formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
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 |
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