }" ,cf484d87-f38a-4d90-b46f-384fd07ff25c__mathematical-expression-and-equation_6.jpg
"\frac { 1 } { 3 } ( 1 8 ^ { h } + 2 ^ { h } + 1 0 ^ { h } )" ,cf6b8ef7-a986-11e1-2397-001143e3f55c__mathematical-expression-and-equation_0.jpg
"M \prime _ { n } = 1 4" ,d04a1ca2-27ee-490e-81ce-eef4a7930d16__mathematical-expression-and-equation_8.jpg
"\xi _ { 3 } = A _ { 9 , 1 0 }" ,d1decc50-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"= ( 1 + i ) . \sqrt { 2 } . [ E ( \frac { 1 } { 2 } \sqrt { 2 } ) - \frac { 1 } { 2 } K ( \frac { 1 } { 2 } , \sqrt { 2 } ) ] =" ,d1decd04-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_16.jpg
"\pi = \frac { 1 } { \pi } \text { r e s p . } \frac { 1 0 0 } { \pi }" ,d241d570-066a-11e8-9854-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"\Phi ( z ) = - \frac { 1 } { 2 \pi i } \int _ { L _ { 1 } } \frac { f _ { 1 } ( x + i ) } { x + i - z } d ( x + i ) + \Phi _ { 1 } ( z ) \text { f o r } z \text { i n } S" ,d295bfa2-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"B _ { 1 . 2 } + B _ { 3 , 4 } \equiv B _ { 7 , 8 } ( f , g ) - B _ { 5 , 6 }" ,d295c07b-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { U _ { N a } V } { P _ { N a } } = C l _ { N a }" ,d3257ae6-a672-11e6-adc0-d485646517a0__mathematical-expression-and-equation_0.jpg
"g _ { i j } ^ { ( k ) } = g _ { i j } ^ { ( k - 1 ) } - a _ { k i } ( a _ { k , k - 1 } g _ { k - 1 , j } ^ { ( k - 1 ) } + a _ { k k } g _ { k j } ^ { ( k - i ) } )" ,d34c3ef2-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"x > 0" ,d3858bef-ba2f-47be-bd9c-286e65141794__mathematical-expression-and-equation_4.jpg
"= \int _ { \Gamma } c _ { i k l m } n _ { k } [ \hat { u } _ { l , m } w _ { i } - w _ { l , m } \hat { u } _ { i } ] d \Gamma = - \int _ { \Omega } K _ { i } w _ { i } d X = - \int _ { \Omega } K _ { i } ( u _ { i } - \hat { u } _ { i } ) d X" ,d3fffe1d-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"b = { l g } _ { a } c" ,d4596ad0-066a-11e8-9854-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"\eta _ { 1 } \prime ( t ) = q ( t ) \eta _ { 1 } ^ { 2 } ( t ) - \frac { 1 } { p ( t ) }" ,d4b1e95a-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { p _ { 1 } } { \sqrt { T _ { 1 } } } = \frac { p _ { 2 } } { \sqrt { T _ { 2 } } }" ,d54c7cc0-0f8d-4874-8b7a-9443253f27c5__mathematical-expression-and-equation_3.jpg
"p ( x , y ) = \sum _ { i , j = 0 } ^ { 4 m + 1 } \alpha _ { i j } x ^ { i } y ^ { j }" ,d5642222-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"p 2 : = a 2 + T \times p 3 + M \times p 1 ;" ,d5642312-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\mathbf { P } ( \alpha , \beta ) = ( \alpha \mathbf { E } + \beta \mathbf { L } ) ^ { - 1 }" ,d5642366-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"D _ { 3 } I I I = 2 7 4 m m" ,d5b31e5f-418c-4a84-bb73-d654ac60b31a__mathematical-expression-and-equation_9.jpg
"u = a _ { 0 } + a ," ,d60c998e-aaed-4787-826f-d64400e503d0__mathematical-expression-and-equation_14.jpg
"\frac { d z } { d s } = \sin \alpha" ,d613e9a7-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_15.jpg
"\frac { 1 } { 2 } \phi _ { x ^ { 1 } , x ^ { 2 } } ( v ) = v ( f ( x ^ { 1 } , x ^ { 1 } ) - f ( x ^ { 1 } , x ^ { 2 } ) ) + ( 1 - v ) ( f ( x ^ { 2 } , x ^ { 1 } ) - f ( x ^ { 2 } , x ^ { 2 } ) )" ,d613ea4f-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\max _ { a \le x \le b } | y ( x ) | \le \sqrt { ( b - a ) } \parallel y \parallel _ { 2 }" ,d613ea66-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\kappa _ { 6 } = \frac { 1 } { 6 3 } p ( 1 - 3 1 p + 1 8 0 p ^ { 2 } - 3 9 0 p ^ { 3 } + 3 6 0 p ^ { 4 } - 1 2 0 p ^ { 5 } )" ,d613eb12-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\lambda _ { k } = \lambda _ { i k } + \frac { V _ { k } - V _ { i k } } { V _ { c k } - V _ { i k } } ( \lambda _ { c k } - \lambda _ { i k } )" ,d76f12e2-cedf-4cab-95ef-38fc0f00fa98__mathematical-expression-and-equation_1.jpg
"\sum _ { k = 1 } ^ { 3 } k a ^ { i } _ { j , k } = m _ { i } v _ { j } ^ { ( i + 1 ) }" ,d775007e-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_3.jpg
"t ^ { h } . v = q _ { I } ^ { 0 } . v - \phi _ { m } = \psi _ { h } ^ { m }" ,d8269cfc-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"+ ( 1 / \phi ( n ) ) E _ { x _ { j } } \sum _ { m = 0 } ^ { \phi ( n ) - 1 } ( h ( X _ { m } , Y _ { m } , Y _ { m + 1 } ) - f ( X _ { m } , Y _ { m } ) ) ^ { 2 } - ( \phi ( n ) / n ) a \prime _ { n } ( x _ { j } ) ^ { 2 } ." ,d8de5548-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\parallel [ F \prime ( x _ { n } ) - F \prime ( x _ { n - 1 } ) ] - [ F \prime \prime ( x _ { n - 1 } ) ( x _ { n } - x _ { n - 1 } ) ] \parallel \le 3 M _ { 3 } \parallel x _ { n } - x _ { n - 1 } \parallel ^ { 2 }" ,d9960b63-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\mathbf { c } ^ { T } ( \mathbf { R } + \mathbf { L } ) \mathbf { c } > 0 ," ,d9960b90-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg
"m _ { 1 } \parallel u \parallel \le \parallel u \parallel _ { [ W ^ { 1 } _ { 2 } ( \Omega ) ] ^ { 3 } } \le m _ { 2 } \parallel u \parallel" ,d9960bb7-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( \mathbf { d } \prime \Sigma \mathbf { d } ) ^ { 1 / 2 } + M ^ { 1 / 2 } \max _ { 1 \le k \le N } | c _ { k } - \bar { c } | [ \sum _ { i = 1 } ^ { p } d _ { i } ^ { 2 } ] ^ { 1 / 2 } \ge ( \mathbf { d } \prime ( \operatorname { c o v } \mathbf { S } ) \mathbf { d } ) ^ { 1 / 2 }" ,d9960cce-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"n \in J _ { N - 1 }" ,d9960d2b-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\forall \epsilon > 0" ,da4ab5df-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg
"I = I _ { 1 } + I _ { 2 } + I _ { 3 } + \dots ," ,da5eef70-c41c-11e3-93a3-005056825209__mathematical-expression-and-equation_6.jpg
"\alpha _ { r } \ge 0" ,db2b7120-316f-4ee0-a140-b1ef8f2fd100__mathematical-expression-and-equation_6.jpg
"\frac { d ^ { 2 } s } { d t ^ { 2 } } t ," ,db8f8ad0-02d3-11e4-a680-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"i = 2 , 3 , 4" ,dbb912a2-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg
"P ( \mathcal { L } _ { M } \le x ) = D ( x ) + D ^ { ( R ) } ( x )" ,dbb913ee-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\partial l / \partial x = ( l _ { x } ^ { 2 } - 1 , l _ { x } l _ { y } , l _ { x } l _ { z } )" ,dbeb47b2-1faa-44f5-b709-c19b11f6b533__mathematical-expression-and-equation_16.jpg
"\nabla ^ { 2 } _ { p } ( \Gamma \overline { v } _ { z } ) + \frac { v } { \Gamma } ( \Gamma \overline { v } _ { z } ) + \mu g \lambda ^ { - 1 } J _ { p } [ h , g \lambda ^ { - 1 } \nabla ^ { 2 } _ { p } ( z _ { 0 } + z _ { 1 } ) + \lambda ] = 0 . ( X X , 2 1 )" ,dc4a0495-3d92-4675-bd9b-68fe6e8aeeb5__mathematical-expression-and-equation_2.jpg
"D _ { \phi } = E _ { 2 } t _ { 1 } + 2 E _ { 1 } t _ { 2 }" ,dc71dbab-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\le c h ^ { k + 1 } \parallel U \parallel _ { k + 3 , \tilde { \Omega } } \parallel _ { \psi } v \parallel _ { 1 , \delta _ { h } } ." ,dc71dd0a-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\mu _ { i } \mu _ { j } = \mu \mu _ { 0 }" ,dd1c52c9-7bcd-4789-a9d3-b52480896bd9__mathematical-expression-and-equation_8.jpg
"= \Delta t ^ { 3 } [ \frac { 4 } { 3 } \frac { \partial ^ { 3 } W ^ { \kappa _ { 5 } } } { \partial t ^ { 3 } } - \frac { 1 } { 3 } \frac { \partial ^ { 3 } W ^ { \kappa _ { 6 } } } { \partial t ^ { 3 } } - ( \theta + 2 \delta ) \frac { \partial ^ { 3 } W ^ { \kappa _ { 7 } } } { \partial t ^ { 3 } } - ( \frac { 1 } { 2 } - 2 \delta ) \frac { \partial ^ { 3 } W ^ { \kappa _ { 8 } } } { \partial t ^ { 3 } } ]" ,dd27be04-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\partial \Omega = \bar { \Gamma } _ { u } \cup \bar { \Gamma } _ { P } \cup \bar { \Gamma } _ { K }" ,dd27be84-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\tilde { \sigma } | \langle 0 , \theta ^ { * } \rangle = \sigma" ,dd27bf7b-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_9.jpg
"[ p a v ] = [ p b v ] = [ p c v ] = 0 ," ,dd5f6255-d2ce-4c8c-9707-5d9353001e4d__mathematical-expression-and-equation_15.jpg
"+ C h ^ { 2 } \parallel u \parallel ^ { 2 } _ { C ( I ; H ^ { 2 } ( \Omega ) ) } ," ,ddddc74f-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\frac { \parallel R ( u , v ) \parallel _ { 1 } } { \parallel v - u \parallel _ { L ^ { \infty } ( 0 , h _ { 1 } ) } } \le \mathrm { c o n s t } \parallel v - u \parallel _ { L ^ { \infty } ( 0 , h _ { 1 } ) } ^ { 1 / 2 } ." ,de93f839-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { \partial ^ { 2 } \epsilon } { \partial t ^ { 2 } } - \alpha \frac { \partial ^ { 2 } T } { \partial t ^ { 2 } } + ( \chi _ { 1 } + \chi _ { 2 } ) ( \frac { \partial \epsilon } { \partial t } - \alpha \frac { \partial T } { \partial t } ) + \chi _ { 1 } \chi _ { 2 } ( \epsilon - \alpha T ) = \frac { 1 } { E _ { H } } \frac { \partial ^ { 2 } \sigma } { \partial t ^ { 2 } } +" ,df03e603-f90f-4aad-8976-b8b2323fc271__mathematical-expression-and-equation_7.jpg
"\le C _ { 1 } h ^ { - 1 / 2 } \parallel g \parallel _ { C ^ { 2 } } ( \sum _ { k = 1 } ^ { K _ { 1 } } \int _ { 0 } ^ { l _ { k } } ( v ^ { 2 } + | \frac { \partial v } { \partial \xi } | ^ { 2 } ) d \xi ) ^ { 1 / 2 }" ,df4bafe4-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\le \int _ { S } \{ | \mathcal { N } ^ { T } ( \mathbf { u } _ { n } , \mathcal { F } _ { n } ) \mathbf { M } \mathcal { N } ( \mathbf { u } _ { n } , \mathcal { F } _ { n } ) | | \mathcal { F } _ { n } - \mathcal { F } _ { 0 } | +" ,df4bb0fb-3c8d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { 1 } { \tau } - \frac { d \varpi } { d s } = 0" ,df833d5c-a89c-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"z = d \dots ( a )" ,dfc65ed0-faab-11e6-97b4-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"\int _ { 0 } ^ { \infty } \int _ { \omega } ^ { 2 \omega } ( f _ { h } ( u ) ( t ) - f _ { h } ( v ) ( t ) ) ( u \prime ( t ) - v \prime ( t ) ) d t \chi ( h ) d h = 0" ,dfff6f37-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\int _ { D } ( E y _ { n } - y _ { d } ) ^ { 2 } r d r d z \rightarrow \int _ { D } ( y - y _ { d } ) ^ { 2 } r d r d z" ,dfff6f94-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\parallel E y _ { h } ^ { * } - E y _ { h } \parallel _ { 1 , r , \hat { D } } \le C \parallel y _ { h } ^ { * } - y _ { h } \parallel _ { 1 , r , D _ { h } } \le \tilde { C } h ." ,dfff6fa0-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_8.jpg
"R _ { 6 } ( \theta * ) = \{ \theta : F ( \theta ) \subseteq F ^ { = } ( \theta * ) \} \cap R _ { 1 } ( \theta _ { * } )" ,dfff70a5-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\sigma \ge \beta \} \le \sup \{ \rho ( _ { \sigma } t _ { \alpha } ^ { w _ { 1 } } x _ { 1 } , _ { \sigma } t _ { \alpha } ^ { w _ { 2 } } x _ { 2 } ) \frac { 1 + ( \sigma - \alpha ) r _ { 0 } } { 1 + \sigma - \alpha } : ( w _ { 1 } , w _ { 2 } , \sigma ) \in U \times U \times R , \sigma \ge" ,dfff70b5-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_2.jpg
"< ( 2 - m _ { 1 } - 1 ) / ( 1 - m _ { 1 } ) = ( 1 - m _ { 1 } ) / ( 1 - m _ { 1 } ) = 1 ." ,e0b68ac9-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\dot { v } = v ( [ q _ { 2 } u + q _ { 1 } ] + \text { c o n j . } )" ,e0b68b93-3c8d-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathbf { B } = \sum _ { i = 1 } ^ { n } \beta _ { i } \mathbf { b } _ { i } \mathbf { b } _ { i } ^ { T }" ,e16e1a65-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\Gamma _ { 2 } ^ { 2 } ( \phi ) = \{ ( x _ { 1 } , x _ { 2 } ) \in \mathbf { R } ^ { 2 } | x _ { 2 } = h ( x _ { 1 } ) , x _ { 1 } \in ( \beta , 1 ) \}" ,e16e1a90-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_3.jpg
"J ^ { * } ( \beta _ { h } , \mathbf { q } ^ { * } + \mathbf { p } ^ { h } ( \beta _ { h } ) ) = j ( \dot { a } )" ,e16e1ad0-3c8d-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"y = 0 , 0 4 8 + 0 , 0 3 7 2 5 6 \frac { 1 } { x _ { 1 } }" ,e261beb0-d6b6-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_14.jpg
"c _ { f } = 0 . 0 4 6 8 R _ { \delta } ^ { - \frac { 1 } { 4 } }" ,e31a885b-f50d-4a14-8397-20e02306c770__mathematical-expression-and-equation_5.jpg
"y = - \frac { ( a - x _ { 1 } ) ( x _ { 1 } + y _ { 1 } ) } { a }" ,e360d2c7-594f-11e5-a5f7-00155d010f03__mathematical-expression-and-equation_6.jpg
"\Phi ( \omega ) = - \int _ { \frac { \omega } { k } } \cos 2 k x \pi d \log \Gamma ( x )" ,e3638564-a89c-11e1-1154-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\int \delta y \phi ( \delta y ) d x = - t q u ^ { 2 } t \prime + \int d x q u ^ { 2 } t \prime ^ { 2 }" ,e3ca6db6-4e67-4253-b2c0-e239db9dfd77__mathematical-expression-and-equation_8.jpg
