formula stringlengths 5 635 | image stringlengths 80 86 |
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| \rho _ { w } ( x , t ) ( u _ { i } ( x , t ) - w _ { i } ( x , t ) + e ( x , t ) v _ { i } ( x , t ) ) v _ { i } ( x ) d S = 0 | 76166ebe-9aec-40b5-91ef-4b39d5ade9ab__mathematical-expression-and-equation_12.jpg |
\displaymath { q = 0 j e s t x _ { 0 } = 2 6 3 } | 772be82c-6a05-bada-ae51-0fe7c818b666__mathematical-expression-and-equation_12.jpg |
= \frac { 1 3 0 \times 1 3 0 } { 1 2 - 2 2 } \cdot ( V | 79647400-e953-11e2-9439-005056825209__mathematical-expression-and-equation_8.jpg |
p _ { n } = \frac { a _ { 1 } ( k ^ { n } - 1 ) } { k - 1 } | 79885c7b-fd03-42ae-be98-97f12ee827a1__mathematical-expression-and-equation_1.jpg |
1 5 7 6 - 2 7 5 | 7a06f760-1e73-11e9-aca8-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg |
\frac { 7 : 1 \frac { 3 } { 4 } } { \frac { 7 } { 4 } : \frac { 7 } { 4 } = \frac { 7 } { 4 } \times \frac { 4 } { 7 } = \frac { 2 8 } { 7 } } | 7a1e191a-e545-4ea6-96b9-e9fe2bda97d2__mathematical-expression-and-equation_2.jpg |
x ^ { 4 } + \frac { 3 } { 2 \cdot 7 } x , ^ { 3 } + \frac { 2 } { ( 2 \cdot 7 ) ^ { 2 } } x , ^ { 2 } + \frac { 6 } { ( 2 \cdot 7 ) ^ { 3 } } x , - \frac { 1 4 8 \cdot 6 } { ( 2 \cdot 7 ) ^ { 4 } } = 0 | 7aff88d8-b934-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg |
H = \frac { \rho \prime \prime } { g } V . 1 0 ^ { - 3 } | 7b9c7578-f4a5-4fb6-8d55-faf8703b9221__mathematical-expression-and-equation_0.jpg |
O = 1 1 0 - \frac { 1 0 0 - 0 . 5 } { 2 } = 6 0 . 2 5 \mathrm { c m } | 7c567d05-8916-bc71-c9ca-dae864599c4e__mathematical-expression-and-equation_1.jpg |
R \prime - \cot R = \frac { 2 \sin \frac { a } { 2 } \cos \frac { b + c } { 2 } } { k } | 7c8889eb-100e-4090-bfff-bc69e25531cd__mathematical-expression-and-equation_11.jpg |
\frac { a \in \phi a a \in \psi } { \phi \cap \psi \neq \emptyset } | 7cf08415-6928-4ea7-882d-4528c5e9930c__mathematical-expression-and-equation_3.jpg |
\pi = 3 . 1 4 1 5 9 2 6 5 3 6 | 7d234d3a-170b-4200-8b2c-421ea3924a3d__mathematical-expression-and-equation_13.jpg |
I = 3 \log 0 . 9 8 + 5 . 1 | 7d385cfc-282d-4613-bc19-7720f1cfcc7c__mathematical-expression-and-equation_1.jpg |
R r = P p + Q q | 7e653310-0d86-11e8-8ee8-001b63bd97ba__mathematical-expression-and-equation_0.jpg |
B _ { x } - C _ { x } - M _ { x } = - A _ { x } q _ { x } - \{ \frac { 1 - q _ { x } } { q _ { x } } \log ( 1 - q _ { x } ) \} ( B _ { x } - C _ { x } ) | 7f028452-cc77-4b0c-b9fa-a94e631c2707__mathematical-expression-and-equation_9.jpg |
K _ { 1 } ^ { \gamma , \sigma , \sigma _ { 0 } , \lambda } ( v ) \le c o n s t . ( 1 + v ^ { 2 } ) ^ { - \frac { \sigma } { 2 } } \exp ( - \lambda v ^ { 2 } ) \times | 7f0ab50b-c9c0-4591-bc08-6b83f170d868__mathematical-expression-and-equation_8.jpg |
\mathfrak { S } = \frac { k } { 2 \mathfrak { A } \mathfrak { B } } , \mathfrak { A } = [ 3 + 2 \frac { b } { r } ( 2 + 2 \sec \frac { a } { 2 } + 5 \tan \frac { a } { 2 } ) ] | 7f54a4ea-37aa-4bd6-8e04-57566866b3a7__mathematical-expression-and-equation_8.jpg |
