formula stringlengths 5 635 | image stringlengths 80 86 |
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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 } } {... | 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... | 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 |
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