"Y = \Sigma y = \Sigma \sin \alpha \cos \beta = \Sigma r \sin \lambda \cos \theta" ,e46b4ee2-1c5f-4924-9aa7-058c79e04a42__mathematical-expression-and-equation_7.jpg
"\alpha = 0 , 1 , 2 , \dots" ,e4b568bb-ac0a-11e1-9713-001143e3f55c__mathematical-expression-and-equation_8.jpg
"S \rightarrow N 1 B 1" ,e4b56a96-ac0a-11e1-9713-001143e3f55c__mathematical-expression-and-equation_5.jpg
"5 5 9 . 7 1 1 5 : 3 = 1 8 6 . 5 7 0 5" ,e4de1c25-88c9-436a-bbb4-3d43bf62e525__mathematical-expression-and-equation_8.jpg
"i _ 1 = \frac { n e } { ( m + n ) r } = i . \frac { n ( m + 1 ) } { m + n }" ,e4ff5da1-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\delta \prime , \epsilon \prime , \zeta \prime" ,e594bf76-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_7.jpg
"Q = \frac { k H K \prime _ 0 } { 2 K _ 0 } = k H q _ r ." ,e59f704e-bc37-11e1-1726-001143e3f55c__mathematical-expression-and-equation_0.jpg
"D _ 1 ( x _ 1 / a _ n )" ,e5eaf932-1ee2-11e2-1726-001143e3f55c__mathematical-expression-and-equation_3.jpg
"( I , \Omega _ E , ( \{ S _ K \} _ { K \in \mathcal { K } } , \rho ) )" ,e6477d51-ac0a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_0.jpg
"+ \frac { ( 2 \pi ) ^ { 2 s } } { c ^ s \Gamma ( s ) ^ 2 } \sum _ { k = 1 } ^ \infty \int _ 0 ^ \infty \eta ^ { s - 1 } ( \eta + k ) ^ { s - 1 } d \eta \{ \frac { 1 } { e ^ { - 2 \pi i \eta ( w _ 1 + w _ 2 ) - 2 k w _ 2 \pi i } - 1 }" ,e658f0e0-5600-436a-9073-21cf9695f010__mathematical-expression-and-equation_4.jpg
"\lim _ { n = \infty } s _ n = \frac { 1 } { 2 }" ,e66dfee0-5a87-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_15.jpg
"+ \frac { 1 } { \epsilon } \sum _ { r = 1 } ^ { l } \int _ { k \Delta } ^ { t } M \{ | \phi ^ { ( r ) } ( X ^ { ( \epsilon ) } ( s ) , Y ^ { ( \epsilon ) } ( s ) ) - \phi ^ { ( r ) } ( X ^ { ( \epsilon ) } ( k \Delta ) , \hat { Y } _ { \epsilon } ( s ) ) | ^ 2 / N _ { k \Delta } \} d s ." ,e723aa86-ac0a-11e1-1360-001143e3f55c__mathematical-expression-and-equation_6.jpg
"u _ I ( e _ 2 ) = ( - 1 , - 1 )" ,e723ac0e-ac0a-11e1-1360-001143e3f55c__mathematical-expression-and-equation_5.jpg
"O R = \frac { e ^ 2 x _ 1 ^ 3 } { a ^ 4 } , R Q = - \frac { e ^ 2 y _ 1 ^ 3 } { b ^ 4 }" ,e766e7e2-e8ef-11ea-86d3-00155d012102__mathematical-expression-and-equation_8.jpg
"1 9 ) \pm a \sqrt { \frac { s } { a ^ 2 + b ^ 2 } } \pm b \sqrt { \frac { s } { a ^ 2 + b ^ 2 } } . 2 0 ) 2 0 , 1 5 , 1 2 . a \sqrt { \frac { s } { a ^ 2 + b ^ 2 + c ^ 2 } } ," ,e7d3a284-6d8a-45f6-894f-53ae1050c22a__mathematical-expression-and-equation_0.jpg
"\frac { d \omega } { d t } = \frac { \sqrt { \alpha \prime ^ 2 + \gamma \prime ^ 2 + ( \alpha \gamma \prime - \gamma \alpha \prime ) ^ 2 } } { 1 + \alpha ^ 2 + \gamma ^ 2 }" ,e7dfe75b-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"v c _ 1 \equiv \sin t" ,e7dfe825-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\tilde { \mathbf { x } } = \mathbf { x } + \mathbf { n }" ,e7ff15be-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"l = 1 , \dots , m" ,e7ff17da-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { d \omega } { d t } = \frac { \alpha \prime } { r \prime } \sin \omega - \frac { \beta \prime } { r \prime } \cos \omega" ,e87a2b7b-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"C _ 3 + C _ 2 = \binom { \alpha } { \alpha - 1 } ( - a )" ,e87a2bef-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
"3 ) \dots F _ 1 ( x _ 1 , y _ 1 , a ) = 0 ," ,e8fa4c40-00cf-11eb-98c2-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"l = \frac { 2 p } { 2 a } \frac { \beta N } { 3 6 0 } L" ,e9952180-c41c-11e3-93a3-005056825209__mathematical-expression-and-equation_3.jpg
"( \frac { 1 } { m } ) ( - m ) = - 1" ,e99d283d-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
"a = \xi + \eta i" ,e99d288e-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\tan E N L = \frac { d . \tan \alpha } { s }" ,e9b9667f-f280-4da5-a816-3eecf73a13f0__mathematical-expression-and-equation_8.jpg
"[ d \alpha _ 1 + \alpha _ 1 ( \omega _ { 0 0 } - 2 \omega _ { 1 1 } + \omega _ { 3 3 } ) \omega _ 1 \omega _ 3 ] = 0" ,e9fdcfdb-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_3.jpg
"x = 1 0 ( 3 , 4 5 - 3 , 0 ) + 6 9 , 3 = 7 3 , 8 ," ,ea5b2341-bc37-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\bar { p } - \bar { \rho } \frac { \partial ( \phi + \phi \prime ) } { \partial t } = \bar { p } _ 1 - \bar { \rho } _ 1 \frac { \partial \phi _ 1 } { \partial t }" ,ea61d49c-d83e-407c-9db4-9340b278f3f4__mathematical-expression-and-equation_5.jpg
"\{ \mathbf { a } _ { \alpha _ \mu } , \mathbf { a } _ { \beta _ \mu } , \mathbf { j } , \mathbf { b } _ { 1 } , \dots , \mathbf { b } _ { n - 2 } \} \subset C ( v )" ,ea77df9b-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\mathcal { H } ( t , \hat { \lambda } ( t ) , \hat { u } ( t ) ) = \max _ { u \in U } \mathcal { H } ( t , \hat { \lambda } ( t ) , \hat { x } ( t ) , u ) =" ,ea77e002-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"T S Y = 9 0 2 . 3 ^ { * * * } - 1 3 . 3 Z n ^ { * * * } \text { f o r } n = 1 2 \text { a n d } R ^ 2 = 0 . 7 7" ,eaa57620-40f9-11ed-9667-005056822549__mathematical-expression-and-equation_0.jpg
"b \prime = b ( 1 - \eta ) = b ( 1 - \frac { v } { m E } )" ,eac8fb20-1b93-11e4-8e0d-005056827e51__mathematical-expression-and-equation_3.jpg
"g _ i ( t ) = \frac { a _ i ( t ) } { \sum _ { j = 1 } ^ { K } a _ j ( t ) }" ,ead733ba-aa5e-4212-a75e-e87c87d66c53__mathematical-expression-and-equation_5.jpg
"\beta ^ 3 + b \beta ^ 2 + c \beta + d = 0 ," ,eb1105e3-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"v r ^ { ( \frac { k _ 1 } { \mu } - 1 ) } = C" ,eb1106fc-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
"L _ { 4 \check { s } } = ( P _ { 4 \check { s } } ) _ t = - K _ 1 v ( d r ) _ t = - K _ 1 v ^ 2 d t" ,eb1106fc-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\bar { \sigma } = \cap \sigma _ \perp = \wedge \sigma _ \perp" ,eb3ac392-7f95-468f-919a-3e00468813cf__mathematical-expression-and-equation_0.jpg
"\frac { \partial Q } { \partial \dot { u } _ { i 0 } } = \sum _ { i = 1 } ^ { m } g _ { i } ( t ) \epsilon _ { i } ( t ) \frac { \partial \epsilon _ { i } ( t ) } { \partial \dot { u } _ { i 0 } } = 0" ,eb42a92f-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ a _ { 1 2 2 } [ a _ { 2 1 1 } | a _ { k i j } | + a _ { 2 3 3 } | a _ { k i j } | + \dots + a _ { 2 , n + 1 , n + 1 } | a _ { k i j } | ] +" ,eb5dd5de-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\dot { x } _ 1 = x _ 2" ,ec018acc-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_7.jpg
"+ \Gamma H 2 ( n ) \frac { \sigma ^ 2 } { \Delta } \Gamma S V ( n + 1 ) \} \Gamma D V ( n )" ,ec018b55-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\beta _ { s - 1 } ( n ) = r _ 1 ( n + s - 1 ) + \alpha _ { s - 1 } ( n ) r _ 0 ( n + s - 1 )" ,ec018c87-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\alpha \neq 0" ,ec018d24-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\delta = \vec { s } ( \vec { \Omega } _ j \times \vec { T } ) + \vec { s } \vec { C }" ,ec20d6f5-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\text { E C A U } y ( t ) \in Y , 2 ^ { j - 1 } < \omega ( y ( t _ 0 ) ) \le 2 ^ j ," ,ec20d73f-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_17.jpg
"K _ 4 > \psi ( x , \tau )" ,ec20d74d-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_13.jpg
"x = - \frac { \pi } { 2 } + \nu \pi" ,ec20d7d2-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"( I ) ( V ) [ ( R _ U ^ K ( \mathscr { A } ) ) \equiv R _ U ^ K ( \mathscr { B } ) ) ( K | I , U / V ) ]" ,ecce29a5-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\hat { c } _ 2 = z + 1" ,ecce2bba-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"D a _ 2 = d a _ 2 + a _ 2 ( \omega _ { 4 4 } - \omega _ { 3 3 } )" ,ece733ff-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\ge \gamma _ p k ^ { \frac { r - 1 } { 2 } + p } + O ( k ^ { \frac { r - 1 } { 2 } + p - 1 } ) > \frac { 1 } { 2 } \gamma _ p k ^ { \frac { r - 1 } { 2 } + p }" ,ece735cd-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"r + 1" ,ece73619-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_5.jpg
"t = 3 ^ { \mathrm { m } } 2 0 . _ { 4 } ^ { \mathrm { s } }" ,ed10868c-8932-494c-8345-12a8c542232a__mathematical-expression-and-equation_14.jpg
"b _ { i j } = c _ { i j } - g _ { i j }" ,ed526b7d-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"R _ m = Z _ { c n - 1 } Q _ m + E" ,ed526c30-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"s _ 1 , s _ 2 \in S" ,ed9d6170-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\hat { J } _ 1 ( \mu ) = \hat { J } _ 2 ( 1 - \mu )" ,ed9d61aa-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"[ \begin{array} { c c } z ^ { - 1 } ( 1 - 2 z ^ { - 1 } ) & 0 \\ 0 & z ^ { - 1 } ( 1 - 2 z ^ { - 1 } ) \end{array} ] D _ 1 + D _ 2 [ \begin{array} { c c } 1 - z ^ { - 1 } & 0 \\ 0 & 1 - z ^ { - 1 } \end{array} ] = [ \begin{array} { c c } 1 & 0 \\ 0 & 1 \end{array} ]" ,ed9d626f-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\lim _ { h \rightarrow o } \tilde { \Phi } ( h ) \in \overline { \tilde { U } _ 1 } \subset 2 \tilde { U } _ 1" ,edb4e497-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
"[ \omega ^ 1 \omega _ 1 ^ 3 ] + [ \omega ^ 2 \omega _ 2 ^ 3 ] - R _ { 1 2 } ^ 3 [ \omega ^ 1 \omega ^ 2 ] = 0" ,edb4e4ff-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"| \frac { \partial ^ 2 V ( P ) } { \partial x _ i \partial x _ j } | < K _ 4 , | \frac { \partial V ( P ) } { \partial x _ i } | < K _ 4 , | V ( P ) | < K _ 4 , | \frac { \partial V } { \partial t } | < K _ 4" ,edb4e617-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"M _ Q \{ x _ t \} = \mu _ t" ,edb4e659-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"x _ 1 + x _ 2 = \frac { 2 a ^ 2 A ( A \xi - \eta ) } { b ^ 2 + a ^ 2 A ^ 2 }" ,edcb6840-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lambda _ n z _ n ^ 2 ( t ) \le \lambda _ n ^ 2 f _ n d ( t ) z _ n ( t )" ,ee86176e-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\rho _ { 1 , 2 } = \cos T ( \epsilon ) + \epsilon P ( \epsilon ) \pm \sqrt { ( \cos T ( \epsilon ) + \epsilon P ( \epsilon ) ) ^ 2 - 1 - \epsilon Q ( \epsilon ) }" ,ee861826-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\prescript { i } { } { M } . \prescript { i } { } { M } = \tilde { \epsilon }" ,ee8618f4-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_17.jpg
"\tau _ s = \frac { D \Delta p } { 4 L }" ,eee5b568-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { \partial f } { \partial x _ 1 } = 0 , \frac { \partial f } { \partial x _ 2 } = 0 , \frac { \partial f } { \partial x _ 3 } = 0" ,ef0324cd-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\psi ( \omega ) = \sup \{ g ( \mathbf { x } , \xi ( \omega ) ) | \mathbf { x } \in E _ n , \mathbf { x } \in X ( \xi ( \omega ) ) \} =" ,ef286eae-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
"d Y _ t = X _ t d t + g d ^ 2 W _ t" ,ef286f85-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_18.jpg
"d u = f _ 1 d x + f _ 2 d y + f _ 3 d z ," ,ef28bce0-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_9.jpg
"{ \mathcal { S } ( x , \overline { \mathfrak { M } } _ i ) ; \iota \in I }" ,ef56123a-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\lambda _ 2 \ge \frac { B ( M _ 2 , M _ 2 ) } { l _ 2 }" ,ef56124c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\log p = 9 . 2 3 6 4 2" ,ef740a90-cacf-11e7-a351-005056825209__mathematical-expression-and-equation_11.jpg
"U = U _ { m a x } + \frac { 1 } { \kappa } U _ { * } \ln \eta" ,efbfc1ec-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\mathbf { O } _ 2 = ( \begin{array} { c c } 0 & 0 \\ 0 & 0 \end{array} )" ,f02b1435-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"I ( K , h ) = \int _ { \lambda _ { \rho - } } ^ { K } e ^ { - \lambda t } h ( \lambda ) d \rho ( \lambda )" ,f02b163d-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"T _ i ( \phi ) = \int _ U \frac { \partial \phi ( z ) } { \partial z _ i } d z , \phi \in \mathcal { D }" ,f02b167e-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"p _ k = 4 n _ k + 1 , ( k = 1 , 2 , 3 , \dots , n )" ,f03f00d7-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { 1 } { \pi } \int _ { - \infty } ^ { \infty } \frac { d x } { 1 + x ^ 2 } \log ( 1 - e ^ { 2 \pi ( \alpha x - \sqrt { \alpha ^ 3 x ^ 2 + \beta } ) }" ,f03f0117-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { \partial ^ 2 \mu _ 1 } { \partial x ^ 2 } - \frac { \beta } { h _ 0 k } \frac { \partial \mu _ 1 } { \partial t } + \frac { W ( x , t ) } { k h _ 0 } = 0" ,f097f963-bc37-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\lim _ { t \rightarrow \infty } g _ { n + t } ( \mathcal { X } _ { n + t } ) = - \infty" ,f0b6876e-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_5.jpg
