formula stringlengths 5 635 | image stringlengths 80 86 |
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- \frac { 2 } { 3 } u _ { e } \Theta \frac { \partial n _ { e } } { \partial z } - \frac { 2 } { 3 } N _ { e } \Theta \frac { \partial u _ { e } } { \partial z } - n _ { e } \sum _ { k } \alpha _ { k 0 } q _ { 0 } U _ { k } - \Theta \frac { \delta N _ { e } } { \delta t } | a09e13ce-4334-11e1-1121-001143e3f55c__mathematical-expression-and-equation_6.jpg |
C _ { 6 } H _ { 5 } \cdot P ^ { I I I } = P ^ { I I I } \cdot C _ { 6 } H _ { 5 } | a0d76f44-e44a-4aaa-a6ee-9b8d76b16759__mathematical-expression-and-equation_8.jpg |
\langle u _ { n k } | \mathrm { g r a d } _ { k } H ( \mathbf { k } ) | u _ { n k } \rangle = \mathrm { g r a d } _ { k } \epsilon _ { n } ( \mathbf { k } ) | a2363f9c-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_3.jpg |
c = \frac { 1 } { x } \{ D ( v _ { 2 } - w _ { x } ) - D ( v _ { 1 } - w _ { x } ) + w _ { x } [ S ( v _ { 2 } - w _ { x } ) - S ( v _ { 1 } - w _ { x } ) ] \} | a2a081e0-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg |
\sinh x = \sqrt { \cosh ^ { 2 } x - 1 } , | a2d715c0-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg |
v _ { z i } = k _ { K } \cdot v \prime _ { z i } | a39ac456-8eef-48b1-809b-0b0a9deeaf1b__mathematical-expression-and-equation_4.jpg |
c _ { I } = 1 5 k N / m ^ { 2 } | a45fb544-b9f4-11e1-2544-001143e3f55c__mathematical-expression-and-equation_10.jpg |
= t x - \int \frac { a d t } { \sqrt { t ^ { 2 } - 1 } } | a51bfcb0-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg |
\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 7 0 } | a5322f7e-5030-43d2-9e80-4dd05033639e__mathematical-expression-and-equation_12.jpg |
1 c m ^ { 3 } = 0 . 0 0 1 d m ^ { 3 } | a558aa20-dbae-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_10.jpg |
( a - f _ { 1 } ) ( b - f _ { 2 } ) = f _ { 1 } f _ { 2 } | a592f2a0-8655-11e3-8cd6-005056825209__mathematical-expression-and-equation_5.jpg |
= \int _ { a } a ^ { 2 } . \sinh ^ { 2 } u . d u , | a679df00-8373-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_14.jpg |
\frac { d ^ { 4 } y } { d x ^ { 4 } } = - \frac { C b } { E _ { 1 } J _ { 1 } } \cdot y | a6ba1fe9-3240-4472-8e02-cc6dcaf65316__mathematical-expression-and-equation_1.jpg |
\frac { n _ { 1 } } { n _ { 2 } } \rho _ { 1 } V _ { 1 } = P _ { 1 } , \rho _ { 2 } V _ { 2 } = P _ { 2 } , \frac { n _ { 3 } } { n _ { 2 } } \rho _ { 3 } V _ { 3 } = P _ { 3 } \dots 8 | a6e92ba7-335b-11e9-8d85-00155d012102__mathematical-expression-and-equation_13.jpg |
+ \kappa _ { e } \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { k + 1 } \frac { ( n + k ) ! } { ( k + 1 ) ! ( n - 1 ) ! } \lambda _ { 1 , n + k + 1 } \epsilon ^ { n + k + 1 } \alpha _ { e , n } ^ { ( 1 ) } + | a75bbbaf-292e-43b6-844d-80e63ae36524__mathematical-expression-and-equation_12.jpg |
2 \sqrt { g . b ( 1 - \cos \phi ) } = 2 \sin \frac { \phi } { 2 } . \sqrt { 2 g . b } | a7642cd4-cc6d-4550-865a-bf108183d1dd__mathematical-expression-and-equation_7.jpg |
