formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
\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 ... | 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 \... | 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 |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 887