"e = - P _ 2 ( A P _ 2 + B Q _ 2 ) ^ { - 1 } C + ( I _ 1 - B _ 2 ( P A _ 2 + Q B _ 2 ) ^ { - 1 } R ) F ^ { - 1 } C" ,f0b68927-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_7.jpg
"m _ i + m _ j - M \le x _ k ^ m" ,f0b689a5-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_0.jpg
"B K = \sqrt { z }" ,f0da2f19-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { d ^ 2 x } { d y ^ 2 } + x - e ^ y = 0" ,f0ea9120-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"\beta \prime _ 2 = \rho ^ { - 2 } \beta _ 2" ,f0fd320c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"c l K _ 0 = c l K _ 1 = c l K _ 2 = r" ,f0fd3279-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\phi ( a ) = \phi ( \epsilon a + ( 1 - \epsilon ) a ) \ge \phi ( \epsilon a ) + ( 1 - \epsilon ) a \ge ( 1 - \epsilon ) a" ,f0fd32a2-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"p = \frac { 1 } { 1 0 }" ,f178b913-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\cot \alpha - \cot \beta = \frac { b ^ 2 - a ^ 2 } { c v }" ,f178b997-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\lim _ { V \rightarrow 0 } Z _ G ( \omega \prime , V ) = 0" ,f17fcc04-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
"V _ m = V _ 1 ( D _ g T _ g ^ 3 T _ s ^ 3 ) ^ { 1 / 2 } ( \sigma ^ 2 D _ s ^ { - 1 } ) ^ { 1 / 2 }" ,f18fbe80-9732-4b68-9b9e-57380f11bf24__mathematical-expression-and-equation_0.jpg
"\{ \bar { A } ^ R - ( \bar { A } ^ P - A ) ; A \in \mathfrak { U } \}" ,f1cd52c9-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\pi _ 0 \rightarrow \{ \xi _ 1 ^ { ( 0 ) } , \dots , \xi _ s ^ { ( 0 ) } , \eta _ 1 ^ { ( 0 ) } , \dots , \eta _ r ^ { ( 0 ) } \}" ,f1cd53d6-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"M _ { 1 } = \frac { y } { b ^ { + } d ^ { - \sim } f ^ { * } a _ 0 ^ { - \sim } }" ,f247d765-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\frac { d ^ 2 V _ R } { d Z ^ 2 } - ( \xi ^ 2 + i ) V _ R = - \xi \lambda \mathcal { P }" ,f257d131-bc37-11e1-1360-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\sum _ { k = 1 } ^ { n } \frac { 1 } { \sin 2 ^ n x } = c t g x - c t g 2 ^ n x" ,f2ac08a1-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_1.jpg
"y ^ 4 = \frac { a } { 2 } x ^ 3" ,f2ac09ad-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_0.jpg
"= f ( \frac { 1 } { h } - \frac { b } { h } M _ 1 - \frac { b _ { 0 1 } p _ f } { f _ { p 1 } q _ 0 } M _ 2 ) = f ( \frac { 1 } { h } - b _ { 0 1 } F )" ,f311de38-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_5.jpg
"u = \sum _ { n = 0 } ^ { n } \frac { k _ n } { n + 1 } ( \frac { \Delta p } { 2 l } ) ^ n ( R ^ { n + 1 } - r ^ { n + 1 } )" ,f3381ecd-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_1.jpg
"i = ( i a ) b" ,f36e0a32-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"H d ^ 2 E _ 3 = d ^ 2 E \prime _ 3 + 2 ( \lambda _ 1 \omega _ 1 + \tau _ { 3 3 } ) d E \prime _ 3 + ( . ) E \prime _ 3 - p ^ * _ 1 E \prime _ 4 + q" ,f36e0ab8-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_8.jpg
"1 0 - 4 = | 9 - 8 = | 2 - 1 = | 3 - 3 = | 5 - 5 = | 1 0 - ? = 1 0" ,f3ac2c83-224b-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_8.jpg
"( \frac { x } { a } ) ^ 2 + ( \frac { y } { b } ) ^ 2 - ( - \frac { z } { c } ) ^ 2 = 1" ,f3b88f86-a1bf-486b-845e-15ca829daf57__mathematical-expression-and-equation_0.jpg
"F _ { n + 1 } ( 0 , p _ 1 , \dots , p _ n ; 0 , q _ 1 , \dots , q _ n ; 0 , r _ 1 , \dots , r _ n )" ,f3dea2ef-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"I ^ \beta ( \begin{array} { c c c } \lambda x , & \lambda y , & \lambda z \\ \mu l , & \mu m , & \mu n \end{array} ) = \lambda ^ \beta \mu ^ { 1 - \beta } I _ 3 ^ \beta ( \begin{array} { c c c } x , & y , & z \\ l , & m , & n \end{array} ) , \lambda , \mu > 0" ,f3dea2fa-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_5.jpg
"P _ \eta [ S ( \theta + \Delta ) - S ( \theta ) ] - P _ \eta [ S ( \theta ) - S ( \theta + \Delta ) ] =" ,f3dea334-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"R _ n = O _ p ( n ^ { - 3 / 4 } )" ,f3dea3c5-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_10.jpg
"b ( \frac { \hat { r } } { \bar { r } } q ) \ge b ( q + \bar { r } \bar { p } + \bar { v } ) + \mu \forall q \in V \setminus \frac { 1 } { \bar { r } } ( \hat { o } - \bar { p } )" ,f3dea4e2-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"f ( x ) = [ f ( A ) - f ( 1 ) ] . L x + f ( 1 )" ,f3f06fe8-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\pi _ 0 = \frac { t g \rho } { \pi }" ,f3fc6100-3e1b-11e4-b6b9-001018b5eb5c__mathematical-expression-and-equation_2.jpg
"O _ a ( I _ { 1 x } ) \stackrel { . } { \implies } O _ b ( I _ { 2 t } )" ,f43f159c-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"| \int _ { \tau _ 1 } ^ { \tau _ 2 } [ v ( r , \psi + \omega \tau / \epsilon ) - v _ 0 ( r ) ] d \tau \parallel \le \frac { 1 } { 2 } \epsilon" ,f43f1747-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\tau \in \langle \tilde { \tau } , \tau _ 1 \rangle" ,f43f1797-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_11.jpg
"L _ 0 = \{ a ^ n | n \ge 1 \}" ,f4affd95-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\alpha ( x ) - \alpha \le \alpha ( 1 - \delta ) \frac { \log \log x } { \log x } ( x \ge x _ 0 )" ,f50e74e3-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"r \ge r _ 0" ,f52a98fa-79ec-4cd9-8f01-12b1f90b6bee__mathematical-expression-and-equation_3.jpg
"= \frac { 1 } { 2 b } \sqrt { 1 6 s ( s - a ) ( s - b ) ( s - c ) } ," ,f56bb5ee-3336-11ec-af5b-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\sin \beta = \frac { 4 } { 9 } ; d ) \cos \alpha = \frac { 1 8 } { 2 5 } \operatorname { t g } \beta = 1 \frac { 5 } { 9 } ; e ) \cos \alpha = \frac { 7 } { 2 4 } \cos \beta = \frac { 3 5 } { 3 8 }" ,f56fd4f0-3336-11ec-af5b-001b63bd97ba__mathematical-expression-and-equation_4.jpg
"m = 5 , n = 3 , h = 3 0 , s = 1 2 , r = 2 0 ." ,f5726c43-3336-11ec-af5b-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\tan 2 a = \frac { 2 a _ { 1 2 } } { a _ { 1 1 } - a _ { 2 2 } } ." ,f578d970-d3b7-11e2-b791-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
"\parallel ( I - S _ { r y } S _ { y u } ) ^ { - 1 } S _ { r y } \parallel _ M < \frac { 1 } { v _ 2 ( p ) }" ,f579678a-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"B ^ 0 = \frac { h _ n } { h \prime \prime _ n } - 1 = \frac { h \prime \prime \prime _ n } { h \prime \prime _ n }" ,f5d6d870-73f4-11e4-9605-005056825209__mathematical-expression-and-equation_1.jpg
"\int _ { \mathbf { R } ^ \infty } z _ k ^ 2 d v ( z _ 1 , z _ 2 , \dots ) < \infty" ,f6462e12-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\langle \overline { T } \delta ( u , v ) ; \delta ( u , v ) \rangle = \sum _ n \sum _ m \sum _ p \sum _ q \delta ( n - 1 , m - 1 ) \delta ( p , q ) S ( n + p , m - q ) =" ,f6462e57-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\beta : = ( \lambda , \phi _ 1 , \dots , \phi _ p ) ^ T" ,f6462eb2-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_2.jpg
"+ b _ 1 t _ 1 + b _ 2 t t _ 1 + b _ 3 t ^ 2 t _ 1 + b _ 4 t ^ 3 t _ 1 + \dots" ,f6a3343b-40e3-11e1-1729-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\sphericalangle a o p = 2 \alpha _ 3" ,f6a33563-40e3-11e1-1729-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\mathbf { f } ( s ) = \mathbf { f } _ S ( s ) + \mathbf { f } _ { N S } ( s ) = \mathbf { 0 }" ,f6ac1d4c-c0f3-4051-beb6-e22681639ac1__mathematical-expression-and-equation_2.jpg
"v * = - \frac { 0 , 1 9 } { \mathrm { l g } \frac { z _ 0 } { H } } \frac { u _ 2 } { 1 - \frac { 0 , 2 6 } { \mathrm { l g } \frac { z _ 0 } { H } } \frac { H } { L } } ," ,f6af44b2-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\check { s } _ 1 = \frac { V _ 1 } { \check { s } _ 1 } = \frac { 1 5 } { 1 0 0 0 } = 0 , 0 1 5" ,f6b9b988-6bfe-11e5-aeea-001b21d0d3a4__mathematical-expression-and-equation_4.jpg
"k = 1 , 2 , \dots , n" ,f6c2b40c-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\hat { G } _ { i k h } ^ { i } \stackrel { \mathrm { d e f } } { = } \dot { \partial } _ { h } \hat { G } _ { i k } ^ { i } \stackrel { \mathrm { d e f } } { = } \dot { \partial } _ { h } \dot { \partial } _ { k } \hat { G } _ { i } ^ { i } \stackrel { \mathrm { d e f } } { = } \dot { \partial } _ { h } \dot { \partial } _ { k } \dot { \partial } _ { i } \hat { G } ^ { i }" ,f6c2b493-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg
"p _ k ( X ) = \sum _ { r = 1 } ^ k \frac { \partial ^ r a ^ n } { \partial y ^ { \alpha _ 1 } \dots \partial y ^ { \alpha _ r } } H _ { i _ 1 \dots i _ k } ^ { \alpha _ 1 \dots \alpha _ r } \frac { \partial } { \partial y _ { i _ 1 \dots i _ k } ^ \eta } \text { f o r } k \ge 1 ," ,f6c2b50b-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_10.jpg
"k = 0 , 1 ; \phi ^ { ( 4 ) } ( 0 , 0 ) = \phi ^ { ( 4 ) } ( \pi , 0 ) = 0 , \epsilon \ge 0" ,f6c2b52d-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\delta \frac { \tau } { h } ( \alpha + \beta x + \delta \beta h ) \ge 0" ,f6c2b599-570a-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"t > s" ,f7123076-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_14.jpg
"R ( s , t ) = \lim _ { \substack { a , a \prime \rightarrow - \infty \\ b , b \prime \rightarrow + \infty } } \int _ { a } ^ { b } \int _ { a \prime } ^ { b \prime } f ( s , \lambda ) \overline { f ( t , \mu ) } \text { d d } F ( \lambda , \mu )" ,f71230d1-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg
"u _ i = ( K _ { 1 i } , K _ { 2 i } ) \tilde { y } _ i" ,f7123147-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_2.jpg
"u = C e ^ { - b t } \sin ( \omega _ 1 t + \gamma )" ,f739f2b0-1b93-11e4-8e0d-005056827e51__mathematical-expression-and-equation_6.jpg
"u = 0 . 5" ,f7608d90-7a06-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"( P _ { s m } ) _ { i j } = - p \delta _ { i j } + \mu _ { s m } ( \Delta v _ { s m } ) _ { i j } + \mu _ { s m 2 } \Theta v _ { s m } \delta _ { i j }" ,f78ab0ef-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\beta _ 2 \prime = \sigma ^ { - 2 } \beta _ 2 + \sigma ^ { - 1 } \sum _ { t = 2 n + 1 } ^ { i } \gamma _ 1 ^ t c _ t ^ { 2 n }" ,f7a461fa-570a-11e1-1090-001143e3f55c__mathematical-expression-and-equation_20.jpg
"\rho ^ w = ( \rho _ { A A } \cup \rho _ { B A } \cup \rho _ { B B } ) ^ w" ,f7a4634d-570a-11e1-1090-001143e3f55c__mathematical-expression-and-equation_0.jpg
"d e g \{ \tilde { p } _ { i i } ( z ) \} > d e g \{ \tilde { p } _ { j i } ( z ) \}" ,f7dd9661-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\mathbf { a b } = ( x _ 1 \mathbf { i } + y _ 1 \mathbf { j } + z _ 1 \mathbf { k } ) ( x _ 2 \mathbf { i } + y _ 2 \mathbf { j } + z _ 2 \mathbf { k } )" ,f815b01e-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\overline { \mathbf { K } } \subset \overline { \mathbf { R } } \subset \overline { \mathbf { L } } ." ,f87a0099-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_6.jpg
"d \alpha = 2 \omega _ { 2 1 \wedge } \omega _ { 2 3 }" ,f87a01fc-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"S = [ \bigcup _ { \alpha \in \Lambda } P _ \alpha ] \cup M ^ *" ,f87a0204-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"d \sigma \prime = \sin \theta \prime d \theta \prime d \phi \prime" ,f87a024e-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\Sigma \frac { \psi ( x _ k ) } { f \prime ( x _ k ) } = \alpha _ 1" ,f8cf62f6-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"+ \frac { x } { r ^ 5 } ( 3 x y \cos \alpha \prime + ( - x ^ 2 + 2 y ^ 2 - z ^ 2 ) \cos \beta \prime + 3 y z \cos" ,f8cf63e5-40e3-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\cos 4 \alpha = \cos ^ 4 \alpha - 6 \cos ^ 2 \alpha \sin ^ 2 \alpha + \sin ^ 4 \alpha" ,f8fbdad0-853a-11e4-a354-005056825209__mathematical-expression-and-equation_7.jpg
"= \overline { \lim } _ { h \rightarrow 0 ^ + } \frac { 1 } { h } \{ W ( t + h , x ^ * ( t + h ; t , x ) ) - W ( t + h , x ( t + h ; t , x ) ) \} +" ,f9562fec-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_4.jpg
"P _ 2 - P a a r" ,f9563082-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\langle 0 , 1 \rangle \le x \le \langle 1 , 1 \rangle" ,f9563112-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_0.jpg
"X = [ \begin{array} { c c c } 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & - 1 & 1 \end{array} ]" ,f96ce7ef-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_8.jpg