P \frac { N - 1 } { D } = p _ { 1 } \frac { n _ { 1 } - 1 } { d _ { 1 } } + p _ { 2 } \frac { n _ { 2 } - 1 } { d _ { 2 } } + p _ { 3 } \frac { n _ { 3 } - 1 } { d _ { 3 } } \dots | a80fe189-63df-11e8-ae35-00155d012102__mathematical-expression-and-equation_0.jpg |
c _ { m } = c _ { m - 2 } + 4 \frac { u _ { m - 1 } g _ { m - 1 } } { p _ { m - 1 } } | a882a785-ae87-4d45-8ba4-52cdb63669c8__mathematical-expression-and-equation_2.jpg |
1 5 8 0 - 8 0 9 | a90cf213-2e37-4669-84e8-0b57fc4274c2__mathematical-expression-and-equation_9.jpg |
\alpha _ { 1 } \doteq 2 8 ^ { \circ } 2 0 \prime | aacae850-d035-11ea-b03f-5ef3fc9bb22f__mathematical-expression-and-equation_17.jpg |
\cos \eta _ { 2 } \pm \sqrt { \frac { 1 + c _ { 2 } } { 2 + a _ { 2 } + c _ { 2 } } } = \pm \sqrt { \frac { 1 + C m } { 2 + ( A + C ) m _ { 2 } } } | aaf257c1-7ea5-482c-86fb-e2d625fe4668__mathematical-expression-and-equation_3.jpg |
F _ { ( d ) } = k _ { ( d ) } \gamma _ { g } [ \frac { 1 } { r _ { c } } - \frac { 1 } { r _ { g } } \pm \frac { 3 \phi _ { p } } { 4 r _ { p } } ] | ab2aba9a-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg |
( Z _ { i e } - 1 ) ( \sigma + 1 ) + \kappa F P _ { i e } = \frac { 1 } { \gamma _ { i } Z _ { i i } } | ab2abc25-4334-11e1-3052-001143e3f55c__mathematical-expression-and-equation_7.jpg |
C D = \Delta E = O B | acef22b0-e3d1-11e3-bbd5-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg |
\theta _ { 3 } = \beta g a _ { 3 } ( \Delta T \prime + q _ { 3 } ) / I _ { 2 } \lambda \mu | ad88592e-4334-11e1-7459-001143e3f55c__mathematical-expression-and-equation_7.jpg |
U _ { E B } = \frac { k T } { e } \ln ( U _ { 0 } / \alpha I _ { 0 } ) - \ln R _ { s } ] | ad885a9c-4334-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\Delta g \prime = ( g - \gamma ) + \Delta g _ { t } = \Delta g _ { B + t } + 2 \pi f \delta H | adb8bc0f-367b-44a9-90e1-1a3a441cfb31__mathematical-expression-and-equation_2.jpg |
z = \frac { \phi } { \psi } = \frac { p } { P } | ade41470-35eb-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg |
+ 0 . 1 3 | + 0 . 5 3 | - 0 . 0 4 | + 0 . 3 4 | - 0 . 1 0 | + 0 . 5 2 | + 0 . 3 2 | + 0 . 1 0 | - 0 . 0 4 | + 0 . 5 4 | + 1 . 1 1 | + | adf9aa92-7a2a-4be3-a950-2b9e2c73915f__mathematical-expression-and-equation_0.jpg |
\begin{array} { c c } p + 1 & m \\ p & m _ { p } - m \\ p - 1 & \mu _ { p - 1 } \\ \vdots & \vdots \\ 1 & \mu _ { 1 } \\ 0 & \mu _ { 0 } \end{array} \begin{array} & + \Sigma ( \mu _ { p } - m _ { p } + m _ { p - 1 } ) \dots & ( \mu _ { 1 } - m _ { 1 } + m _ { 0 } ) \\ & m _ { p 1 } & m _ { 0 } \end{array} | ae03b230-ff5d-11e9-baca-005056825209__mathematical-expression-and-equation_1.jpg |
\frac { A - y _ { 1 } } { A - y _ { 2 } } = \frac { A - y _ { 2 } } { A - y _ { 3 } } | ae0e1560-cf87-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_4.jpg |
\frac { 0 , 0 0 1 2 9 3 2 } { 1 + 0 , 0 0 3 6 7 t } \frac { b } { 7 6 0 } | ae94fbb0-ee5d-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg |
h _ { 0 } + \frac { 1 } { h _ { 1 } + \frac { 1 } { h _ { 2 } + \dots } } | aebefd47-25f6-4ba5-8f60-d3156fb5cb4f__mathematical-expression-and-equation_1.jpg |
