formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
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 ... | 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{a... | 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 } } \fra... | 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.