[ \frac { u ^ { 2 } } { a ^ { 4 } } + \frac { v ^ { 2 } } { b ^ { 4 } } + \frac { w ^ { 2 } } { c ^ { 4 } } ] [ \cos \omega ^ { 2 } + \cos \pi ^ { 2 } ] - [ \frac { v } { b ^ { 2 } } \cos \pi - \frac { w } { c ^ { 2 } } \cos \omega ] ^ { 2 } = \frac { u ^ { 2 } } { a ^ { 4 } } | 7fdb0802-53a9-449b-9a5c-d4954fc2d3a0__mathematical-expression-and-equation_6.jpg |
F ( x + 2 \pi ) - F ( x ) = \phi ( x ) | 80655160-e3d6-4c6b-a8ea-f79ce93455c1__mathematical-expression-and-equation_2.jpg |
S _ { 5 } = 5 0 , 3 1 1 + \frac { 5 + 5 } { 9 . 3 4 2 \cdot 7 . 8 6 9 } [ \frac { 1 5 1 0 \cdot 6 } { 4 } ( 6 1 . 6 5 - 1 8 . 3 2 5 - 8 . 3 2 5 ) - 2 1 2 . 1 3 2 4 ( 9 . 3 4 2 | 81519b53-afa8-4c1c-8cab-e5395fd3472d__mathematical-expression-and-equation_16.jpg |
[ i k . r ] = [ i k . ( r - 1 ) ] - \frac { [ r i . ( r - 1 ) ] } { [ r r . ( r - 1 ) ] } [ r k . ( r - 1 ) ] | 81817a1a-e2e4-0667-e293-1102b62257e9__mathematical-expression-and-equation_5.jpg |
\frac { h } { l } \cdot \frac { c } { x } = \operatorname { t g } ( 0 0 1 : h h l | 8185e3f0-0f1c-11de-8858-0030487be43a__mathematical-expression-and-equation_10.jpg |
v _ { 0 } ^ { 2 } . \frac { d ^ { 3 } W } { d s ^ { 2 } . d t } = \frac { 2 U _ { 1 } } { \tau } | 81f6ff5d-59f2-4cfe-903d-aa89afef047b__mathematical-expression-and-equation_5.jpg |
e ^ { \frac { 2 K \pi l } { p } } = ( e ^ { \frac { K \pi i } { p } } ) ^ { 2 } = ( \cos \frac { K \pi } { p } + i \sin \frac { K \pi } { p } ) ^ { 2 } = \cos ^ { 2 } \frac { K \pi } { p } + | 82856d60-eec1-11e6-8d33-005056825209__mathematical-expression-and-equation_7.jpg |
= ( A ^ { 2 } - B ^ { 2 } ) \cos ^ { 2 } \phi + B ^ { 2 } | 82e8c5df-d311-4fe4-9ce5-d1e9174ffeb8__mathematical-expression-and-equation_3.jpg |
R _ { 1 } = Z ^ { - 1 } L | 82ff032a-d71d-46a5-86f5-52fc3d7d1149__mathematical-expression-and-equation_4.jpg |
\psi _ { 2 } ( x ) = ( \frac { \psi \prime _ { 1 } , x } { 1 . 2 . \phi \prime x } ) ; ( \psi _ { 3 } ( x ) = ( \frac { \psi \prime _ { 2 } x } { 1 . 2 . 3 . \phi \prime \prime x } ) | 845e8017-bf5b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_1.jpg |
R e g . M B V I , p . 6 7 5 n . 1 2 6 8 . - [ Z ] . | 85106490-c357-11e0-8bdc-0030487be43a__mathematical-expression-and-equation_0.jpg |
A = 6 \cdot 2 0 \cdot 1 0 ^ { 2 3 } , | 854fd580-5d99-11e6-9dd6-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg |
d A _ { 2 } = f \omega _ { 1 } A _ { 0 } + \omega _ { 2 } A _ { 1 } - c \omega _ { 2 } A _ { 2 } ; | 856ff630-5484-45bb-9d84-1ac60c8975e6__mathematical-expression-and-equation_15.jpg |
\frac { v } { u } = \frac { \sin y } { \cos y - 1 } = - \cot \frac { y } { 2 } \text { d a h e r } V = \frac { \pi } { 2 } + \frac { y } { 2 } | 87e32180-e348-11e8-9445-5ef3fc9bb22f__mathematical-expression-and-equation_21.jpg |
= \lambda _ { m } v _ { m } \frac { v _ { m } + v _ { m - 1 } - v _ { m } + v _ { m - 1 } } { ( v _ { m } - v _ { m - 1 } ) ( v _ { m } + v _ { m - 1 } ) } = \frac { 2 \lambda _ { m } v _ { m - 1 } v _ { m } } { ( v _ { m } - v _ { m - 1 } ) ( v _ { m } + v _ { m - 1 } ) } | 88377de6-6c0f-4c36-8b4e-1e240dfd66f0__mathematical-expression-and-equation_3.jpg |
\hat { h } _ { m } = h _ { s } - \eta . | 8879a770-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_2.jpg |
\frac { \partial \sigma _ { 1 } } { \partial \sigma _ { x } } = l _ { 1 } ^ { 2 } + 2 [ l _ { 1 } \frac { \partial l _ { 1 } } { \partial \sigma _ { x } } \sigma _ { x } + l _ { 2 } \frac { \partial l _ { 2 } } { \partial \sigma _ { x } } \sigma _ { y } + l _ { 3 } \frac { \partial l _ { 3 } } { \partial \sigma _ { x }... | 8881cb40-4ffd-4353-bab7-80f001a58b02__mathematical-expression-and-equation_2.jpg |
\frac { 2 } { \sqrt { \pi } } \int _ { 0 } ^ { n h p } e ^ { - t ^ { 2 } } d t ; | 89c7f09f-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_0.jpg |
- z R _ { n } | 89c83f42-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_21.jpg |
c ^ { 2 } x ^ { 2 } = \eta ^ { 2 } [ x ^ { 2 } + c ^ { 2 } x ^ { 2 } + y ^ { 2 } + 2 c y z + c ^ { 2 } z ^ { 2 } ] | 89c8b3f3-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_8.jpg |
\delta z = d z = \frac { d z } { d t } d t | 89c90264-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_4.jpg |
\mathcal { L } \rho _ { n , 1 } = 1 | 8a5aec70-7aa3-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg |
\begin{array} { c c c c c c c } a & b & c & d & e & f & g \\ 0 & \frac { 1 } { 3 } & \frac { 1 } { 2 } & \frac { 2 } { 3 } & 1 & 2 & \infty \end{array} | 8ad25960-3947-11e4-8413-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg |
P _ { E } = p \cdot \Delta T / ( \vec { E } ^ { T } \cdot \vec { \Gamma } ^ { * } ) ( \vec { \Gamma } ^ { T } \cdot \vec { E } ^ { * } ) | 8b069a41-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg |
\Sigma \Delta ^ { 2 } = ( M - M _ { 1 } ) ^ { 2 } + ( M - M _ { 2 } ) ^ { 2 } \dots ( M - M _ { N } ) ^ { 2 } | 8b5166ba-a679-11e6-adc0-d485646517a0__mathematical-expression-and-equation_0.jpg |
A _ { 1 } = 9 3 7 + 5 0 7 + [ ( 4 0 8 0 + 2 2 0 6 ) ( 6 1 . 6 5 - 3 . 8 2 5 ) + 4 ( 4 9 0 0 + 2 6 5 0 | 8bea8d32-0b89-4489-92a2-8dc2df1ace7a__mathematical-expression-and-equation_9.jpg |
\theta \prime \prime = \psi + N \prime \prime | 8c84de30-0b4e-11e4-a8ab-001018b5eb5c__mathematical-expression-and-equation_8.jpg |
| = a b \prime c \prime \prime + a \prime b \prime \prime c + a \prime \prime b c \prime - a \prime \prime b \prime c - a b \prime \prime c \prime - a \prime b c \prime \prime | 8c9f9e50-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_9.jpg |
Y = b _ { 1 } + b _ { 2 } + b _ { 3 } = 0 . 0 0 8 9 u ^ { 3 } \log \text { n a t } \frac { 1 9 } { 1 9 - v } + 0 . 0 0 0 8 2 2 u ^ { 3 } ( v ^ { 2 } - 2 ) \\ Y = + 0 . 0 1 3 5 4 \log \text { n a t } \frac { 1 9 + \mathfrak { R } } { 1 4 } + 0 . 0 0 1 2 5 ( 2 5 - \mathfrak { R } ^ { 2 } ) | 8d0bb4c4-5ea3-4b39-b47f-0421296045a0__mathematical-expression-and-equation_11.jpg |