C _ { x } = c \cos \alpha | aec3d0d0-0a78-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg |
\mathfrak { S } I ( a + b ) = \frac { \mathfrak { B } _ { 1 } s _ { 1 } ^ { 2 } ( S - s _ { 1 } ) ^ { 2 } } { 3 H J S } = ( I l \prime ) | af16f910-421d-11e3-ac54-005056825209__mathematical-expression-and-equation_1.jpg |
\sum _ { p ^ { m } = q } ^ { \infty } f ( \frac { x } { p ^ { m } } ) | afab5759-587f-4fb2-8221-4d8d22524f09__mathematical-expression-and-equation_1.jpg |
\Delta v _ { \_ } = \pm 1 , 2 7 | afc204bd-f1e8-45ef-97a8-0f65574184a0__mathematical-expression-and-equation_4.jpg |
G ( \rho _ { 1 } , \rho _ { 2 } , \Delta \rho , \phi _ { 1 } \phi _ { 2 } \Delta \phi ) = \frac { 1 } { s ( 1 ) s ( 2 ) } \int _ { \phi _ { 1 } } ^ { \phi _ { 1 } + \Delta \phi } d \phi \int _ { \phi _ { 2 } } ^ { \phi _ { 2 } + \Delta \phi } d \psi \int _ { \rho _ { 1 } } ^ { \rho _ { 1 } + \Delta \rho } r d r \int _ ... | aff80336-61e5-46af-8145-85c502b00026__mathematical-expression-and-equation_2.jpg |
\Pi = \sum _ { i = 1 } ^ { m } ( \frac { 1 } { 2 } ( r _ { r } ^ { ( j ) } ) ^ { T } ( \mathbf { E } ^ { ( j ) } ) ^ { T } \mathbf { K } ^ { ( j ) } \mathbf { E } ^ { ( j ) } r _ { r } ^ { ( j ) } + \frac { 1 } { 2 } ( r _ { r } ^ { ( j ) } ) ^ { T } ( \mathbf { E } ^ { ( j ) } ) ^ { T } \mathbf { K } ^ { ( j ) } \math... | b0179d35-3ded-443d-977b-9d3fc597008e__mathematical-expression-and-equation_6.jpg |
\epsilon = \epsilon _ { 0 } + \dot { \epsilon } _ { s } + \epsilon _ { t } [ 1 - \exp ( - \frac { t } { \tau \prime } ) ] | b03f2523-f752-4fe7-bcdb-f7272fae1eef__mathematical-expression-and-equation_0.jpg |
F _ { y } = F _ { y k } + F _ { y l } + F _ { y m } | b0d11137-7c33-4f95-8671-98987db7a5db__mathematical-expression-and-equation_7.jpg |
C ( \bar { \epsilon } ^ { p } ) = \frac { d N _ { t } } { d \bar { \epsilon } ^ { p } } | b19900df-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\chi _ { z z } = \frac { [ N q ^ { 2 } / ( \epsilon _ { v a c } m ) ] } { \omega _ { 0 } ^ { 2 } - \omega ^ { 2 } - i \omega \Gamma } | b19901c8-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg |
A D = A M \tan y | b1b635f0-bc8f-11e2-9592-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg |
S = \sigma T ^ { \alpha - 1 } | b20f8a70-3f08-11e6-8746-005056825209__mathematical-expression-and-equation_7.jpg |
+ i R l m \Psi ( m , n , t ) - \alpha ^ { 2 } ( m , n ) \Theta ( m , n , t ) | b267e8d9-4334-11e1-1431-001143e3f55c__mathematical-expression-and-equation_15.jpg |
R _ { 1 } = \sqrt { K _ { 1 } \sqrt { \frac { 9 ( m ^ { 2 } K _ { 2 } - n ^ { 2 } K _ { 1 } ) } { \pi ^ { 2 } ( n ^ { 2 } K _ { 1 } ^ { 2 } - m ^ { 2 } K _ { 2 } ^ { 2 } ) } } } = 2 4 , 3 6 6 \dots \mathrm { c m } | b2aff5cd-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_4.jpg |
k = \frac { 3 } { \pi } K = 9 . 0 2 9 8 . . d m ^ { 3 } . | b2aff5d3-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
K = \frac { 1 } { 3 } ( 4 S - M ) v = 1 5 , 7 0 6 4 7 d m ^ { 3 } . | b2b01ceb-c058-11e6-96bf-001b63bd97ba__mathematical-expression-and-equation_10.jpg |