"Q _ { h k } = [ q _ { 0 0 } ^ T , q _ { 1 0 } ^ T , \dots , q _ { h 0 } ^ T , q _ { 0 1 } ^ T , \dots , q _ { 0 k } ^ T , \dots , q _ { 1 1 } ^ T , \dots , q _ { h k } ^ T ] T" ,f96ce8f2-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\mathbf { V } ^ { ( 2 ) } = \operatorname { I m } [ \begin{array} { c c c c } 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & - 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & - 1 & 0 \end{array} ]" ,f96ce905-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"z ^ * ( z _ 1 - l ( x _ 1 ) ) \ge \alpha \ge z ^ * ( z _ 2 - l ( x _ 2 ) )" ,f96cea10-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\mathbf { W } . \mathbf { c _ 1 } = \iint \nabla ( \mathbf { v } . d \mathbf { p } ) . \mathbf { c _ 1 } - \iint ( d i v \mathbf { v } \mathbf { c _ 1 } ) . d \mathbf { p }" ,f98cbec7-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_3.jpg
"y _ v = b ^ 2 - \frac { b ^ 2 \xi ^ 2 } { a ^ 2 } ," ,f98cbeec-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ 1 = y _ 0 \cdot \cos \alpha" ,f98cc0d7-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\frac { 1 } { 2 } m ( v \prime ^ { 2 } - v ^ { 2 } ) = h \nu _ { r a d }" ,fa0366e8-bfe4-495d-830d-c4112f8583ef__mathematical-expression-and-equation_5.jpg
"y = \sqrt { \frac { 1 } { n } } = \pm b" ,fa09ac30-d3b7-11e2-b791-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"\frac { d p } { d \rho } = a ^ 2 ," ,fa17eb95-bc37-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { \sin ( z a + \alpha \prime ) } { \sin z a } = 0 . 6 8 8 2 = p ;" ,fa38fbed-2b9d-4c24-9b1b-deec60d9cce8__mathematical-expression-and-equation_6.jpg
"V ^ * ( x ) : = \inf _ { \pi } V ( \pi , x ) , x \in X ," ,fa42fd63-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
"h a t { S } _ n = \prod _ { i = 1 } ^ { n } \hat { \underline { b } } _ i ( \underline { X } _ 1 , \underline { X } _ 2 , \dots , \underline { X } _ { i - 1 } ) \underline { X } _ i" ,fa42fe94-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
"x \cdot 1 = 1 \star ( 1 \star x )" ,fa42fef7-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_13.jpg
"W _ { I I } = \frac { 1 } { 3 2 } 3 , 1 4 . 0 , 0 7 ^ { 3 } ( 2 0 - 1 4 ) = 2 , 0 2 . 1 0 ^ { - 4 } m ^ { 3 }" ,fab828f0-d6b1-11ea-903c-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg
"\tilde { J } _ x ^ { r + 1 } E \xrightarrow { [ \kappa _ { r + 1 } ( X , Y ) ] ^ { - 1 } } J _ x ^ 1 ( B , \tilde { J } _ x ^ r E )" ,fb0eb612-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_6.jpg
"i _ 1 = 1 , \dots , k" ,fb0eb73a-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\int _ 0 ^ T E ( t ) d t \le C ( | ( w _ t , w ) _ \Omega | _ 0 ^ T ] | + \gamma ^ 2 | ( \nabla w _ t , \nabla w ) _ \Omega | _ 0 ^ T | + | ( b w , w ) _ \Omega | _ 0 ^ T |" ,fb0f9c98-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_10.jpg
"u ( s ) = - F ( s ) x ( s ) + G v ( s )" ,fb0f9d13-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"B _ 1 \equiv \frac { u _ 2 } { A _ { 1 3 } } - \frac { u _ 3 } { A _ { 1 2 } } = 0" ,fb1affd8-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\delta _ 2 ^ 5 \equiv c _ 2 ( \bmod \lambda ^ 5 ) ," ,fb1b00ef-40e3-11e1-1121-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\frac { 2 7 . 3 \text { k r . } } { 8 9 } = 0 . 3 0 \text { k r }" ,fb438693-e256-11e6-95ce-001999480be2__mathematical-expression-and-equation_1.jpg
"m ^ 2 ( \Delta N _ g ) = m _ { \Sigma } ^ 2 + m _ E ^ 2" ,fb9393a0-2883-4226-943a-0603aa66ba16__mathematical-expression-and-equation_1.jpg
"\frac { 1 } { \delta _ 1 } = \frac { a \prime } { \delta a \prime _ 1 }" ,fbb2d6b0-287f-11e9-844c-005056827e51__mathematical-expression-and-equation_5.jpg
"+ r _ 1 r _ 2 \cdot \tan \frac { \alpha } { 2 } \tan \frac { \beta } { 2 } ]" ,fbdd1787-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
"I I \equiv \frac { x } { \alpha } + \frac { y } { \beta } - 1 = 0" ,fbdd17cb-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ 1 = x \prime _ 1 + \lambda _ { 1 2 } x \prime _ 2 + \dots + \lambda \prime _ { 1 n } x \prime _ n" ,fbdd191a-40e3-11e1-1027-001143e3f55c__mathematical-expression-and-equation_7.jpg
"i = 1 , \dots , r" ,fbe38f59-ac0a-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"y ( t ) = C _ C ( \beta ) x _ C ( t ) + N _ C ( \beta ) d ( t )" ,fbe39027-ac0a-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg
"a _ 1 \parallel y \parallel ^ 2 + a _ 2 \parallel y \prime \parallel ^ 2 \le \bar { c } + \int _ { t _ 0 } ^ t ( \phi _ 1 \parallel y \parallel ^ 2 + \phi _ 2 \parallel y \prime \parallel ^ 2 ) d s ," ,fbe6ed1c-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\frac { 2 f \prime _ 1 ( t ) } { f \prime ( t ) } = \frac { 2 f _ 2 ( t ) } { f _ 1 ( t ) } + \frac { f \prime \prime ( t ) f _ 1 ( t ) } { f \prime ^ 2 ( t ) }" ,fcab1629-40e3-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"h ( \omega | x ) = c ( x ) [ 1 - \frac { 2 } { N } \sum _ { i = 1 } ^ { k } \frac { P ( \omega _ i ) } { Q } ] ^ { - \frac { N } { 2 } + k }" ,fcbef91a-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"f ( \nabla ) = \bar { f } ( \nabla ) S ^ { - 1 } ( \nabla )" ,fcbefb6d-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\lim _ { t \rightarrow \infty } \inf f ( t ) = \inf _ { t \ge 0 } f ( t )" ,fcbefb78-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"3 4 \frac { 1 } { 2 } m - 1 6 \frac { 3 } { 4 } m = ?" ,fcbf773b-0943-453a-82d9-038b145ad193__mathematical-expression-and-equation_4.jpg
"u \prime ( t ) = ( A + B ) u ( t ) + f ( t )" ,fcc4062e-570a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\sum _ \nu \cos a x _ \nu \sin b x _ \nu = \frac { 1 } { 2 } \sum _ \nu \sin ( a + b ) x _ \nu - \frac { 1 } { 2 } \sum _ \nu \sin ( a - b ) x _ \nu ," ,fd4bf0aa-7127-635e-b733-ce2826e93884__mathematical-expression-and-equation_2.jpg
"p = \pm \frac { b ^ 2 } { a }" ,fd4ee380-5c0f-11e7-85f6-005056825209__mathematical-expression-and-equation_6.jpg
"\phi ( v ) \psi \prime \prime ( v ) - \psi ( v ) \phi \prime \prime ( v ) = 0" ,fd79b035-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\int _ 0 ^ r \phi ( r ) d r = \frac { r } { \pi } \int _ 0 ^ { \frac { \pi } { 2 } } \psi ( r \sin \phi ) \sin \theta d \theta" ,fd79b18c-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"d s ^ 2 = \frac { k ^ 4 } { 4 } \frac { 1 + f _ 1 ^ 2 } { f _ 1 ^ 4 } ( d \alpha ^ 2 + f _ 1 ^ 2 d \beta ^ 2 )" ,fd79b1c0-40e3-11e1-1431-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\frac { l _ v } { d } = 7 2 0 0 P e ^ { - 0 . 6 }" ,fd7f0b3d-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_0.jpg
"k b = k \prime b \prime , k a = k \prime a \prime" ,fd92eb3c-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\parallel T _ { \Delta t } ^ { \gamma } \mu _ p \parallel _ { \mu p } \le ( 1 + h C )" ,fd92eb82-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
"| Q _ n - P | = O ( \epsilon _ n )" ,fd92ec83-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_10.jpg
"u _ 1 ^ N ( t , x ) = \sum _ { j = 1 } ^ { N - 1 } w _ j ( t ) L _ j ( x ) + ( \Delta + d ( t ) ) L _ N ( x )" ,fd92ed16-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\le \mu \phi ( \mu ^ 2 . \mathbf { 1 } , \delta ^ 2 . 1 , \dots , \delta ^ 2 . \mathbf { 1 } ) \int _ { t } ^ { t + 1 } f ( s ; \mu ^ 2 . \mathbf { 1 } ) d s + \delta \le \infty ," ,fd9efd6b-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_6.jpg
"j = 0 , 1 , \dots , n + 3" ,fd9eff4a-570a-11e1-1278-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\mathbf { D } \prime \prime \prime = \frac { 0 \prime 5 2 } { V \sqrt { \mathbf { B } \prime \prime \prime } }" ,fdd34d68-6182-b600-6a06-c0af8786d669__mathematical-expression-and-equation_3.jpg
"I _ 2 + 6 O H _ 2 + 5 C l _ 2 = 1 0 C l H , 2 I O _ 3 H" ,fde92b10-0af5-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"u _ z = \frac { u \prime _ z } { \beta ( 1 + \frac { v } { c ^ 2 } u \prime _ x ) }" ,fe48260a-40e3-11e1-1278-001143e3f55c__mathematical-expression-and-equation_0.jpg
"P _ 1 \equiv p x - y _ 0 y + p x _ 0 = 0 ." ,fe482659-40e3-11e1-1278-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\sum _ { j = 1 } ^ { m } x _ { i j } = 1 ," ,fe69c5ad-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"G _ m ^ k ( d ) \le k m [ ( d - 2 ) ( k - 1 ) + 1 ] i f d \ge 3" ,fe781f05-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_2.jpg
"e ^ { ( n + 1 ) \sqrt { ( - 1 ) } \phi } \eta _ { 2 1 } \dots \eta _ { n + 1 , n } = \det | X , X \prime , \dots , X ^ { ( n ) } | ." ,fe781fe4-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_2.jpg
"y _ j = a _ j + \lambda _ 0 ( u _ 1 - p a _ 1 ) + \sum _ { i = 1 } ^ { l } \lambda _ i ( v _ i - p a _ { i + 1 } + a _ i ) + W" ,fe782000-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\Phi ( z ) = \sum _ { j = 1 } ^ { m } \int _ { 0 } ^ { 1 } \frac { f _ j ( t ) } { \psi _ j ( t ) - z } d \psi _ j ( t )" ,fe782064-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_2.jpg
"x = S _ { k \in K } \{ x _ k ^ * \}" ,fe782086-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_8.jpg
"| | | u _ L ( t ) | | | \le C \eta < C _ 1 \eta < R _ 1 \le R \text { f o r } t \ge t _ 0 ." ,fe7820e0-570a-11e1-2028-001143e3f55c__mathematical-expression-and-equation_10.jpg
"k _ 3 \cos \sqrt { k _ c + 1 } ( u + v ) + k _ 4 \sin \sqrt { k _ c + 1 } ( u + v ) + \frac { k _ c } { k - 1 }" ,ff097809-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_14.jpg
"m = \frac { M } { \frac { 4 } { 3 } \pi K ^ { 3 ^ \cdot } }" ,ff09791f-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"w _ { A \vee B \vee C \vee \dots \vee K } = \bigoplus _ { i = 0 } ^ { n - k } ( ( - 1 ) ^ i \bigoplus _ { | d | = k + i , A \vee B \vee C \vee \dots \vee K \subset d } w _ d ^ 0 )" ,ff49c307-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"Z ( 0 , N ) [ \begin{array} { c } N \\ 0 \end{array} ]" ,ff49c4d9-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg
"2 ^ { q \prime - 1 } ( 1 + \frac { \lambda c _ 2 } { c _ 1 } ) ^ { q \prime } [ \int _ T ^ t k _ 2 ^ { p \prime } ( t - \sigma ) d \sigma ] ^ { q \prime / p \prime } \exp [ 2 ^ { q \prime - 1 } ( 1 + \frac { \lambda c _ 2 } { c _ 1 } ) ^ { q \prime } ]" ,ff505641-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\parallel f \parallel _ { \hat { p } } = ( \int _ { R ^ n } ( 1 + | x | ^ 2 ) ^ p | f ( x ) | ^ 2 d x ) ^ { 1 / 2 }" ,ff5056d2-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\le ( \int _ { R ^ n } | f ( y ) | ^ 2 . \sigma ( y ) ^ { 2 p } d y ) ^ { 1 / 2 }" ,ff5056d4-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"e _ 4 \prime = - 4 \lambda e _ 2 - 2 \mu e _ 3" ,ff505761-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_5.jpg
"( U V A _ 1 B _ 1 ) = \lambda ," ,ffa9618a-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"Q _ 1 + 3 0 = 4 S ," ,ffa962ec-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { c } { x } l + \frac { ( l - x ) ^ 2 } { 2 r } = ( s _ 1 + c )" ,uuid:219ca550-0d35-11e5-b309-005056825209__mathematical-expression-and-equation_3.jpg
"r \prime ( 1 + \frac { d \alpha } { d \phi } ) = \lambda" ,uuid:69fb0fa2-55e1-4de4-b85e-8923626f0f1e__mathematical-expression-and-equation_3.jpg
"A M = u _ 1 , B M = u _ 2 , C M = u _ 3" ,uuid:786f05e0-feae-4302-98f4-35e1dcabf058__mathematical-expression-and-equation_2.jpg
"\frac { 1 } { 2 } ( \Gamma _ 1 + \Gamma _ 2 ) \equiv x ^ 2 + y ^ 2 - ( u _ 1 + u _ 2 ) x + u _ 1 u _ 2 = 0" ,uuid:ca108de7-34ab-4f97-903d-2cc8077df9f4__mathematical-expression-and-equation_1.jpg
"\frac { d x ^ 2 } { d x } = 2 x ^ { 2 - 1 }" ,uuid:f2d29e0b-e656-45b4-8b90-12130f54c4bc__mathematical-expression-and-equation_0.jpg
"d _ { 1 } = 2 d _ { 2 } + 2 \Re ( \frac { \cosh a w - 1 } { a \sinh a w } ) = 2 . 4 \cdot 1 0 ^ { - 3 } m" ,249e4844-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"b _ { r } = \frac { I } { n ( m - 2 r ) } ( \frac { \partial u } { \partial x } \frac { \partial \theta _ { r } } { \partial y } - \frac { \partial u } { \partial y } \frac { \partial \theta _ { r } } { \partial x } )" ,4efe45cc-7929-4043-800b-063b84fae1ee__mathematical-expression-and-equation_0.jpg
"( x + c ^ { 2 } ) ^ { 2 } + ( x - a + c ^ { 2 } ) ^ { 2 } - b ^ { 2 } = ( a + b ) ^ { 2 }" ,32d5d8ed-45de-4bcb-8174-f0aa7bf01d70__mathematical-expression-and-equation_17.jpg
"+ \frac { 2 } { v } [ \frac { 1 } { ( 1 - P ^ { 2 } v ^ { 2 } ) ^ { 1 / 2 } } + \frac { 1 } { ( 1 - Q ^ { 2 } v ^ { 2 } ) ^ { 1 / 2 } } ] d D = 2 d t" ,69898cbe-f2e9-44d8-9ee8-0de124073d57__mathematical-expression-and-equation_5.jpg
"L _ { t } = L _ { t 1 } + L _ { t } \prime + L _ { t } \prime \prime + L _ { t } \prime \prime \prime + L _ { t 2 } = 5 9 6 \text { m k g }" ,9ff44460-32d4-11e6-a344-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"u _ { 1 } = - \frac { a } { 2 } + \sqrt { ( \frac { a } { 2 } ) ^ { 2 } + b }" ,3877d9a6-df28-11e1-6101-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\alpha ( p ) = - ( p _ { 0 } - p _ { s } ) ^ { - 1 } ( p - p _ { s } )" ,1926dff3-c893-4670-8d74-2b212b7e0103__mathematical-expression-and-equation_0.jpg
"\Omega _ { 1 } = \frac { \alpha c } { 1 + \alpha c } \Omega" ,9f21383a-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg
"u _ { t } - \sum _ { i , j = 1 } ^ { n } a _ { i , j } ( u _ { x _ { 1 } } , \dots , u _ { x _ { n } } ) u _ { x _ { i } x _ { j } } + c u _ { t } - b \Delta u _ { t } = g" ,046d3d5b-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\sphericalangle N C q = \sphericalangle M C A \prime" ,027a842d-2bc6-4cfb-bf93-954d2e1dae36__mathematical-expression-and-equation_1.jpg
": 1 2 = ( y - 1 5 0 ) : y" ,5aa33ba0-4629-11e7-80b4-001018b5eb5c__mathematical-expression-and-equation_7.jpg
"- ( 1 8 3 ) -" ,945e79cd-5570-4d87-963a-7a64a569e2ab__mathematical-expression-and-equation_0.jpg
"( \nabla \nu _ { * } ) ( X _ { x } , Y _ { x } , \xi _ { x } ) = \nabla ^ { V ^ { \perp } } _ { X _ { x } } v _ { * } ( Y , \xi ) = \Pi _ { V ^ { \perp } } ( \overline { \nabla } _ { X _ { x } } v _ { * } ( Y , \xi ) )" ,0c39dbd0-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_8.jpg
"- \frac { 1 } { I } \int ( \bar { x } v _ { 2 } - \bar { z } \lambda _ { 2 } ) ( \bar { y } v _ { 2 } - \bar { z } \mu _ { 2 } ) d w _ { y } -" ,18c350a3-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg
"E = \sqrt { B J } = E _ { i }" ,0ecd69e3-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"R c \equiv P a + Q b" ,66eea700-d034-11e3-93a3-005056825209__mathematical-expression-and-equation_3.jpg
"k _ { 1 } y + \psi \prime = \frac { \pi } { 4 }" ,5da87cd5-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg
"- 0 , 0 0 2 x _ { 5 } + 0 , 0 5 4 0 6 x _ { 6 } - 0 , 0 1 5 5 9 x _ { 7 } + 0 , 0 0 0 0 8 x _ { 8 } + 0 , 0 0 0 0 2 x" ,0a9e1690-b582-11ea-9b5d-005056825209__mathematical-expression-and-equation_3.jpg
"\frac { 1 } { 2 } l \times 4 = \frac { 4 } { 2 } l = 4 l : 2 = 2 l ," ,12ed8617-3598-11ec-b695-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"F ( \pi ) = \frac { \pi } { \sqrt { c ^ { 2 } - a ^ { 2 } - b ^ { 2 } } }" ,29bd9d80-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"A _ { 1 } = 1 ," ,442829cf-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\frac { \partial \Psi } { \stackrel { ( \alpha ) } { \partial C _ { K L } } } = 0" ,18c35029-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_18.jpg
"- u _ { z } + L _ { v } \frac { d ( i _ { d } - i _ { k } ) } { d t } + R _ { v } ( i _ { d } - i _ { k } ) + L _ { z } \frac { d i _ { d } } { d t } +" ,23c01d88-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"1 3 9 9 ) \sqrt { 6 2 9 2 6 9 3 6 0 2 2 5 }" ,3f3f5f76-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_20.jpg
"N a _ { 2 } O + H _ { 2 } O = 2 N a O H + 3 5 \cdot 4 4 \text { K a l . }" ,2c4c1e0e-901d-4119-9c63-cbeb0f2f4654__mathematical-expression-and-equation_2.jpg
"\epsilon _ { k l } = u _ { l , k } + \phi _ { k l }" ,1ea66cac-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\psi ( z ) = \psi ( a t _ { 0 } + x )" ,0f9f61ce-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_11.jpg
"L = 1 8 9 3 0 0 0 c m \doteq 0 . 0 0 1 9 H ." ,4b749f00-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_6.jpg
"C _ { p } = \Sigma ( P \sin \alpha ) ," ,9755f628-1d00-11ea-b563-001999480be2__mathematical-expression-and-equation_7.jpg
"( i = 1 , 2 )" ,3855e372-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"C _ { 1 } = C \frac { S } { R + S } ." ,7386ef2d-87a4-4e86-bdef-aafb150f113c__mathematical-expression-and-equation_0.jpg
"[ | \dot { v } | _ { L _ { p } ( \Omega ) ^ { 3 \times 3 } _ { p } } ^ { p } + | v | _ { L _ { 2 p / ( 3 - p ) } ( \Gamma ) ^ { 3 } } ^ { p } ] ^ { \frac { 1 } { p } }" ,7997e1f5-a33a-4139-896c-bfae3ca0dfcd__mathematical-expression-and-equation_2.jpg
"Y _ { n } ( t ) = L _ { n } ( [ G t ] )" ,01d7e9fb-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_9.jpg
"Q ( N ) = Q ( N - 1 ) . e ^ { A . Q ( N - 1 ) }" ,0011ebbe-bc38-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
"2 S O _ { 2 } + 4 H _ { 2 } O + 4 J = 2 H _ { 2 } S O _ { 4 } + S + 4 H J ;" ,6eef6120-2f96-4e3e-9803-3a577a717806__mathematical-expression-and-equation_5.jpg
"V = X _ { 0 } + X _ { 1 } \rho + X _ { 2 } \rho ^ { 2 } + X _ { 3 } \rho ^ { 3 } + \dots" ,94d99eac-d0a2-4376-937c-bdf6f91c5702__mathematical-expression-and-equation_8.jpg
"a x ^ { 2 } + c y ^ { 2 } + f = 0" ,0d229550-860b-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_11.jpg
"\alpha _ { 2 } = \frac { y _ { 1 } } { b }" ,46067dd5-4027-42a4-9dbd-411449324eab__mathematical-expression-and-equation_13.jpg
"\frac { \xi } { 2 l } ( 1 + \eta ( \xi , \nu ) ) + \frac { g } { 1 6 l ^ { 2 } \nu ^ { 2 } } ( x _ { 0 } + \xi ) ^ { 2 } = 0 ." ,0e4662d4-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\tan \delta = k \frac { C } { C _ { v } } \frac { 2 } { \pi } ( 1 + \kappa ) [ \frac { 1 } { U _ { m } } \int _ { x _ { m i n } } ^ { x _ { m a x } } ( a + b x ) d x - \frac { \kappa d } { \epsilon U _ { m } ^ { 2 } } \int _ { x _ { m i n } } ^ { x _ { m a x } } \frac { ( a + b x ) ^ { 2 } } { x } d x ]" ,0c708f31-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"u v x = x \implies v u x = x ;" ,3855e30a-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\rho \prime = a" ,7fc14cf0-7aa3-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_13.jpg
"L _ { 1 } = 4 ( \sqrt { x ^ { 2 } + \rho ^ { 2 } } - \rho - x ) + 2 \rho ( \log 2 - 1 )" ,38efd020-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg
"T ( b ) = \frac { \pi } { 2 } \frac { b ^ { 2 } R S } { \ln ^ { 2 } ( 1 - b ) } = \frac { \pi } { 2 } \frac { ( 1 + \frac { b } { \sqrt { 2 } } + \frac { b ^ { 2 } } { \sqrt { 3 } } + \dots ) ( 1 + \frac { b } { 2 \sqrt { 2 } } + \frac { b ^ { 2 } } { 3 \sqrt { 3 } } + \dots ) } { ( 1 + \frac { 1 } { 2 } b + \frac { 1 } { 3 } b ^ { 2 } + \dots ) ^ { 2 } }" ,97198e4b-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\tau \in U \implies | \phi ( \tau ) - \phi ( t ) | \ge \frac { c } { 2 } | \tau - t |" ,4fbec42b-a8e1-4374-8c71-a9412f537717__mathematical-expression-and-equation_2.jpg
"\xi = v" ,8ed54acb-d4a7-4dcc-b6ac-285aa5e55fbf__mathematical-expression-and-equation_8.jpg
"( J _ { x } ) = 2 v F \int _ { 0 } ^ { \frac { 1 } { 2 } } ( e _ { x } ^ { 2 } \delta z + z ^ { 2 } \delta z ) = 2 v F \int _ { 0 } ^ { \frac { 1 } { 2 } } ( e _ { x } ^ { 2 } \delta z + \delta \frac { z ^ { 3 } } { 3 } )" ,77cab820-d210-11e2-b081-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"\frac { d \phi } { d t } = k \phi" ,0fd8688d-ce3a-4fc1-9f0c-e5917a44fc2a__mathematical-expression-and-equation_12.jpg
"\bar { x } \in \bar { x } _ { \bar } { F } , Q . E . D ." ,975b7ad0-ddff-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_8.jpg
"C = c A" ,5bee98cc-2c4c-4434-a991-4b342d5ddf90__mathematical-expression-and-equation_2.jpg
"7 + 2 5 + 1 4 + 2 + 3 6 = 8 4" ,6258fd98-68bf-4041-a2fa-4b3c9be4c841__mathematical-expression-and-equation_5.jpg
"( x ^ { 3 } _ { - } p x - q ) = ( x - 2 w ) ( x + w \pm \sqrt { - ( 3 w ^ { 2 } - p ) } ) = x ^ { 3 } - p x - 2 w ( 4 w ^ { 2 } - p ) ( 1 7" ,7bc54945-b934-11e1-1154-001143e3f55c__mathematical-expression-and-equation_0.jpg
"J _ { s 2 } = \int _ { \omega d > \omega _ { d m i n } } ^ { \infty } \frac { \sin ( k _ { 8 } ) \sin ( k _ { 9 } ) } { \omega d [ \omega d - 4 \sqrt { ( 1 - k ) } ] ^ { 2 } } \cdot d ( \omega d )" ,2051ab73-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\sqrt { ( x - 3 ) ^ { 2 } } = 4 ( 3 + \sqrt { x - 3 } )" ,756aae96-f8cf-42f9-9987-0ced5291d2b9__mathematical-expression-and-equation_0.jpg
"C = \frac { \pi } { 4 } ( \frac { a } { 2 } - \frac { 1 } { M } + \frac { a } { 1 - e ^ { M \alpha } } )" ,772946ac-e1d5-4e67-8471-2f212dc27351__mathematical-expression-and-equation_1.jpg
"I _ { D T } = - 1 0 0 0 a _ { 1 } , A _ { D T } = 1 0 0 0 a _ { 0 }" ,47030b49-420f-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
"a \{ 1 0 1 0 \} \infty P , c \{ 0 0 0 1 \} 0 P ," ,5ee77e38-feb6-4f5f-a66c-905ca7a27053__mathematical-expression-and-equation_1.jpg
"r _ { A } ^ { B } \in \mathbb { R }" ,0620b97b-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_22.jpg
"Y _ { l } = 3 \text { f o r } A _ { l } < Q _ { l }" ,3ef684ee-2e3b-4c7f-a00a-9cc4928fb8cd__mathematical-expression-and-equation_1.jpg
"= K _ { 3 } S b O _ { 3 } S + H _ { 2 } O + A g" ,8403c89b-d366-4d70-951f-2d882d876e47__mathematical-expression-and-equation_1.jpg
"V = F ( \sum _ { 1 } ^ { n } \alpha _ { n } x _ { n } )" ,6fb4d981-c4d3-40a8-b6ed-f6bfffa8567a__mathematical-expression-and-equation_2.jpg
"H _ { 2 } O = H _ { 2 } + O , 1 8 = 2 + 1 6 , j e s t" ,4c89e040-3241-11ec-a216-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"X = \{ x \} \cup \{ a \in A - D : \Theta ( a , x ) \in S \}" ,01d92527-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\lambda + i \int \frac { ( 1 - e ^ { 2 } ) d \phi } { ( 1 - e ^ { 2 } \sin ^ { 2 } \phi ) \cos \phi } = C" ,54305b77-a30c-4216-8ae5-8bd44eff5aa9__mathematical-expression-and-equation_0.jpg
"\beta \prime _ { 2 } \sin \alpha \neq 0 ," ,01d92666-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_6.jpg
"B _ { 1 } = E _ { 1 }" ,9f429143-9992-4737-afcf-7a18999bff23__mathematical-expression-and-equation_19.jpg
"a _ { 1 } \rho \cup a _ { 1 } \rho ^ { 2 } \cup \dots \cup a _ { 1 } \rho ^ { n } = V" ,046d3d26-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\alpha = \alpha _ { 1 } \sqrt { \mu } + \alpha _ { 2 } \mu + \alpha _ { 3 } \mu \sqrt { \mu }" ,5dabd88f-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg
"a = A r c T h \frac { Q } { p }" ,04a81185-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg
"h \prime - \alpha \prime = 0" ,3c0d74b6-8d77-497c-82ef-150607a2c508__mathematical-expression-and-equation_6.jpg
"2 A \prime A \prime \prime A \prime \prime \prime - A \prime \prime ^ { 3 } - A A \prime \prime \prime ^ { 2 } + A A \prime \prime A ^ { I V } - A \prime ^ { 2 } A ^ { I V } +" ,5dbec47a-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_6.jpg
"A _ { 0 } = ( a _ { 0 } , a _ { 1 } , a _ { 2 } , a _ { 3 } ) ( x , \gamma ) ^ { 3 }" ,740f7fba-6bba-4285-b27b-b78f9132b19b__mathematical-expression-and-equation_11.jpg
"\sum _ { v = s + 1 } ^ { ( s , s \prime ) } \alpha _ { v } \mu _ { k } ^ { v } = \beta _ { 1 } ^ { ( s , s \prime ) } \mu _ { k } ^ { m - 1 } + \beta _ { 2 } ^ { ( s , s \prime ) } \mu _ { k } ^ { m - 2 } + \dots + \beta _ { m } ^ { ( s , s \prime ) } , ( k = 1 , 2 , \dots , m ) ." ,3c10017d-3105-11e9-8847-005056a2b051__mathematical-expression-and-equation_8.jpg
"\gamma _ { v } = c _ { v } / R" ,1cf70d96-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg
"r _ { j } ( a , b ) = s _ { j } ( a _ { i } , b _ { i } )" ,0a7a7845-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg
"2 C B \times B D = C B ^ { 2 } + B A ^ { 2 }" ,206e85f6-6c3d-4abf-8ea8-6de04a7c7dd8__mathematical-expression-and-equation_0.jpg
"h = 4 . 9 5 4 c m" ,875e7370-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_16.jpg
"+ [ ( 1 + y ^ { 2 } ) d x ^ { 2 } + ( 1 + x ^ { 2 } ) d y ^ { 2 } - 2 x y d x d y ] / [ 2 \rho ^ { 2 } ( 1 + x ^ { 2 } + y ^ { 2 } ) ]" ,39b0e032-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\rho ^ { 2 } = 2 a ^ { 2 } ( 1 + \cos \frac { 2 p } { p + 2 q } \phi )" ,49056faf-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( \frac { \tilde { \Delta y } } { \Delta t } ) = \frac { 1 } { n m T } ( \tilde { y } _ { n + 1 } - \tilde { y } _ { 1 } )" ,18c350ed-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg
"0 . P r ( E ) \le 1 \cdot D ( 0 , 2 \pi ) C ( r )" ,72f9c221-ea40-486c-a654-3b2cf15389e4__mathematical-expression-and-equation_2.jpg
"\align* 9 3 \times 5 & = ( 9 2 + 1 ) 5 = 4 6 5 \\ 7 9 \times 5 & = ( 7 8 + 1 ) 5 = 3 9 5 \\ 5 7 \times 5 & = ( 5 6 + 1 ) 5 = 2 3 5 \align*" ,3fbfdaa0-e709-11e8-9210-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg
"( \underbrace { A B : A C + B C } ) = a b : A B" ,39d62109-332a-11ec-9f2d-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"I _ { i } \sim O _ { i } \times k \times j \times \frac { e ^ { - ( \mu _ { 1 } x _ { 1 i } + \mu _ { 2 } x _ { 2 i } ) } } { X _ { i } ^ { 2 } }" ,0a1c8fab-a0fd-4307-8967-6f76ee2bd00f__mathematical-expression-and-equation_0.jpg
"a = 3 x , b = 3 y , c = 3 z ." ,098e7370-d3b8-11e2-b791-5ef3fc9bb22f__mathematical-expression-and-equation_14.jpg