S _ { 1 } > S _ { 3 } > S _ { 5 } > S _ { 7 } \dots , | 8d522570-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_20.jpg |
\frac { p \prime \prime } { q \prime \prime } = \frac { n p \prime + p } { n q \prime + q } | 8d66e851-22b1-11ec-af09-001b63bd97ba__mathematical-expression-and-equation_0.jpg |
T = 1 . 6 4 3 | 8e3e6ac9-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_5.jpg |
\frac { 1 } { p _ { y } } = [ \beta \beta ] | 8e3e9229-f46c-11e7-ae40-001b63bd97ba__mathematical-expression-and-equation_9.jpg |
c = m \sqrt { \omega } [ ( 1 3 ) ( 0 2 ) ( 2 4 ) ( 4 0 ) ] ^ { \frac { 1 } { 4 } } | 8e4270b9-9f68-4da3-bdba-909246eedaea__mathematical-expression-and-equation_14.jpg |
x \cos \phi + y \sin \phi - 2 r \sin \phi \cos \phi = 0 | 8e512500-7ad7-11e8-9690-005056827e51__mathematical-expression-and-equation_9.jpg |
a _ { i } = l _ { i } - X = l _ { i } - x + x - X = l _ { i } - x + F _ { 2 } , | 8ecce6e0-ee57-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg |
H = \frac { a + n } { n } \cdot \frac { 1 } { 1 0 . 0 0 0 } | 8f03e9ca-7da1-4cb8-9fa8-6d769b8420c8__mathematical-expression-and-equation_1.jpg |
\mu \mu ( = 0 . 0 0 1 \mu ) = 1 . 1 0 ^ { - 7 } | 8f0b57d0-d5e1-11e3-85ae-001018b5eb5c__mathematical-expression-and-equation_5.jpg |
( \frac { d x \prime } { d x } ) _ { u } | 8f494140-76ad-11e4-9605-005056825209__mathematical-expression-and-equation_7.jpg |
A l = A l _ { o } + d A l | 8fb8d7db-b9f4-11e1-6101-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\dot { u } _ { 2 } = - \frac { 1 } { L } ( E u _ { o } - p ) \exp ( - t / T ) | 9033ad63-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg |
u = \frac { ( s - p ) ^ { 2 } } { 2 L s _ { 0 } } + \frac { s - p } { E } | 9033ad8f-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_15.jpg |
- z \le u _ { 1 } \le + z | 9033ada8-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg |
s \prime _ { 2 } = \min z \prime = s \prime _ { 2 } | 9033adae-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg |
+ 2 ( u x - y z ) h + 2 ( u y - x z ) i + 2 ( u z + x y ) k | 90612a28-cae8-45b3-9b19-303280e547c0__mathematical-expression-and-equation_14.jpg |
u = u _ { 1 } \pm u _ { 2 } \pm u _ { 3 } | 917104d0-ee57-11ea-a0d6-5ef3fc9bb22f__mathematical-expression-and-equation_1.jpg |
u = 3 | 91a06bf0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_5.jpg |
\Delta = 1 / k _ { i } = c / ( n _ { i } \omega ) = ( 2 \pi ) ^ { - 1 } c / ( n _ { i } f ) | 91abf256-100f-4a1e-bf0a-5cd1e8cfe5a4__mathematical-expression-and-equation_7.jpg |
( 2 2 + 3 1 + 1 0 ) \text { d n í } = 6 3 | 91ee2570-1012-11e9-91df-005056825209__mathematical-expression-and-equation_0.jpg |
\frac { \delta ^ { 2 } n } { \delta r ^ { 2 } } + \frac { 2 } { r } \cdot \frac { \delta n } { \delta r } - \frac { n } { L _ { 2 } } = 0 | 923c4e35-b9f4-11e1-6101-001143e3f55c__mathematical-expression-and-equation_1.jpg |
= \delta - 0 . 6 \delta | 923cc630-e953-11e2-9439-005056825209__mathematical-expression-and-equation_9.jpg |
u _ { z } = 0 | 92efa340-2578-45fd-aa43-dc63fcf5ae05__mathematical-expression-and-equation_8.jpg |
z _ { 2 } = ( R ^ { 2 } \cos ^ { 2 } \chi + 2 R H + H ^ { 2 } ) ^ { 1 / 2 } - ( R ^ { 2 } \cos ^ { 2 } \chi + 2 R h + h ^ { 2 } ) ^ { 1 / 2 } . | 9346552a-024d-4f94-ad49-b6b941531d2a__mathematical-expression-and-equation_5.jpg |
A n \times n B = A D : A B | 94ac9e8b-c2d6-11e7-bf53-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
( p \And q ) \rightarrow q | 94e37e8a-b8ca-4417-9779-cfce3f4f0626__mathematical-expression-and-equation_14.jpg |
q \in \{ 0 , 1 , \dots \} | 95547c27-bd12-4d2a-9c7e-b06c036af80b__mathematical-expression-and-equation_12.jpg |
w = \frac { d k } { d s } = \frac { 2 4 . y } { ( 1 + 4 x ) ^ { 3 } } | 958321b3-2983-4410-b805-a3d8dea7b22c__mathematical-expression-and-equation_3.jpg |
= - \frac { \sigma _ { r } ( z ) } { \sigma ( z ) } [ 1 - \frac { \sigma _ { s } ^ { 2 } ( z ) } { \sigma _ { t } ^ { 2 } ( z ) } ] | 958e5f52-06ec-441b-9a13-03a8f5422332__mathematical-expression-and-equation_0.jpg |
p _ { 1 } = \frac { a _ { 1 } } { v } , p _ { 2 } = \frac { a _ { 2 } } { v } , \dots p _ { n } = \frac { a _ { n } } { v } . | 95cf74a0-19ee-11e5-b642-005056827e51__mathematical-expression-and-equation_1.jpg |
v = \frac { u } { x } \sqrt { A ^ { 2 } + B ^ { 2 } } ; | 95ff6b0e-4334-11e1-1331-001143e3f55c__mathematical-expression-and-equation_3.jpg |
n _ { 2 } ^ { 2 } = n , \text { č i l i } n _ { 2 } = \sqrt { n } ; | 9686c34e-4334-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\frac { \partial ^ { 2 } \bar { e } _ { r r } } { \partial \theta ^ { 2 } } - 2 \frac { \partial ^ { 2 } ( r \bar { e } _ { r \theta } ) } { \partial r \partial \theta } + \frac { \partial ^ { 2 } ( r ^ { 2 } \bar { e } _ { \theta \theta } ) } { \partial r ^ { 2 } } - r \frac { \partial \bar { e } _ { r r } } { \partia... | 97198cfd-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\phi _ { 1 } = \phi _ { 2 } = \arctan \frac { v _ { 0 } ^ { 2 } } { g x } = \arctan \frac { 2 h } { x } | 97e32dc0-311e-11eb-acc7-5ef3fc9bb22f__mathematical-expression-and-equation_12.jpg |
\Delta \Theta _ { i } \text { e t } S \prime \Delta \Theta _ { i } | 98269950-3064-11e9-bda0-005056a2b051__mathematical-expression-and-equation_0.jpg |
\rho = - \frac { 3 e } { 4 \pi R ^ { 3 } } v | 98a5f960-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_10.jpg |
l _ { 2 3 } = \frac { J _ { 2 0 } - J _ { 1 0 } } { \hbar \omega } a u = \frac { \gamma } { \beta } | 98a5f966-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg |
+ \frac { 4 } { \pi ^ { 2 } } \frac { d _ { 1 } } { d _ { 2 } } \sum _ { k = 1 } ^ { \infty } \frac { \eta _ { 2 k - 1 } } { ( 2 k - 1 ) ^ { 3 } } t h ( 2 k - 1 ) \frac { \pi } { 2 } \frac { d _ { 2 } } { d _ { 1 } } ; | 98a5fa9b-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg |
E = E \prime = \frac { 1 } { 2 } ( E + E \prime ) = J t | 98c8f458-6b5d-4805-8c41-e7b8a2d0e03d__mathematical-expression-and-equation_0.jpg |
V \sqrt { | \dot { x } | } [ \frac { 1 } { \sqrt { | \dot { x } | } } ] \prime \prime + q ( x ) \dot { x } ^ { 2 } = Q ( T ) | 990d60fe-2ffe-4f04-82f4-175a5681f56d__mathematical-expression-and-equation_3.jpg |
w _ { i j } ^ { ( 3 ) } = \frac { 2 \pi } { \hbar } \sum _ { \sigma } \sum _ { \sigma \prime } ( \hbar \omega ( \sigma ) ) ( \hbar \omega ( \sigma \prime ) ) S _ { j i } ^ { ( 2 ) } ( \sigma ) S _ { j i } ( \sigma \prime ) | 9979c595-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_4.jpg |
m \ddot { y } = e E | 9979c6ad-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\frac { 1 } { 2 } ) y y = [ ( 0 , - 1 ) + ( 1 , - 1 ) + ( 0 , 2 ) + ( 1 , 2 ) ] | 99f4227c-6527-4112-a0a6-38fbb0d2f5e8__mathematical-expression-and-equation_5.jpg |
n \prime _ { i } = 2 m - 2 \mu - 2 | 9a13d593-7500-4120-9d11-89894ba79824__mathematical-expression-and-equation_17.jpg |
w = a _ { 0 } + a _ { 1 } z + a _ { 2 } z ^ { 2 } + \dots + a _ { n } z ^ { n } + \dots | 9aa863b0-7d97-11e7-921c-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg |
\tau = \tau _ { 0 } \cos \phi + \beta \sin \phi | 9b285ed0-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_5.jpg |
S \sim 1 0 \delta ^ { 2 } r _ { 0 } ^ { 2 } | 9b285ed4-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg |
t _ { R } \prime e ^ { i \partial _ { R \prime } } . t _ { L } \prime e ^ { i \partial _ { L \prime } } - r _ { R } \prime e ^ { i \delta _ { R \prime } } . r _ { L } \prime e ^ { i \delta _ { L \prime } } = 1 | 9b285efd-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_12.jpg |
( l _ { 0 } w _ { I I } ) = 2 \rho w [ Z - m ] | 9b58782f-1bb9-47e9-baa6-1ac5ab23ce1f__mathematical-expression-and-equation_6.jpg |
\frac { \omega _ { 3 } - \omega _ { 2 } } { \omega _ { 4 } - \omega _ { 2 } } = - \frac { z _ { 4 } } { z _ { 3 } } , \frac { \omega _ { 4 } - \omega } { \omega _ { 6 } - \omega } = - \frac { z _ { 6 } } { z _ { 5 } } | 9b819780-0fca-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg |
\dots + [ \Delta i , q ^ { N ( f ) } _ { ( K - 1 ) } ] ^ { [ 0 , 1 ] } _ { [ ( K ) ] } ( 1 + i ) ^ { t + 1 - ( K ) } \} - | 9e9bd451-0e5a-11eb-b87e-005056a54372__mathematical-expression-and-equation_3.jpg |
v = \sqrt { 2 \times 1 0 \times 4 5 } = \sqrt { 9 0 0 } = 3 0 | 9ec2c690-7806-11e5-a2d8-005056825209__mathematical-expression-and-equation_3.jpg |
\frac { ( n - n _ { 1 } ) \frac { S } { n } } { ( s - n _ { 2 } \delta ) t } > \frac { ( n - n _ { 1 } - n _ { 2 } ) \frac { S } { n } } { ( s - n _ { 3 } \delta ) t } | 9f7cf4a0-e953-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg |
D = 0 , 1 4 + 2 \kappa _ { g l } t _ { g l } \mu _ { g l } = 0 , 1 4 + 2 \cdot 1 , 5 \cdot 0 , 0 1 5 \cdot 0 , 6 = 0 , 1 6 7 m | 9fffccfe-b529-4466-aa0b-ba75aef74a9e__mathematical-expression-and-equation_5.jpg |
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