\frac { d ^ { 2 } u } { d z \prime ^ { 2 } } - ( \frac { h ^ { 2 } p ^ { 2 } } { c ^ { 2 } } \cos ^ { 2 } z \prime - A ) u = 0 | b2c50bf7-4d6a-470f-8fda-738c7a9dba98__mathematical-expression-and-equation_2.jpg |
\Delta ^ { 2 } y = \Delta y _ { k - 1 } - \Delta y _ { k } | b45a421c-e2fb-4561-b918-03209f485d39__mathematical-expression-and-equation_6.jpg |
A x ^ { 2 } + B x y + C y ^ { 2 } + . | b49e87a5-c04a-11e6-8cf4-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
\sum _ { \substack { j \\ P _ { j } \in \mathcal { X } _ { l } ^ { k } } } x _ { j } ^ { k } = x _ { j } ^ { * k } | b5893fae-4ddb-4e94-b483-aa876d0182b6__mathematical-expression-and-equation_7.jpg |
O = 4 0 0 \text { k o r } | b63df2b0-e3d1-11e3-bbd5-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg |
J ( z ) \equiv F _ { 1 } ( z ) \exp [ \int q ( a _ { 1 } + b ) d z ] | b63e938b-dfe0-4e9b-82ba-c007c9ba1284__mathematical-expression-and-equation_0.jpg |
\epsilon _ { M } = \frac { 1 } { 3 } ( \dot { \epsilon } _ { 1 1 } + \dot { \epsilon } _ { 2 2 } + \dot { \epsilon } _ { 3 3 } ) | b6c0b014-e63f-4ec7-870a-ac63862bb168__mathematical-expression-and-equation_3.jpg |
d ( \sigma _ { n + 1 } ^ { 1 } , \sigma _ { n + 1 } ^ { 2 } ) \le d ( \sigma _ { n } ^ { 1 } , \sigma _ { n } ^ { 2 } ) | b6d6924b-26a8-4ec8-b0cb-041e077f9b97__mathematical-expression-and-equation_1.jpg |
f _ { D } = - r _ { D } i _ { D } | b6e537c2-48d3-425a-971a-95c328227e27__mathematical-expression-and-equation_9.jpg |
\frac { B } { \mu } [ 1 - \frac { p _ { 2 } } { p _ { 1 } } + \frac { 1 } { \kappa - 1 } ( 1 - [ \frac { p _ { 2 } } { p _ { 1 } } ] ^ { \frac { \kappa - 1 } { \kappa } } ) ] | b7051290-4421-11e4-af1d-001018b5eb5c__mathematical-expression-and-equation_3.jpg |
\frac { M } { J } \le \frac { k \prime \prime } { e \prime \prime } | b7073bd2-e228-11e2-a0b3-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg |
\sin \phi _ { 0 } = a _ { 1 } ^ { 0 } : M | b724e18c-e097-4682-9633-a5b359a25b1f__mathematical-expression-and-equation_3.jpg |
\frac { \frac { a } { x } + \frac { a } { a + b } } { \frac { a } { x } - \frac { b } { a + b } } = \frac { a + b } { b } | b76fb110-369c-41e5-ad27-b9c6b34f03af__mathematical-expression-and-equation_5.jpg |
H _ { 1 } = \frac { 2 I _ { 1 } } { r } . | b8441740-0c73-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg |
\delta = \log \mu - \log m = \frac { c } { a ^ { 2 } \gamma C } [ q \cos ( \gamma s - q t ) - \frac { b n u } { r } \sin ( \gamma s - q t ) ] + T - \log m | b89d17bd-d665-4633-ba86-0f50eeee616f__mathematical-expression-and-equation_7.jpg |
x + \frac { [ p a b ] } { [ p a a ] } y = \frac { [ p a o ] } { [ p a a ] } | b8f37228-7979-40e4-8845-6c09ffa9028d__mathematical-expression-and-equation_2.jpg |
p = \pi d \text { u n d } q = \frac { \pi d ^ { 2 } } { 4 } | b93c0130-e83e-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_1.jpg |
\bar { b } _ { 1 3 } = \bar { r } _ { 1 3 } \frac { \bar { \sigma } _ { 1 } } { \bar { \sigma } _ { 3 } } | b9784fd0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg |
\frac { m \prime n \prime _ { 1 } - n \prime m \prime _ { 1 } } { m \prime _ { 2 } n \prime _ { 3 } - n \prime _ { 2 } m \prime _ { 3 } } = \frac { m n _ { 1 } - n m _ { 1 } } { m _ { 2 } n _ { 3 } - n _ { 2 } m _ { 3 } } | b97e9218-3225-4485-b74b-33796dff9aef__mathematical-expression-and-equation_3.jpg |
\text { P o s t o } l = \frac { 1 } { \rho } | bbc8e16d-b34f-41f1-94d2-e64e6f8062f7__mathematical-expression-and-equation_24.jpg |
+ 2 \epsilon _ { 3 1 } ^ { 2 } [ ( \epsilon _ { 3 3 } + \epsilon _ { 1 1 } ) ^ { 2 } - \epsilon _ { 3 3 } \epsilon _ { 1 1 } - \epsilon _ { 2 2 } ^ { 2 } ] + 1 2 \epsilon _ { 1 2 } \epsilon _ { 2 3 } \epsilon _ { 3 1 } ( \epsilon _ { 1 1 } + \epsilon _ { 2 2 } + \epsilon _ { 3 3 } ) | bbe84160-f903-42b1-82a0-0fd0b770f4fb__mathematical-expression-and-equation_8.jpg |
\tau _ { 2 } = \frac { s _ { 2 } } { 2 r } \sqrt { \frac { l } { g } } | bc1902d0-0bb5-11e5-b309-005056825209__mathematical-expression-and-equation_3.jpg |
1 9 1 8 / - 2 3 | bc73f8ee-443e-11eb-836c-00505684fda5__mathematical-expression-and-equation_18.jpg |
\alpha _ { 3 } x + \beta _ { 3 } y + \gamma _ { 3 } z = 0 | bf758ff5-e361-4a9b-9810-147cfbd5cb88__mathematical-expression-and-equation_5.jpg |
\sqrt { n } . \frac { \partial S _ { n } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) } { \partial \beta } = \frac { 1 } { \sqrt { n } } \sum _ { i = 1 } ^ { n } s \prime _ { \beta } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) . I ( s _ { i } ( x _ { i } , y _ { i } ; \beta ^ { 0 } ) \le s _ { [ h _ { n } ] } ( x _ { i } , ... | bfb5e7d7-6892-4d86-8f88-5b2f69ec7479__mathematical-expression-and-equation_1.jpg |
W ^ { n e w } = W ^ { c u r r e n t } + \gamma ( \frac { 1 } { M } - W ^ { c u r r e n t } ) | c02541cb-238d-44b9-8d21-b04b60eb06b2__mathematical-expression-and-equation_0.jpg |
0 . 4 0 0 : 0 . 6 0 0 = 0 . 3 5 2 : x | c0e8c0eb-e257-11e6-9504-001999480be2__mathematical-expression-and-equation_0.jpg |
\Gamma ( 1 + \sigma ) \zeta ( 1 + \sigma ) = \frac { 1 } { \sigma } + a _ { 1 } \sigma + a _ { 2 } \sigma ^ { 2 } + \dots | c11cfebc-1776-4411-a15a-19246ab32267__mathematical-expression-and-equation_3.jpg |
( \frac { a + b } { 2 b } ) + ( \frac { a + b } { 2 b } ) + ( 1 - \frac { a } { b } ) + 1 | c15da0f1-4be8-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg |
- \frac { 1 } { 2 ^ { 2 } } \log \frac { b \prime ^ { 2 } } { b \prime _ { 3 } } - \dots ] | c1d0bcb0-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg |
\int _ { a } ^ { b } f ( x ) d x - \tilde { L } _ { n } | \le \frac { 1 1 n h ^ { 5 } } { 7 2 0 } \tilde { B } _ { 4 } = \frac { 1 1 L ^ { 5 } } { 7 2 0 n ^ { 4 } } \tilde { B } _ { 4 } , ` | c1eef158-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg |
d _ { i _ { 1 } } ^ { 2 } + \frac { 1 } { h } d _ { i _ { 2 } } ^ { 2 } + d _ { i _ { 3 } } ^ { 2 } | c1eef1b7-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\frac { d ^ { 2 } G } { d y ^ { 2 } } \ge 0 | c29cc596-045d-4be6-9040-3362f3b499a4__mathematical-expression-and-equation_7.jpg |
Z _ { s } = - 7 \lambda _ { s } \mu _ { s } \nu _ { s } | c3575fa3-e0a4-4c48-8b89-7141b022f2f6__mathematical-expression-and-equation_12.jpg |