"\bar { A } _ { 1 } = E _ { U } t _ { U } + 2 E _ { C } s + E _ { L } t _ { L } = A _ { 1 }" ,19993e80-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_5.jpg
"^ { 2 } i _ { s } = i ^ { \beta } = i ^ { \alpha } + i ^ { 0 }" ,19993f56-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\Gamma ( \frac { 1 } { 2 } ) = 2 \int _ { 0 } ^ { \infty } e ^ { - z ^ { 2 } } d z = \sqrt { \pi } = 1 , 7 7 2 5 ," ,16f52750-0a0b-11e3-9439-005056825209__mathematical-expression-and-equation_6.jpg
"\mathcal { F } _ { 1 } = \frac { a _ { 1 } } { a _ { 0 } } , \mathcal { F } _ { 2 } = \frac { a _ { 2 } } { a _ { 1 } } \cdot \frac { a _ { 1 } } { a _ { 0 } } , \dots \mathcal { F } _ { i } = \frac { a _ { i } } { a _ { i - 1 } } \cdot \frac { a _ { i - 1 } } { a _ { i - 2 } } \cdot \dots \cdot \frac { a _ { 1 } } { a _ { 0 } } . J e" ,7271e233-d533-40fb-ac8c-76bbe7846005__mathematical-expression-and-equation_0.jpg
"D : \delta = f : f \prime" ,85b46b02-a6c5-4852-ab64-0c29548c0a3b__mathematical-expression-and-equation_4.jpg
"\frac { d x } { d u } = \sum _ { \mu } \frac { u ^ { \mu } v ^ { \mu + 1 } } { \mu ! \Gamma ( s + \mu + 2 ) }" ,3a0f70ab-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg
"V \prime ( x ) U ^ { T } ( x ) - U \prime ( x ) V ^ { T } ( x ) = - E" ,3a5e8490-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\omega ^ { 1 } = 0" ,47ac2050-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\nabla ^ { 2 } \beta _ { i } - \frac { 1 + \mu } { 2 } ( \frac { \partial ^ { 2 } \beta _ { i } } { \partial x _ { j } ^ { 2 } } - \frac { \partial ^ { 2 } \beta _ { j } } { \partial x _ { i } \partial x _ { j } } ) - \frac { 2 G _ { c } } { E ^ { * } t ( h + s ) } ( \beta _ { i } + \frac { \partial w } { \partial x _ { i } } ) = 0" ,153e6f50-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\text { i f } x ( i ) \le y ( i )" ,0b5a768d-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\overline { M } _ { k } = [ \mathfrak { M } _ { k } - M _ { k } ]" ,1138eb4b-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\mu ( \sigma ) = i \omega ( \sigma ) t" ,9979c596-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_8.jpg
"H = H _ { 0 } + \Delta H = 1 2 3 1 -" ,1e3fedb0-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_6.jpg
"+ 2 \frac { 3 } { 4 } + 3 \frac { 1 } { 4 }" ,2bf6ee13-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"v = 2 - 3 + 2 = 1" ,1f3c1383-290b-11e8-8c71-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"H _ { e } ^ { A } = 4 I _ { s } [ \beta ( \frac { a ( \bar { z } - t ) } { \pi } + \frac { 1 } { 2 } ) - \beta ( \frac { a ( \bar { z } + t ) } { \pi } + \frac { 1 } { 2 } ) ]" ,9a4ea250-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg
"H _ { 1 } = - i \omega ^ { - 1 } P _ { 2 } ( x _ { 1 } , x _ { 2 } ) \frac { d Z _ { 2 } } { d x _ { 3 } } , H _ { 2 } = i \omega ^ { - 1 } P _ { 1 } ( x _ { 1 } , x _ { 2 } ) \frac { d Z _ { 1 } } { d x _ { 3 } }" ,18f458c7-a428-4bb6-bde8-a20b7ce99f01__mathematical-expression-and-equation_10.jpg
"h ) \sqrt { 1 2 0 0 } ?" ,6602b2cc-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"G ^ { m q } _ { B \kappa s } ( \theta _ { 0 } ) = O _ { m \kappa } \{ - i \cdot 2 ^ { 2 m + 2 s } [ s ! ( m + s ) ! / ( 2 m + 2 s ) ! ] P ^ { m } _ { m + 2 s } ( \cos \theta _ { 0 } ) + \dots" ,98a5f9e9-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_13.jpg
"U = \frac { A _ { \alpha } } { ( x - a ) ^ { \alpha } } + \frac { A _ { \alpha - 1 } } { ( x - a ) ^ { \alpha - 1 } } + \dots + \frac { A _ { 1 } } { x - a } + \frac { f _ { a } ( x ) } { \Phi _ { a } ( x ) }" ,6ece1643-d8c7-11e6-a316-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"[ m \cos ( M - N ) + n t ] ^ { 2 } = k ^ { 2 } . \sin ^ { 2 } \psi ," ,26b0a400-3d62-11e8-baa7-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg
"B _ { 1 } ^ { 3 } = B _ { 3 } ^ { 1 } = - \frac { 1 } { 6 } ( 2 A \prime - 3 x ^ { 1 } )" ,0620b978-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_12.jpg
"\mathcal { B } _ { 0 } = \frac { 4 } { 3 }" ,973bf9b0-ee61-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"\times \int _ { k r _ { 1 } } ^ { k R _ { 0 } } J _ { m + 2 n + 1 / 2 } ( x ) H _ { q + 2 s + 3 / 2 } ^ { ( 1 ) } ( x ) ( d x / x ) + ( k R _ { 0 } ) ^ { - 1 / 2 } J _ { m + 2 n + 1 / 2 } ( k R _ { 0 } ) \times" ,98a5f98c-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_11.jpg
"n _ { 1 } , n _ { 2 } \in N" ,36546d77-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\bar { Q _ { n } } = | V _ { n } | ^ { - 1 } \sum _ { t \in V _ { n } } Q _ { n } \circ \theta _ { t }" ,0024bac0-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg
"E ( X + Y ) = E ( X ) + E ( Y )" ,968e04b0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg
"\lim _ { t \rightarrow \infty } \sup t ^ { n - 1 } \int _ { \gamma ( t ) } ^ { \infty } p ( x ) d x > 0" ,0028418f-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg
"v _ { \nu } = \frac { x _ { 0 } - x _ { \nu } } { s _ { \nu } \prime } \Delta x + \frac { y _ { 0 } - y _ { \nu } } { s _ { \nu } \prime } \Delta y + \underbrace { ( s _ { \nu } \prime - s _ { \nu } ) } _ { l _ { \nu } } ." ,0d97b18d-23df-cfa9-f837-18ecbb0cada6__mathematical-expression-and-equation_2.jpg
"c o s i = \sqrt { - \tan ( \alpha - \Omega ) \tan ( \beta - \Omega ) }" ,0b4c5c2a-40e4-11e1-3052-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\frac { \partial h } { \partial t } \xi \eta \zeta d t ." ,89c86670-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_0.jpg
"[ x _ { 1 } ( \omega ) , \dots , x _ { n } ( \omega ) ] \in A" ,4371abf6-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg
"1 5 0 0 : 2 2 . 6 = 6 6 \text { r o u r }" ,71c2566a-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_11.jpg
"b ^ { * } = - \frac { \beta } { \beta ^ { * } } \frac { \beta ^ { 4 } } { \beta ^ { * 4 } } b" ,1a69faf6-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg
"Q = \{ [ \xi _ { 1 } , \xi _ { 2 } ] \in R ^ { 2 } ; | \xi _ { 1 } - \frac { 1 } { 2 } | + | \xi _ { 2 } | \le \frac { 1 } { 2 } \}" ,34fd1bdc-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\omega _ { 1 } \prime = 2 K \lambda ," ,37f172d9-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_9.jpg
"H _ { \beta } ^ { \gamma } \circ H _ { \alpha } ^ { \beta } = H _ { \alpha } ^ { \gamma }" ,47babbb1-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\cos \alpha = \cos \alpha \prime - \epsilon \sin \alpha \prime" ,1333f4de-bdf8-11e6-b796-001b63bd97ba__mathematical-expression-and-equation_8.jpg
"M = \frac { Q } { g }" ,85c65cf0-7d1e-11e7-89ee-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg
"v = M / ( E J )" ,4bc11c20-2ff3-4e61-a0f6-8572066d74a5__mathematical-expression-and-equation_0.jpg
"+ b _ { 1 0 } g _ { 1 0 } - b _ { 2 0 } g _ { 2 0 } = 0 ," ,126ab771-40e4-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"u ( 1 + v _ { 0 } - n _ { 0 } ) + \sum _ { t = 1 } ^ { T - 1 } \delta ^ { t } u ( 1 + \phi x _ { t - 1 } - \beta _ { t - 1 } - n _ { t } ) + \delta ^ { T } u ( 1 + \phi x _ { T - 1 } - \beta _ { T - 1 } )" ,397b7c50-dde0-4100-8957-d43c8c7388fa__mathematical-expression-and-equation_4.jpg
"\parallel \{ 2 ^ { k \bar { s } } T _ { 1 , k , l , j } \} ^ { \infty } _ { k = 0 } | L _ { \bar { p } } ( l _ { \infty } ) \parallel \le" ,07df0bbb-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_8.jpg
"m = h ^ { 2 } + k ^ { 2 }" ,9979c4d7-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_10.jpg
"\int _ { a } ^ { b } f ( x ) d x = [ F ( x ) + C ] _ { x = a } ^ { x = b } = | _ { a } ^ { b } F ( x ) = F ( b ) - F ( a ) ." ,2f472600-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"+ a + ( + b ) = + a + b = a + b" ,43d24a3f-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\frac { d F } { d x } = \frac { d F } { d r } \cdot \frac { x - u } { r }" ,55fa6187-78ed-4a93-9b3f-eece7dba9cc3__mathematical-expression-and-equation_10.jpg
"a k = a ^ { 0 } k" ,13ecb618-b6a3-49c9-9400-354084d77775__mathematical-expression-and-equation_4.jpg
"R ( x ) = \frac { \phi _ { 1 } ( x ) } { \Theta ^ { n } ( x ) }" ,3a09a4c1-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_10.jpg
"\{ \begin{array} { c c c c c c } d _ { 1 } & u _ { \infty } & a _ { 1 } & i _ { 1 } & d _ { 1 } \prime & \dots \\ u _ { \infty } & e _ { 1 } & b _ { 1 } & j _ { 1 } & e _ { 1 } \prime & \dots \end{array} \}" ,381e9d33-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg
"M ( x ^ { 2 } ) = \frac { 1 } { \pi h ( t ) \sqrt { D } } \int _ { - \infty } ^ { \infty } e ^ { - \frac { \alpha _ { 1 1 } n ^ { 2 } - 2 \alpha _ { 1 2 } u v + \alpha _ { 2 2 } v ^ { 2 } } { h ( t ) \cdot D } }" ,99fcf451-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_18.jpg
"\delta _ { 4 } = 1 7 ." ,971d9aa0-66bd-11e5-8a99-005056825209__mathematical-expression-and-equation_11.jpg
"\hat { \theta } = ( Z \prime M Z ) ^ { - 1 } Z \prime M y" ,1998d614-12f7-4fae-b774-f75610f06b9c__mathematical-expression-and-equation_0.jpg
"u _ { 2 } = u _ { o } t - \frac { L } { E } \dot { u } _ { o } [ 1 - \exp ( - t / T ) ]" ,9033ad82-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\angle a \prime b O = \angle a O b = \omega" ,6f5a546d-f7ba-4ae1-95d4-b321b0e3cb97__mathematical-expression-and-equation_11.jpg
"\{ \begin{array} { c } \hat { x } ( t ) = - \sum _ { i = 1 } ^ { n ( t ) } \frac { x ( \tau ^ { - i } ( t ) ) } { H _ { i } ( \tau ^ { - i } ( t ) ) } - \frac { x ( T ) } { ( h ( \tau ^ { - 1 } ( T ) ) - 1 ) H _ { n ( t ) } ( \tau ^ { - n ( t ) } ( t ) ) } \\ \hat { x } ( t ) = - \frac { x ( T ) } { h ( \tau ^ { - 1 } ( T ) ) - 1 } , T _ { 0 } \le t \le T , \end{array}" ,08bd5e64-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg
"b _ { i } = \frac { 1 } { \pi } \int _ { 0 } ^ { 2 \pi } F ( x ) \sin i x d x" ,0402f7cb-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg
"( d a _ { 3 } + 3 a _ { 2 } \omega + \omega _ { 3 } ^ { 1 } ) \wedge" ,07df0ba5-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_26.jpg
"n \psi = n p = n p _ { 1 }" ,0995825a-84ca-4375-afae-a7abf7ae47e9__mathematical-expression-and-equation_0.jpg
"L _ { 1 , 2 } = - 2 w _ { 1 , e } \frac { c h s \cos s + s h s \sin s } { s h 2 s - \sin 2 s } + \frac { 2 } { \kappa } w \prime _ { 1 , e } \frac { c h s s \in s } { s h 2 s - \sin 2 s }" ,1138ecae-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\log \tan \sigma = 8 . 0 9 6 9 1 - 1 0" ,1bfc1901-8f46-4a7a-bda3-aab273016034__mathematical-expression-and-equation_2.jpg
"1 + \cot ^ { 2 } \phi = \csc ^ { 2 } \phi ; \frac { 1 } { \mathrm { s n } ^ { 2 } \phi } = 1 + \frac { A ^ { 2 } } { B ^ { 2 } } = \frac { A ^ { 2 } + B ^ { 2 } } { B ^ { 2 } }" ,0b0fb410-3a1a-11e9-9fd6-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg
"x \in C ^ { 0 }" ,47babc56-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_11.jpg
"\frac { 1 } { \alpha _ { n } } \int _ { t _ { 1 } } ^ { t ^ { - } } U ( t ) ^ { n } d t = ( a + b s ) ^ { n } - ( a + b x ) ^ { n }" ,0ecd6a43-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\bar { \omega } _ { p } ^ { ( 0 ) } = - \frac { a } { d } C _ { 5 } ^ { ( 0 ) }" ,2051ac44-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg
"P = ( 1 0 0 ) \infty P \infty (" ,06c84603-e3ab-11e6-a668-001999480be2__mathematical-expression-and-equation_4.jpg
"x = \tan ^ { 2 } \omega" ,516592f3-54ad-4bf9-8449-e664af4df51d__mathematical-expression-and-equation_8.jpg
"\Delta D \prime _ { n } = D \prime _ { n } - \overline { D \prime }" ,9b4b702e-e8e9-42e0-9032-2997791d50c4__mathematical-expression-and-equation_13.jpg
"5 , 8 \% P b _ { 3 } O _ { 4 }" ,40171b16-df3d-11e1-1232-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\sigma = \sum _ { i = 1 } ^ { i = n } \frac { K _ { i s } / h a } { K _ { i t } / h a }" ,084e5960-b5b2-11ea-9c77-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"h + \frac { \partial f ( x , y , z , \dots ) } { \partial y } . i + \frac { \partial f ( x , y , z , \dots ) } { \partial z } . k + \dots" ,35aa05cc-b81c-4426-8f5b-7470441affa5__mathematical-expression-and-equation_11.jpg
"p ^ { 2 } + q r = ( p + q u ) ^ { 2 }" ,0cc65872-5fe8-4adb-bf33-709dccb25d4c__mathematical-expression-and-equation_2.jpg
"\frac { u _ { 2 m - 1 } + u _ { 2 m } } { O _ { 2 m } ^ { 2 } } + \frac { u _ { 2 m } + u _ { 1 } } { O _ { 1 } ^ { 2 } } = - \frac { 1 } { 2 }" ,079fa77b-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_13.jpg
"+ 2 \epsilon _ { 2 3 } ^ { 2 } [ 2 ( \epsilon _ { 2 2 } ^ { 2 } + \epsilon _ { 3 3 } ^ { 2 } ) + 3 \epsilon _ { 2 2 } \epsilon _ { 3 3 } - \epsilon _ { 1 1 } ^ { 2 } ] + 2 \epsilon _ { 3 1 } ^ { 2 } [ 2 ( \epsilon _ { 3 3 } ^ { 2 } + \epsilon _ { 1 1 } ^ { 2 } )" ,1cf70e88-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_10.jpg
