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\tilde { \mathbf { x } } = \mathbf { x } + \mathbf { n }
e7ff15be-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg
l = 1 , \dots , m
e7ff17da-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_5.jpg
\frac { d \omega } { d t } = \frac { \alpha \prime } { r \prime } \sin \omega - \frac { \beta \prime } { r \prime } \cos \omega
e87a2b7b-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
C _ 3 + C _ 2 = \binom { \alpha } { \alpha - 1 } ( - a )
e87a2bef-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
3 ) \dots F _ 1 ( x _ 1 , y _ 1 , a ) = 0 ,
e8fa4c40-00cf-11eb-98c2-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg
l = \frac { 2 p } { 2 a } \frac { \beta N } { 3 6 0 } L
e9952180-c41c-11e3-93a3-005056825209__mathematical-expression-and-equation_3.jpg
( \frac { 1 } { m } ) ( - m ) = - 1
e99d283d-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_4.jpg
a = \xi + \eta i
e99d288e-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_5.jpg
\tan E N L = \frac { d . \tan \alpha } { s }
e9b9667f-f280-4da5-a816-3eecf73a13f0__mathematical-expression-and-equation_8.jpg
[ d \alpha _ 1 + \alpha _ 1 ( \omega _ { 0 0 } - 2 \omega _ { 1 1 } + \omega _ { 3 3 } ) \omega _ 1 \omega _ 3 ] = 0
e9fdcfdb-570a-11e1-1726-001143e3f55c__mathematical-expression-and-equation_3.jpg
x = 1 0 ( 3 , 4 5 - 3 , 0 ) + 6 9 , 3 = 7 3 , 8 ,
ea5b2341-bc37-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
\bar { p } - \bar { \rho } \frac { \partial ( \phi + \phi \prime ) } { \partial t } = \bar { p } _ 1 - \bar { \rho } _ 1 \frac { \partial \phi _ 1 } { \partial t }
ea61d49c-d83e-407c-9db4-9340b278f3f4__mathematical-expression-and-equation_5.jpg
\{ \mathbf { a } _ { \alpha _ \mu } , \mathbf { a } _ { \beta _ \mu } , \mathbf { j } , \mathbf { b } _ { 1 } , \dots , \mathbf { b } _ { n - 2 } \} \subset C ( v )
ea77df9b-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg
\mathcal { H } ( t , \hat { \lambda } ( t ) , \hat { u } ( t ) ) = \max _ { u \in U } \mathcal { H } ( t , \hat { \lambda } ( t ) , \hat { x } ( t ) , u ) =
ea77e002-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
T S Y = 9 0 2 . 3 ^ { * * * } - 1 3 . 3 Z n ^ { * * * } \text { f o r } n = 1 2 \text { a n d } R ^ 2 = 0 . 7 7
eaa57620-40f9-11ed-9667-005056822549__mathematical-expression-and-equation_0.jpg
b \prime = b ( 1 - \eta ) = b ( 1 - \frac { v } { m E } )
eac8fb20-1b93-11e4-8e0d-005056827e51__mathematical-expression-and-equation_3.jpg
g _ i ( t ) = \frac { a _ i ( t ) } { \sum _ { j = 1 } ^ { K } a _ j ( t ) }
ead733ba-aa5e-4212-a75e-e87c87d66c53__mathematical-expression-and-equation_5.jpg
\beta ^ 3 + b \beta ^ 2 + c \beta + d = 0 ,
eb1105e3-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
v r ^ { ( \frac { k _ 1 } { \mu } - 1 ) } = C
eb1106fc-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg
L _ { 4 \check { s } } = ( P _ { 4 \check { s } } ) _ t = - K _ 1 v ( d r ) _ t = - K _ 1 v ^ 2 d t
eb1106fc-bc37-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg
\bar { \sigma } = \cap \sigma _ \perp = \wedge \sigma _ \perp
eb3ac392-7f95-468f-919a-3e00468813cf__mathematical-expression-and-equation_0.jpg
\frac { \partial Q } { \partial \dot { u } _ { i 0 } } = \sum _ { i = 1 } ^ { m } g _ { i } ( t ) \epsilon _ { i } ( t ) \frac { \partial \epsilon _ { i } ( t ) } { \partial \dot { u } _ { i 0 } } = 0
eb42a92f-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
+ a _ { 1 2 2 } [ a _ { 2 1 1 } | a _ { k i j } | + a _ { 2 3 3 } | a _ { k i j } | + \dots + a _ { 2 , n + 1 , n + 1 } | a _ { k i j } | ] +
eb5dd5de-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg
\dot { x } _ 1 = x _ 2
ec018acc-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_7.jpg
+ \Gamma H 2 ( n ) \frac { \sigma ^ 2 } { \Delta } \Gamma S V ( n + 1 ) \} \Gamma D V ( n )
ec018b55-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
\beta _ { s - 1 } ( n ) = r _ 1 ( n + s - 1 ) + \alpha _ { s - 1 } ( n ) r _ 0 ( n + s - 1 )
ec018c87-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
\alpha \neq 0
ec018d24-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_12.jpg
\delta = \vec { s } ( \vec { \Omega } _ j \times \vec { T } ) + \vec { s } \vec { C }
ec20d6f5-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
\text { E C A U } y ( t ) \in Y , 2 ^ { j - 1 } < \omega ( y ( t _ 0 ) ) \le 2 ^ j ,
ec20d73f-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_17.jpg
K _ 4 > \psi ( x , \tau )
ec20d74d-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_13.jpg
x = - \frac { \pi } { 2 } + \nu \pi
ec20d7d2-570a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg
( I ) ( V ) [ ( R _ U ^ K ( \mathscr { A } ) ) \equiv R _ U ^ K ( \mathscr { B } ) ) ( K | I , U / V ) ]
ecce29a5-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_4.jpg
\hat { c } _ 2 = z + 1
ecce2bba-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
D a _ 2 = d a _ 2 + a _ 2 ( \omega _ { 4 4 } - \omega _ { 3 3 } )
ece733ff-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_11.jpg
\ge \gamma _ p k ^ { \frac { r - 1 } { 2 } + p } + O ( k ^ { \frac { r - 1 } { 2 } + p - 1 } ) > \frac { 1 } { 2 } \gamma _ p k ^ { \frac { r - 1 } { 2 } + p }
ece735cd-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
r + 1
ece73619-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_5.jpg
t = 3 ^ { \mathrm { m } } 2 0 . _ { 4 } ^ { \mathrm { s } }
ed10868c-8932-494c-8345-12a8c542232a__mathematical-expression-and-equation_14.jpg
b _ { i j } = c _ { i j } - g _ { i j }
ed526b7d-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
R _ m = Z _ { c n - 1 } Q _ m + E
ed526c30-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
s _ 1 , s _ 2 \in S
ed9d6170-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
\hat { J } _ 1 ( \mu ) = \hat { J } _ 2 ( 1 - \mu )
ed9d61aa-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg
[ \begin{array} { c c } z ^ { - 1 } ( 1 - 2 z ^ { - 1 } ) & 0 \\ 0 & z ^ { - 1 } ( 1 - 2 z ^ { - 1 } ) \end{array} ] D _ 1 + D _ 2 [ \begin{array} { c c } 1 - z ^ { - 1 } & 0 \\ 0 & 1 - z ^ { - 1 } \end{array} ] = [ \begin{array} { c c } 1 & 0 \\ 0 & 1 \end{array} ]
ed9d626f-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg
\lim _ { h \rightarrow o } \tilde { \Phi } ( h ) \in \overline { \tilde { U } _ 1 } \subset 2 \tilde { U } _ 1
edb4e497-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
[ \omega ^ 1 \omega _ 1 ^ 3 ] + [ \omega ^ 2 \omega _ 2 ^ 3 ] - R _ { 1 2 } ^ 3 [ \omega ^ 1 \omega ^ 2 ] = 0
edb4e4ff-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
| \frac { \partial ^ 2 V ( P ) } { \partial x _ i \partial x _ j } | < K _ 4 , | \frac { \partial V ( P ) } { \partial x _ i } | < K _ 4 , | V ( P ) | < K _ 4 , | \frac { \partial V } { \partial t } | < K _ 4
edb4e617-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
M _ Q \{ x _ t \} = \mu _ t
edb4e659-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
x _ 1 + x _ 2 = \frac { 2 a ^ 2 A ( A \xi - \eta ) } { b ^ 2 + a ^ 2 A ^ 2 }
edcb6840-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_1.jpg
\lambda _ n z _ n ^ 2 ( t ) \le \lambda _ n ^ 2 f _ n d ( t ) z _ n ( t )
ee86176e-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_9.jpg
\rho _ { 1 , 2 } = \cos T ( \epsilon ) + \epsilon P ( \epsilon ) \pm \sqrt { ( \cos T ( \epsilon ) + \epsilon P ( \epsilon ) ) ^ 2 - 1 - \epsilon Q ( \epsilon ) }
ee861826-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
\prescript { i } { } { M } . \prescript { i } { } { M } = \tilde { \epsilon }
ee8618f4-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_17.jpg
\tau _ s = \frac { D \Delta p } { 4 L }