\parallel u _ { h } \parallel _ { V } \le r _ { 0 } : = \zeta ^ { - 1 } ( \parallel g \parallel _ { V \prime } + \parallel F ( 0 ) \parallel _ { V \prime } ) | c36e174a-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\eta = \frac { \omega } { \Omega _ { 0 } } , Q ^ { 2 } = \frac { k / m } { \Omega _ { 0 } ^ { 2 } } , q ^ { 2 } = \frac { g / l } { \Omega _ { 0 } ^ { 2 } } | c3d23e28-5417-4f0f-a737-9b561396e321__mathematical-expression-and-equation_3.jpg |
\hat { e } _ { w } ( \xi ) = \rho + \sigma \hat { z } ( \xi ) | c42ecedc-e09b-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg |
g ( \xi _ { 0 } , t ^ { * } ) - \bar { g } ( \xi _ { 0 } ) = C \cos ( \omega ^ { * } t ^ { * } + \phi ( \xi _ { 0 } ) ) | c4922dac-0d12-4348-9cdc-a1300a8df2b5__mathematical-expression-and-equation_9.jpg |
\sum _ { i = 1 } ^ { M } \frac { 1 } { W _ { k } } p _ { i k } t _ { i } | c4ed6480-e09b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg |
x = \lambda ( \nu \tilde { \omega } \theta ) | c537f01c-11b4-47c7-a9b2-6cb450422bdb__mathematical-expression-and-equation_9.jpg |
\tilde { A } = C ^ { T } A C | c5b7b829-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg |
\frac { 1 } { 2 } | w | _ { 1 } ^ { 2 } \le \parallel \nabla w - \beta \parallel _ { 0 } ^ { 2 } + \parallel \beta \parallel _ { 0 } ^ { 2 } | c5b7b854-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\parallel ( I _ { M } \eta ) \prime \prime \parallel _ { 0 , \infty , I } \le C _ { 2 } | c5b7b9fc-e09b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\frac { 1 3 0 . 2 0 0 \times 1 0 0 } { 6 0 0 . 0 0 0 + 1 0 0 . 0 0 0 } = 1 8 . 6 0 \% , \text { t . j . } 6 \% | c5c5bd7c-20ed-11ea-8e31-005056a54372__mathematical-expression-and-equation_0.jpg |
^ { n } D _ { u } v = \frac { \Gamma ( n + 1 ) } { \Gamma ( 1 ) \Gamma ( n + 1 ) } { } ^ { 0 } D _ { u } { } ^ { n } D _ { v } + \frac { \Gamma ( n + 1 ) } { \Gamma ( 2 ) \Gamma ( n ) } D _ { u } ^ { n - 1 } D _ { v } | c6123e97-3542-48e5-8c18-880bec6f71e5__mathematical-expression-and-equation_16.jpg |
\frac { \partial \Theta _ { * } } { \Theta _ { * } } = \frac { \log \Theta _ { * } \prime } { M } - 1 \Theta _ { * } { } ^ { 2 0 9 ) } | c62a6860-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg |
A = [ \begin{array} { c c } \alpha + \beta \delta & \beta \gamma \\ \delta & \gamma \end{array} ] | c681721f-e09b-11e1-1121-001143e3f55c__mathematical-expression-and-equation_1.jpg |
F . - i A | c6b58dff-8b76-43ec-81c0-c01d34a98241__mathematical-expression-and-equation_2.jpg |
Q + P \dddot { x } + M x ^ { 2 } + \dots + C x ^ { m - 2 } + B x ^ { m - 1 } + A x ^ { m } | c764d5f2-0844-696d-8412-87bf73fafc71__mathematical-expression-and-equation_11.jpg |
( 7 2 _ { 2 } - 7 3 . ) | c78e0232-5417-4f0a-8d8c-95279914c707__mathematical-expression-and-equation_0.jpg |
v = \frac { I } { 4 k ( I + k ) } [ \mu ^ { 3 } + \mu ^ { 2 } + ( 4 k - 5 ) \mu + 3 ( 1 - 4 k ^ { 2 } ) ] , | c9270436-9d51-4277-af23-fbfb9e805d17__mathematical-expression-and-equation_7.jpg |
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