"M g x _ { 0 } = m _ { 1 } g x _ { 1 } + m _ { 2 } g x _ { 2 } + \dots =" ,208ff050-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_9.jpg
"\dots \mathbf { u } _ { S 3 } = \frac { 1 } { 3 } ( u _ { V } e ^ { j 2 / 3 \pi } + u _ { C 6 } e ^ { j \pi / 3 } ) = \frac { 1 } { 3 } [ u _ { V } e ^ { j 2 / 3 \pi } + ( u _ { C 4 } + u _ { C 5 } ) e ^ { j }" ,5fb896c3-a5e9-4906-8c8d-8f3bc5faad91__mathematical-expression-and-equation_21.jpg
"\zeta = \zeta _ { 1 } + \zeta _ { 2 } + \zeta _ { 3 } + \dots" ,959bd1a2-de39-4feb-a174-09bcacb166d7__mathematical-expression-and-equation_1.jpg
"3 = \frac { 5 \times 6 } { 1 0 }" ,08326dca-e631-4952-9e6d-45f904520556__mathematical-expression-and-equation_5.jpg
"\frac { P + Q } { 2 } + \frac { 1 } { 2 } \sum _ { k = 1 } \frac { F ( r _ { 2 } ) - F ( r _ { 1 } ) } { k + 4 } ( r _ { 2 } ^ { k + 4 } - r _ { 1 } ^ { k + 4 } ) \binom { \frac { 1 } { 2 } } { \frac { k + 3 } { 2 } }" ,30654e80-df3d-11e1-1287-001143e3f55c__mathematical-expression-and-equation_2.jpg
"\frac { D w } { D t } = \frac { \partial w } { \partial t } + u \frac { \partial w } { \partial x } + v \frac { \partial w } { \partial y } + w \frac { \partial w } { \partial z } = Z - \frac { 1 } { \rho } \frac { \partial p } { \partial z }" ,1b3dee2f-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
"Z _ { 1 } - Z _ { 2 } = \pm 2 p" ,1c1d5157-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_3.jpg
"\frac { r _ { j + 1 } - r _ { j } } { 2 } = \epsilon _ { j } \prime ; \frac { r _ { j + 2 } - r _ { j + 1 } } { 2 } = \epsilon _ { j } \prime \prime ; \dots ; \frac { r _ { j + j \prime } - r _ { j + j \prime - 1 } } { 2 } = \epsilon _ { j } ^ { ( j \prime ) }" ,3f277f55-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"Q \prime _ { \mu } = Q _ { \mu } - \frac { \partial \log F } { \partial \xi ^ { \mu } }" ,0e4660e2-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_3.jpg
"Y = - 0 . 3 + 0 . 2 0 0 X" ,2a55dc88-4ce4-11e1-1726-001143e3f55c__mathematical-expression-and-equation_8.jpg
"\sphericalangle m c b + c b m = R ," ,17a619d0-e929-11e4-a794-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"\frac { \partial p _ { 0 } } { \partial t } = - p _ { 0 } \frac { \partial c } { \partial s }" ,43b6a980-d866-4b84-97b9-407007e64205__mathematical-expression-and-equation_2.jpg
"\frac { v d v } { e ^ { - \frac { v } { 2 5 } } | 1 - e ^ { \frac { v } { 2 5 } } ( 0 . 0 0 4 5 - 0 . 0 0 0 0 7 1 5 v ^ { 2 } ) | } = - 0 . 1 g d \lambda" ,3b1cc537-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"\Sigma \frac { 1 } { \cos ^ { 3 } \alpha } = 2 \times 1 9 . 5 1 4" ,2574b750-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_5.jpg
"= \hat { 2 } < E _ { p } \frac { \tau _ { p } } { \mu _ { p } } \sum _ { k = \alpha , \beta } \kappa _ { k } [ 1 - \frac { \mu _ { k } } { \mu _ { p } } \ln ( 1 + \frac { \mu _ { p } } { \mu _ { k } } ) ]" ,9a4ea058-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg
"x _ { 0 } ^ { 2 } + y _ { 0 } ^ { 2 } = ( 2 r ) ^ { 2 }" ,8e512500-7ad7-11e8-9690-005056827e51__mathematical-expression-and-equation_6.jpg
"\frac { 1 5 } { 2 2 } : 1 7 \frac { 1 } { 4 } = x ." ,05fd0c1d-224c-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_13.jpg
"x = \frac { a + b } { 2 }" ,39dda871-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_3.jpg
"> 1 - \lambda ," ,02b32dd6-ac0b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_15.jpg
"V = \frac { B ( v + x ) } { 3 } - \frac { b x } { 3 } = \frac { B v } { 3 } + \frac { x } { 3 } ( B - b" ,4cce0e06-2dac-11ec-b355-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\parallel \kappa _ { 3 , 0 } + p \kappa _ { 3 , 1 } + p ^ { 2 } \kappa _ { 3 , 2 } \dots + , \kappa _ { 4 , 0 } + p \kappa _ { 4 , 1 } + p ^ { 2 } \kappa _ { 4 , 2 } + \dots" ,11f9f260-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_11.jpg
"P = P ( t ) > 0" ,5841cd7d-be8f-491c-adb3-1a631f6252fd__mathematical-expression-and-equation_11.jpg
"1 a + 1 6 b ( a + b ) ( 6 a + 1 1 b ) - 4 ( 3 a + 4 b ) ( 4 a + 5 b ) ( a + 2 b ) =" ,3790b91e-eb13-11ec-b47a-00155d01210b__mathematical-expression-and-equation_29.jpg
"= 1 + \frac { 1 } { n } \sum _ { \lambda = 2 , 4 , \dots } ^ { \infty } \frac { ( - 1 ) ^ { \frac { \lambda } { 2 } } } { ( \lambda + 1 ) ! } ( \frac { 2 m \pi } { n } ) ^ { \lambda } \mathbf { B } _ { \lambda - 1 } ( n ) \dots" ,324aafa8-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
"I \prime = V \prime Y \prime" ,11f9f2c4-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg
"f ( a , t ) = \sum _ { i = 1 } ^ { N } a _ { i } \phi _ { i } ( t )" ,0ecd6a07-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\mathfrak { A } ) _ { v } = 8 E J _ { o } \delta \epsilon \frac { h } { l ^ { 2 } + 8 h ^ { 2 } }" ,1f382a37-9c7a-4355-af65-c71a6907cdfa__mathematical-expression-and-equation_5.jpg
"W = 5 . 3 0 8 \times 0 . 0 1 5 = 8 0 \text { O h m } ;" ,5f9431f0-00cf-11eb-916b-5ef3fc9bb22f__mathematical-expression-and-equation_9.jpg
"w = \frac { N p } { t g \alpha }" ,329ff308-87f8-4a23-b9cf-22021f5abd13__mathematical-expression-and-equation_7.jpg
"R _ { 1 } = - x _ { 4 } x _ { 5 } ( 1 + \lambda _ { 1 } ) ," ,079fa6ba-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"\sum _ { i = 1 } ^ { n } 1 / x _ { j } = a / b" ,49b13f44-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\bar { b } c = \omega _ { 1 } L _ { 1 } J _ { 1 } ( 1 - \sigma ) \frac { x } { \sqrt { 1 + x ^ { 2 } } }" ,08084bbd-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_15.jpg
"+ \Delta _ { 3 } ( e ^ { N } ) . \int _ { \{ | 2 ( \sqrt { \lambda _ { n , h } } - 1 ) | > \epsilon \} \cap B _ { n , N } }" ,0024ba86-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_16.jpg
"\int _ { x \prime \prime \prime } ^ { x \prime \prime \prime \prime } y \partial x + \int _ { x \prime \prime \prime } ^ { x \prime \prime \prime \prime } u \partial x = \int _ { x \prime \prime \prime } ^ { x \prime \prime \prime \prime } y _ { 1 } \partial x + \int _ { x \prime \prime \prime } ^ { x \prime \prime \prime \prime } u _ { 1 } \partial x" ,53784c9d-30fa-4688-8585-30b9b60edc48__mathematical-expression-and-equation_4.jpg
"+ \frac { \alpha _ { 1 } \gamma _ { 1 } } { p _ { 1 } } f _ { 1 } f _ { 3 } + \frac { \beta _ { 1 } \gamma _ { 1 } } { p _ { 1 } } f _ { 2 } f _ { 3 } + \frac { \gamma _ { 1 } \gamma _ { 1 } } { p _ { 1 } } f _ { 3 } f _ { 3 } + \dots" ,8e3eb976-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_2.jpg
"\begin{array} { c c c c c c c } & \text { F e } & \text { A g } & \text { C u } & \text { P b } & \text { P t } & \text { N i } \\ \alpha . 1 0 ^ { 6 } & + 1 7 , 1 5 & + 2 , 1 2 & + 1 , 3 4 & 0 , 0 & - 0 , 6 0 & - 2 1 , 8 \\ \beta . 1 0 ^ { 6 } & - 0 , 0 4 8 & + 0 , 0 1 5 & + 0 , 0 0 9 & 0 , 0 & - 0 , 0 1 1 & - 0 , 0 5 \end{array}" ,45885af0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_4.jpg
"- \frac { r } { R a } - \frac { 2 } { a } ) + \frac { 1 6 v - 1 7 } { 4 R r } s ^ { 2 } + b ( \frac { 3 } { 2 R } + \frac { 2 r } { a } ( \frac { b } { s } ) ^ { 2 } + ( 2 v - 1 ) ( 4 - \frac { r } { R } ) ] n _ { r } +" ,9f78db5d-ae15-4865-be6f-0dc2fb2f4ea7__mathematical-expression-and-equation_6.jpg
"\frac { Q V _ { 2 } ^ { 2 } } { 2 g } \alpha _ { 2 } = W r ( \frac { \pi - 2 } { 2 \pi } ) \dots 7 )" ,04a6f5cd-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"w _ { i } = H _ { i } x _ { i }" ,039047c6-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_3.jpg
"B ( Z ) = \frac { \int _ { 0 } ^ { E _ { m a x } } \sigma ^ { \pi } ( E ) N ( E ) d E } { \int _ { 0 } ^ { E _ { m a x } } E N ( E ) d E }" ,9d8e639f-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg
"Q _ { s i } = 1 + \frac { u _ { 2 } } { U }" ,9a4ea091-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_5.jpg
"- ( X d x + Y d y + Z d z ) = d U" ,51d36ba0-0c73-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
"y \prime = \frac { f _ { 1 } f _ { 2 } } { \Delta } \frac { y } { x }" ,2438f5e0-1b94-11e4-8e0d-005056827e51__mathematical-expression-and-equation_6.jpg
"\mathbf { a } _ { k } \alpha + \mathbf { a } _ { 1 } ( x _ { 1 } - \alpha a _ { 1 k } ) + \mathbf { a } _ { 2 } ( x _ { 2 } - \alpha a _ { 2 k } ) + \dots + \mathbf { a } _ { r } ( x _ { r } - \alpha a _ { r k } ) + \dots" ,17ebdd42-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_4.jpg
"\{ P _ { n ( \Lambda _ { \theta _ { 0 } } + \frac { 1 } { \sqrt { n } } h ) } \}" ,0024ba88-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg
"\frac { 1 } { p Z ( p ) } = \int _ { 0 } ^ { \infty } A ( t ) e ^ { - p t } d t ." ,08ebfcc4-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
"0 = a t j t + b j t + d t" ,01d92630-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_10.jpg
"x - x _ { 0 } = \theta" ,039b5170-9944-11de-9613-0030487be43a__mathematical-expression-and-equation_5.jpg
"\mathrm { p } \cap \mathrm { p } \prime < \mathrm { p } ," ,4c97a13c-ab88-4e31-b611-8544a3052e6e__mathematical-expression-and-equation_4.jpg
"\frac { e ^ { 2 } } { 4 } = D ^ { 1 } _ { 2 }" ,5c30c26f-6bff-11e5-aeea-001b21d0d3a4__mathematical-expression-and-equation_22.jpg
"i _ { 1 } = 2 I _ { 1 } + 3" ,71d128dd-4abf-42d2-adf2-36f7c75c3efe__mathematical-expression-and-equation_7.jpg
"= \int _ { B } \int _ { B } \frac { 1 } { A } f ( z ) d \kappa _ { m - 1 } ( z ) d v ( x ) = 0" ,3bb9a7d3-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"m _ { T } \cdot C ^ { 2 } | v _ { T } ( z , t ) | e ^ { i \omega _ { c } t } - G I _ { T } \cdot D ^ { 2 } | v _ { T } ( z , t ) | e ^ { i \omega _ { c } t } ( 1 + i \delta _ { T } / \pi ) =" ,1f7999cd-3c62-11e1-7459-001143e3f55c__mathematical-expression-and-equation_7.jpg
"L P ( 0 ) = L P _ { m i n } - \frac { F P _ { m i n } } { k ^ { * } }" ,227c99f0-ed5f-11ec-95f3-005056827e51__mathematical-expression-and-equation_1.jpg
"\rcases t _ { 0 } = \alpha _ { 1 } x _ { 0 } + x _ { 1 } \\ t _ { 1 } = x _ { 0 } + \alpha _ { 1 } x _ { 1 } \rcases" ,6e081ab0-148e-11de-b5d5-0030487be43a__mathematical-expression-and-equation_0.jpg
"[ A _ { 1 1 } + n ( n + 1 ) p ^ { 2 } ] u ^ { 2 } + 2 n ( n + 1 ) p q u v + [ A _ { 2 2 } + n ( n + 1 ) q ^ { 2 } ] v ^ { 2 } +" ,3f3ca384-df28-11e1-1154-001143e3f55c__mathematical-expression-and-equation_5.jpg
"w = a _ { 0 } + a _ { 1 } z + a _ { 2 } z ^ { 2 } + \dots + a _ { n } z _ { n } + \dots ," ,9acc1850-7d97-11e7-921c-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg
"[ p v ] = 0 ," ,0561c666-a56b-f851-ec31-04d636e3359c__mathematical-expression-and-equation_9.jpg
"T = | \begin{array} { c c c c } A _ { r , \alpha - r } & A _ { r , \beta - r } & A _ { r , \gamma - r } & . \\ A _ { r + \alpha \prime - \alpha , \alpha - r } & A _ { r + \alpha \prime - \alpha , \beta - r } & \dots & . \\ A _ { r + \alpha \prime \prime - \alpha , \alpha - r } & A _ { r + \alpha \prime \prime - \alpha , \beta - r } & \dots & . \\ \dots & \dots & \dots & . \end{array} |" ,0551bf31-40e4-11e1-1726-001143e3f55c__mathematical-expression-and-equation_5.jpg
"= W ( x _ { 1 } , x _ { 2 } , \dots , x _ { k } , x _ { k + 1 } ) ( a _ { j } + \epsilon )" ,46fe54a9-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
"= e ^ { 2 \pi ( f _ { * } ( x ) + n + j + 1 ) i } = e ^ { 2 \pi f _ { * } ( x ) i } = f ( e ^ { 2 \pi x i } )" ,07df0b68-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"Q = 2 4 . 3 6 0 0 \frac { 1 0 2 N } { 1 0 0 0 H \eta }" ,2bbdfa50-fc9a-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg
"\le c ^ { * } \cdot \parallel ( u _ { \delta } ) ^ { 0 } ( \cdot , t ) \parallel _ { W _ { p } ^ { 2 } ( \mathbb { R } ^ { n - 1 } \times ( - \delta / 2 , \infty ) ) } \le c ^ { * } \cdot \parallel u ( \cdot , t ) \parallel _ { W _ { p } ^ { 2 } ( Q _ { + } ^ { n } ( \alpha , \beta }" ,0c39d915-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_8.jpg
"1 1 0 \times 1 . 1 8 6 = 1 3 0 . 5" ,94db40e5-2b65-4b8a-9d30-2943ed982e0d__mathematical-expression-and-equation_1.jpg
"[ p ] x - [ p b ] y - [ p c ] z - [ p l ] = 0" ,9b195470-c4a3-a7cc-1cc9-3fa25cf1d5e6__mathematical-expression-and-equation_6.jpg
"A _ { n _ { 1 } \dots n _ { p } } = \frac { 1 } { \Gamma ( s ) } \sum _ { \alpha = 1 } ^ { p } C _ { \alpha } \frac { \pi } { \sin s \pi } [ \frac { 2 \pi i } { c _ { \alpha } } ( n _ { \alpha } - v _ { \alpha } ) ] ^ { s - 1 } ," ,89e0ffb6-0634-4e2a-9db7-cc211142cc98__mathematical-expression-and-equation_1.jpg
"x \cdot \frac { \partial F } { \partial x } + y \cdot \frac { \partial F } { \partial y } + z \cdot \frac { \partial F } { \partial z } = 0" ,2fd77d12-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_0.jpg
"Q _ { 1 } = Q _ { 2 } = Q _ { 3 }" ,2168a3b5-c5fa-4012-a710-43918d3ab685__mathematical-expression-and-equation_2.jpg
"3 r \prime + l \prime = 3 ( r \prime + 1 ) - 2 l \prime = 3 ( r + 1 ) - 2 l \prime" ,5d3bd029-972d-4471-b711-26afadf395c2__mathematical-expression-and-equation_14.jpg
"\Delta \phi = \frac { v \Delta t } { r } , \Delta v _ { n } = v \prime \Delta \phi = \frac { v \prime v } { r } \Delta t ," ,1da46920-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_2.jpg
"M S f g" ,5ef7f9d8-c417-4682-9905-8c0a5beef123__mathematical-expression-and-equation_0.jpg
"\xi = \alpha _ { 1 } t" ,53d28b90-d7ae-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_4.jpg
"- 2 x + 4 T ( x , y ) - T ( x , x ) + T ( y , y ) \le 0" ,0469dd78-ac0b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_2.jpg
"| \tau _ { 2 } - \tau _ { 1 } | \le \sigma" ,4094a2c7-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg
"T = \frac { Q } { 2 }" ,4e80e19c-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_8.jpg
"\prime \delta u ^ { h } = d u ^ { h } + \Lambda ^ { k } _ { J i } u ^ { i } ( d \xi ) ^ { J }" ,0efce001-40e4-11e1-2755-001143e3f55c__mathematical-expression-and-equation_3.jpg
"Z ^ { ( k - 1 ) } ( t _ { 0 } ^ { k } ) \neq 0" ,0c39d9e9-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { d ^ { 2 } u } { d x ^ { 2 } } + ( q _ { 2 } - \frac { 1 } { 4 } q _ { 1 } ^ { 2 } - \frac { 1 } { 2 } q _ { 1 } \prime ) u = 0 ." ,6d40e55e-39b9-4212-85ed-b190817cc1dc__mathematical-expression-and-equation_0.jpg
"\mathcal { L } ^ { i } = \frac { 1 } { 2 } \int _ { V } \sigma _ { i j } e _ { i j } d V" ,5fbe9849-e504-4a7d-a78b-28e44a4421c0__mathematical-expression-and-equation_0.jpg
"\align* 1 7 & - 7 & & = & 1 0 \\ 1 7 & - 8 & ( - 7 - 1 ) & = & 9 \\ 1 7 & - 9 & ( - 7 - 2 ) & = & 8 \\ 1 7 & - 1 0 & ( - 7 - 3 ) & = & 7 \align*" ,3378af50-1030-11e5-ae7e-001018b5eb5c__mathematical-expression-and-equation_11.jpg
"\sqrt { x } ;" ,084a3f02-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_5.jpg
"R _ { x \prime } ( \phi , t ) = ( R _ { x \prime _ { 1 } } ( \phi , t ) , \dots , R _ { x \prime _ { n } } ( \phi , t ) ) ^ { T }" ,47babbfc-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_8.jpg
"t > 0" ,08bd5ccd-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_8.jpg
"v = 1 . 2 0 m" ,28baa56d-6761-11e9-bca3-001999480be2__mathematical-expression-and-equation_12.jpg
"n Z _ { 0 } z ^ { n - 1 } + ( n - 1 ) Z _ { 1 } z ^ { n - 2 } + \dots + Z _ { n - 1 } = 0" ,9c7b00d0-7d97-11e7-921c-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg
"( \frac { F _ { o } } { F _ { \iota 0 } } ) ^ { 2 } = 0 , 3 6 8 1 6" ,0011ea20-bc38-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
"T = \epsilon \log \Delta ^ { \circ } + 1 ^ { \circ }" ,3d1f72ce-ec08-49a7-a9ec-45180104d497__mathematical-expression-and-equation_0.jpg
"N = 0 ; \gamma ^ { * } = 1 / 3 0 ; \theta ^ { * } = 1 . 4 ; \mu = 0 . 3 ; \kappa = 1 0 ^ { - 2 } ; \lambda = 0 . 0 3 ; \rho = 1 / 6 0" ,153e6ec1-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg
"r x _ { 0 } + - p _ { 1 } \sigma = 0 ." ,27e827a1-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_5.jpg
"A = \frac { P . x b } { a b }" ,7b144b10-04d9-11e5-91f2-005056825209__mathematical-expression-and-equation_2.jpg
"6 m - 2 m = 4 m" ,1c278840-14e4-11e5-9192-001018b5eb5c__mathematical-expression-and-equation_3.jpg
"\sin ( a x + \alpha ) \sin ( b x + \beta )" ,14fefca0-0a0b-11e3-9439-005056825209__mathematical-expression-and-equation_10.jpg
"\frac { c } { b } \sqrt { b b - x x } ^ { 9 } )" ,3dd2f884-e41f-4c6a-aacf-062a1f31be33__mathematical-expression-and-equation_3.jpg
"\sum _ { i = 1 } ^ { \infty } \psi _ { a } ( \alpha _ { i } )" ,0024baab-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\int _ { a } ^ { b } w ( x ) ( \int _ { a } ^ { x } p ^ { - 1 } ( t ) d t ) ^ { \eta } d x = \infty" ,01d92655-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg
"\mu = \mu _ { 0 } = - \frac { 1 } { 2 } ( 2 + \gamma ) + \frac { 1 } { 2 } \sqrt { ( 4 + \gamma ^ { 2 } ) }" ,3b0c5023-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
"+ \frac { 9 } { 4 } ( 1 - \frac { | \Delta l | } { l } ) ^ { 2 } ] ^ { 1 / 2 }" ,19c168f7-7c23-4cd3-99dd-07ef5510ffe8__mathematical-expression-and-equation_2.jpg
"\sin ^ { 2 } \phi = \frac { z ^ { 2 } } { a ^ { 2 } }" ,5fac6741-9c00-44ba-aebf-f1bc7045e74b__mathematical-expression-and-equation_8.jpg
"2 . \genfrac { ( } { ) } { 0 p t } { } { 4 } { 3 } = 1 2 0 ." ,05f7ea40-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_8.jpg
"+ | | V _ { 1 } | - | V _ { 2 } | | + | | V _ { 2 } | - | V _ { 3 } | | - | | V _ { 1 } | - | V _ { 3 } | | ," ,3b0c51c3-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"t = \frac { t _ { 1 } - t _ { 2 } } { \ln r _ { 1 } - \ln r _ { 2 } } \cdot \ln r + \frac { t _ { 2 } \ln r _ { 1 } - t _ { 1 } \ln r _ { 2 } } { \ln r _ { 1 } - \ln r _ { 2 } }" ,0f6d5b4a-5308-11ea-8ddc-00155d012102__mathematical-expression-and-equation_6.jpg
"A _ { 2 3 } = A _ { 2 1 }" ,249e4a60-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
"\Delta Q = \frac { F _ { m } + F _ { m + 1 } } { 2 } \Delta u" ,79bf0e00-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_0.jpg
"a _ { 2 0 } + a _ { 2 1 } x _ { 0 } + a _ { 2 2 } y _ { 0 } + a _ { 2 3 } z _ { 0 } = 0" ,0a6a7c00-3e68-4146-a8c5-66b7dfef6b35__mathematical-expression-and-equation_9.jpg
"A _ { 1 } B _ { 2 } - A _ { 2 } B _ { 1 } = 0" ,11f9f18c-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg
"[ p c c . 2 ] = [ p c c . 1 ] - \frac { [ p b c . 1 ] } { [ p b b . 1 ] } . [ p b c . 1 ] ," ,4a88cd72-c406-4784-a346-12a713d0c33c__mathematical-expression-and-equation_3.jpg
"\vec { p } ( n ) = ( p _ { 1 } ( n ) , p _ { 2 } ( n ) , \dots , p _ { 5 } ( n ) )" ,53c77add-420f-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg
"t \in \mathbb { G } _ { 3 } ( x ) \cup \mathbb { G } _ { 4 } ( x )" ,0c39d9ee-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_4.jpg
"+ K e ^ { j \alpha } e ^ { \mathbf { p } _ { 2 } t } [ \frac { \mathbf { C } _ { R 2 } } { \mathbf { p } _ { 2 } } e ^ { j \beta } ( 1 - e ^ { - \mathbf { p } _ { 2 } t } ) - ( \frac { \mathbf { C } _ { S 1 } } { \mathbf { p } _ { 1 } } + \frac { \mathbf { C } _ { S 2 } } { \mathbf { p } _ { 2 } } )" ,1f799c43-3c62-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg
"d _ { 0 } = \sqrt { \frac { 1 6 P l _ { 2 } } { 3 \pi k _ { 3 } l } }" ,4e80e1af-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_1.jpg
"q = \frac { 2 \cdot 1 1 0 \cdot 6 \cdot 7 } { 6 0 \cdot 4 } = 2 4 \cdot 4 m m ^ { 2 }" ,3a238330-d411-4242-89cd-bc02279b37a2__mathematical-expression-and-equation_0.jpg
"t \ge t _ { 1 }" ,0c39d9ab-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_11.jpg
"T _ { 0 } = 4 ^ { s } , V _ { 0 } = 6 0 , \epsilon : 1 = 4 , r / T _ { 0 } ^ { 2 } = 0 . 0 4 \text { m m } / \text { s } ^ { 2 } ." ,64bae653-18ca-4083-aa51-7c473bab2de7__mathematical-expression-and-equation_0.jpg
"\int _ { 0 } ^ { \infty } | \mu | ( Q _ { \tau } ) d \tau \le 2 ^ { N } \int _ { 0 } ^ { ( s r ) ^ { - p _ { j } } } v ^ { m } ( \tau ^ { - 1 / \beta _ { j } } , \mu ) d \tau = 2 ^ { N } \beta _ { j } \int _ { s r } ^ { \infty } v ^ { m } ( t , \mu ) t ^ { - \beta _ { j } - 1 } d t" ,39b0dff2-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"- \frac { \pi \cdot d ^ { 3 } } { 6 } \cdot \rho _ { p } \cdot f \cdot \frac { ( C \cdot t - D ) } { [ 1 + \frac { B ^ { 2 } } { v _ { s } ^ { 2 } } ] ^ { \frac { 1 } { 2 } } } = 0" ,01b191b0-bc38-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"L _ { n } ^ { m } = q _ { 3 } P _ { n } ^ { m } ( \eta _ { 0 } ) Q _ { n } ^ { m } ( E _ { 2 } )" ,6f47237f-2895-479b-8f15-a7dec7c22569__mathematical-expression-and-equation_2.jpg
"\le c [ \frac { 1 } { m } + \int _ { T } ^ { t } \frac { d s } { s \omega ( g ( s ) ) } + \int _ { T } ^ { t } \frac { | [ \omega ( g ( s ) ) ] \prime | } { \omega ^ { 2 } ( g ( s ) ) } d s ] < \infty" ,03921ff6-570b-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\lim _ { x \rightarrow \infty } \epsilon f ( x ) = \infty" ,47babc60-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
"\sqrt { v _ { 2 } } = \phi ^ { 2 } ( \epsilon ) + \theta ^ { 2 } \phi ^ { 2 } ( \alpha \epsilon ) + \dots + \theta ^ { 2 n - 2 } \phi ^ { 2 } ( \alpha ^ { n - 1 } \epsilon ) ," ,4791abf5-1bc8-42b4-821a-f98f5c6e8465__mathematical-expression-and-equation_7.jpg
"d _ { 6 X 5 } = 1" ,3f277f27-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_13.jpg
"\langle ( \lambda _ { 1 } I - A ) z _ { n } , z _ { n } \rangle \ge ( \lambda _ { 1 } - M ) \parallel z _ { n } \parallel ^ { 2 }" ,37a928d0-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg
"[ r , \frac { a ^ { 2 } } { b } , \frac { m a } { b } ]" ,68c27795-2993-442a-95f7-bd48a2dad6e8__mathematical-expression-and-equation_4.jpg
"V ^ { ( d ) N } _ { ( t ) } = \sum _ { 1 } ^ { t } K P ^ { ( d ) } ( 1 + i ) ^ { ( t + 1 - K ) } + \sum _ { 1 } ^ { t } K q _ { ( K - 1 ) } V ^ { ( d ) N } _ { ( K ) } ( 1 + i ) ^ { ( t - K ) }" ,9e9bd45c-0e5a-11eb-b87e-005056a54372__mathematical-expression-and-equation_1.jpg
"\align* 1 & = \frac { 6 0 } { 6 0 } \\ \frac { 1 } { 3 } & = \frac { 2 0 } { 6 0 } , \\ \frac { 1 } { } & - \frac { 1 0 } { } \align*" ,7b478b67-3637-11ec-8869-001b63bd97ba__mathematical-expression-and-equation_6.jpg
"= 1 4 + 1 \frac { 1 } { 4 } + 1 = 1 6 \frac { 1 } { 4 }" ,2bf5673d-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_40.jpg
"c = c ^ { * } , e = e ^ { * } ," ,9686c344-4334-11e1-1331-001143e3f55c__mathematical-expression-and-equation_22.jpg
"L \prime _ { 1 } = \frac { X _ { 1 2 } ( \frac { N _ { 3 } } { N _ { 1 } } ) ^ { 2 } + X _ { 1 3 } ( \frac { N _ { 3 } } { N _ { 1 } } ) ^ { 2 } - X _ { 2 3 } ( \frac { N _ { 3 } } { N _ { 2 } } ) ^ { 2 } } { 2 \omega }" ,0d342c41-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg
"| \Psi [ v _ { a } ] - \Psi [ v _ { b } ] | \le C | v _ { a } - v _ { b } | ," ,173d34b5-ea58-4b92-b017-33a2ad44288b__mathematical-expression-and-equation_3.jpg
"F ( x , y , z , a ) = 0" ,5a75688e-9ea7-4484-aa62-7d33263db1f0__mathematical-expression-and-equation_7.jpg
"\xi = r . t g . \alpha _ { o }" ,8ee789e0-de9d-11e7-8cdd-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg
"s ^ { * } ( q ) = \xi ( q ) p ^ { * } + [ 1 - \xi ( q ) ] p ^ { 0 }" ,31eb76bd-4d7c-4478-a5fa-1a1a04fccc19__mathematical-expression-and-equation_1.jpg
"( 2 \prime ) \{ \begin{array} { c } N _ { i k } = b _ { k i } + \sum _ { \rho = 1 } ^ { 3 } b _ { k , \rho } + s \tau _ { \rho ^ { i } } \\ \sum _ { \sigma = 1 } ^ { s } N _ { i \sigma } \tau _ { k \sigma } = b _ { k + s , i } + \sum _ { \rho = 1 } ^ { s } b _ { k + s , \rho } + s \tau _ { \rho ^ { i } } \end{array}" ,019971d0-40e4-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\sum _ { k = 1 } ^ { t } \frac { 1 } { 4 \mu _ { k } S _ { k } } \{ A _ { 0 k } [ ( y _ { 1 k } - y _ { 2 k } ) ^ { 2 } + ( x _ { 1 k } - x _ { 2 k } ) ^ { 2 } ] +" ,23c01e57-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_13.jpg
"a \le t \le b" ,47babc57-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_10.jpg
"7 : 5 = \frac { 1 } { 1 6 5 } : \frac { 1 } { 2 4 5 }" ,60cc5dc9-d663-459f-9c4a-932061679bb7__mathematical-expression-and-equation_0.jpg
"\vec { D } = [ \epsilon ] \epsilon _ { 0 } \vec { E }" ,1c1d502d-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_6.jpg
"d = \sqrt { \frac { V } { 2 m p _ { s } } }" ,509a37e4-c99e-413f-adbf-c2c7d7c03000__mathematical-expression-and-equation_0.jpg
"| ( ( \dot { x } , h ) ) _ { 0 } | \le M _ { 3 } \cdot \parallel h \parallel _ { L ^ { 2 } ( X ) }" ,0ee4af5d-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg
"s = c \prime + c t" ,186f799f-6c55-450c-b493-d0e38aeced8e__mathematical-expression-and-equation_7.jpg
"E _ { a } ^ { * } ( \omega ) = \mathcal { G } _ { 3 3 } ( \omega ) - \frac { 2 \mathcal { G } _ { 1 2 } ^ { 2 } ( \omega ) } { \mathcal { G } _ { 1 1 } ( \omega ) + \mathcal { G } _ { 1 2 } ( \omega ) }" ,1f7999f7-3c62-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg
"\frac { d x } { d \tau } = D [ A ( t ) x + C ( t ) x ( a ) + D ( t ) x ( b ) + \int _ { a } ^ { b } [ d _ { s } G ( t , s ) ] x ( s ) + f ( t ) ]" ,49b13f30-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg
"X = f - \frac { 1 } { 2 ! } f \prime \prime - \frac { 1 } { 4 ! } f \prime \prime \prime \prime + \dots + \frac { ( - 1 ) ^ { n } } { ( 2 n ) ! } f ^ { ( 2 n ) } \pm \dots" ,62262c48-886a-435c-ae8a-f3cbe87f0fe1__mathematical-expression-and-equation_3.jpg
"0 . 4 8 3 5 C O _ { 2 } = 6 2 . 3 2 \% C" ,157266ec-6edd-4370-b076-4c1645105ddf__mathematical-expression-and-equation_0.jpg
"y _ { k } \prime = H ^ { v } e ^ { b H } \{ f \prime [ 1 + o ( 1 ) ] + f H \prime ( v H ^ { - 1 } + b ) [ 1 + o ( 1 ) ]" ,47ac1ff7-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg