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