eee5b568-bc37-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
\frac { \partial f } { \partial x _ 1 } = 0 , \frac { \partial f } { \partial x _ 2 } = 0 , \frac { \partial f } { \partial x _ 3 } = 0
ef0324cd-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_0.jpg
\psi ( \omega ) = \sup \{ g ( \mathbf { x } , \xi ( \omega ) ) | \mathbf { x } \in E _ n , \mathbf { x } \in X ( \xi ( \omega ) ) \} =
ef286eae-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg
d Y _ t = X _ t d t + g d ^ 2 W _ t
ef286f85-ac0a-11e1-1586-001143e3f55c__mathematical-expression-and-equation_18.jpg
d u = f _ 1 d x + f _ 2 d y + f _ 3 d z ,
ef28bce0-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_9.jpg
{ \mathcal { S } ( x , \overline { \mathfrak { M } } _ i ) ; \iota \in I }
ef56123a-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
\lambda _ 2 \ge \frac { B ( M _ 2 , M _ 2 ) } { l _ 2 }
ef56124c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
\log p = 9 . 2 3 6 4 2
ef740a90-cacf-11e7-a351-005056825209__mathematical-expression-and-equation_11.jpg
U = U _ { m a x } + \frac { 1 } { \kappa } U _ { * } \ln \eta
efbfc1ec-bc37-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
\mathbf { O } _ 2 = ( \begin{array} { c c } 0 & 0 \\ 0 & 0 \end{array} )
f02b1435-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
I ( K , h ) = \int _ { \lambda _ { \rho - } } ^ { K } e ^ { - \lambda t } h ( \lambda ) d \rho ( \lambda )
f02b163d-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
T _ i ( \phi ) = \int _ U \frac { \partial \phi ( z ) } { \partial z _ i } d z , \phi \in \mathcal { D }
f02b167e-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg
p _ k = 4 n _ k + 1 , ( k = 1 , 2 , 3 , \dots , n )
f03f00d7-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_5.jpg
\frac { 1 } { \pi } \int _ { - \infty } ^ { \infty } \frac { d x } { 1 + x ^ 2 } \log ( 1 - e ^ { 2 \pi ( \alpha x - \sqrt { \alpha ^ 3 x ^ 2 + \beta } ) }
f03f0117-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_5.jpg
\frac { \partial ^ 2 \mu _ 1 } { \partial x ^ 2 } - \frac { \beta } { h _ 0 k } \frac { \partial \mu _ 1 } { \partial t } + \frac { W ( x , t ) } { k h _ 0 } = 0
f097f963-bc37-11e1-1431-001143e3f55c__mathematical-expression-and-equation_0.jpg
\lim _ { t \rightarrow \infty } g _ { n + t } ( \mathcal { X } _ { n + t } ) = - \infty
f0b6876e-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_5.jpg
e = - P _ 2 ( A P _ 2 + B Q _ 2 ) ^ { - 1 } C + ( I _ 1 - B _ 2 ( P A _ 2 + Q B _ 2 ) ^ { - 1 } R ) F ^ { - 1 } C
f0b68927-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_7.jpg
m _ i + m _ j - M \le x _ k ^ m
f0b689a5-ac0a-11e1-1121-001143e3f55c__mathematical-expression-and-equation_0.jpg
B K = \sqrt { z }
f0da2f19-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_2.jpg
\frac { d ^ 2 x } { d y ^ 2 } + x - e ^ y = 0
f0ea9120-95d3-11e4-9a7e-5ef3fc9bb22f__mathematical-expression-and-equation_0.jpg
\beta \prime _ 2 = \rho ^ { - 2 } \beta _ 2
f0fd320c-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg
c l K _ 0 = c l K _ 1 = c l K _ 2 = r
f0fd3279-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_7.jpg
\phi ( a ) = \phi ( \epsilon a + ( 1 - \epsilon ) a ) \ge \phi ( \epsilon a ) + ( 1 - \epsilon ) a \ge ( 1 - \epsilon ) a
f0fd32a2-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_0.jpg
p = \frac { 1 } { 1 0 }
f178b913-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_2.jpg
\cot \alpha - \cot \beta = \frac { b ^ 2 - a ^ 2 } { c v }
f178b997-40e3-11e1-1331-001143e3f55c__mathematical-expression-and-equation_7.jpg
\lim _ { V \rightarrow 0 } Z _ G ( \omega \prime , V ) = 0
f17fcc04-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_7.jpg
V _ m = V _ 1 ( D _ g T _ g ^ 3 T _ s ^ 3 ) ^ { 1 / 2 } ( \sigma ^ 2 D _ s ^ { - 1 } ) ^ { 1 / 2 }
f18fbe80-9732-4b68-9b9e-57380f11bf24__mathematical-expression-and-equation_0.jpg
\{ \bar { A } ^ R - ( \bar { A } ^ P - A ) ; A \in \mathfrak { U } \}
f1cd52c9-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_2.jpg
\pi _ 0 \rightarrow \{ \xi _ 1 ^ { ( 0 ) } , \dots , \xi _ s ^ { ( 0 ) } , \eta _ 1 ^ { ( 0 ) } , \dots , \eta _ r ^ { ( 0 ) } \}
f1cd53d6-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg
M _ { 1 } = \frac { y } { b ^ { + } d ^ { - \sim } f ^ { * } a _ 0 ^ { - \sim } }
f247d765-ac0a-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg
\frac { d ^ 2 V _ R } { d Z ^ 2 } - ( \xi ^ 2 + i ) V _ R = - \xi \lambda \mathcal { P }
f257d131-bc37-11e1-1360-001143e3f55c__mathematical-expression-and-equation_6.jpg
\sum _ { k = 1 } ^ { n } \frac { 1 } { \sin 2 ^ n x } = c t g x - c t g 2 ^ n x
f2ac08a1-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_1.jpg
y ^ 4 = \frac { a } { 2 } x ^ 3
f2ac09ad-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_0.jpg
= f ( \frac { 1 } { h } - \frac { b } { h } M _ 1 - \frac { b _ { 0 1 } p _ f } { f _ { p 1 } q _ 0 } M _ 2 ) = f ( \frac { 1 } { h } - b _ { 0 1 } F )
f311de38-ac0a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_5.jpg
u = \sum _ { n = 0 } ^ { n } \frac { k _ n } { n + 1 } ( \frac { \Delta p } { 2 l } ) ^ n ( R ^ { n + 1 } - r ^ { n + 1 } )
f3381ecd-bc37-11e1-1119-001143e3f55c__mathematical-expression-and-equation_1.jpg
i = ( i a ) b
f36e0a32-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
H d ^ 2 E _ 3 = d ^ 2 E \prime _ 3 + 2 ( \lambda _ 1 \omega _ 1 + \tau _ { 3 3 } ) d E \prime _ 3 + ( . ) E \prime _ 3 - p ^ * _ 1 E \prime _ 4 + q
f36e0ab8-570a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_8.jpg
1 0 - 4 = | 9 - 8 = | 2 - 1 = | 3 - 3 = | 5 - 5 = | 1 0 - ? = 1 0
f3ac2c83-224b-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_8.jpg
( \frac { x } { a } ) ^ 2 + ( \frac { y } { b } ) ^ 2 - ( - \frac { z } { c } ) ^ 2 = 1
f3b88f86-a1bf-486b-845e-15ca829daf57__mathematical-expression-and-equation_0.jpg
F _ { n + 1 } ( 0 , p _ 1 , \dots , p _ n ; 0 , q _ 1 , \dots , q _ n ; 0 , r _ 1 , \dots , r _ n )
f3dea2ef-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_3.jpg
I ^ \beta ( \begin{array} { c c c } \lambda x , & \lambda y , & \lambda z \\ \mu l , & \mu m , & \mu n \end{array} ) = \lambda ^ \beta \mu ^ { 1 - \beta } I _ 3 ^ \beta ( \begin{array} { c c c } x , & y , & z \\ l , & m , & n \end{array} ) , \lambda , \mu > 0
f3dea2fa-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_5.jpg
P _ \eta [ S ( \theta + \Delta ) - S ( \theta ) ] - P _ \eta [ S ( \theta ) - S ( \theta + \Delta ) ] =
f3dea334-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_6.jpg
R _ n = O _ p ( n ^ { - 3 / 4 } )
f3dea3c5-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_10.jpg
b ( \frac { \hat { r } } { \bar { r } } q ) \ge b ( q + \bar { r } \bar { p } + \bar { v } ) + \mu \forall q \in V \setminus \frac { 1 } { \bar { r } } ( \hat { o } - \bar { p } )
f3dea4e2-ac0a-11e1-1211-001143e3f55c__mathematical-expression-and-equation_4.jpg
f ( x ) = [ f ( A ) - f ( 1 ) ] . L x + f ( 1 )
f3f06fe8-40e3-11e1-1726-001143e3f55c__mathematical-expression-and-equation_5.jpg
\pi _ 0 = \frac { t g \rho } { \pi }
f3fc6100-3e1b-11e4-b6b9-001018b5eb5c__mathematical-expression-and-equation_2.jpg
O _ a ( I _ { 1 x } ) \stackrel { . } { \implies } O _ b ( I _ { 2 t } )
f43f159c-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg
| \int _ { \tau _ 1 } ^ { \tau _ 2 } [ v ( r , \psi + \omega \tau / \epsilon ) - v _ 0 ( r ) ] d \tau \parallel \le \frac { 1 } { 2 } \epsilon
f43f1747-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg
\tau \in \langle \tilde { \tau } , \tau _ 1 \rangle
f43f1797-570a-11e1-1027-001143e3f55c__mathematical-expression-and-equation_11.jpg
L _ 0 = \{ a ^ n | n \ge 1 \}
f4affd95-ac0a-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg