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{\displaystyle 1\leq p\leq \infty ,} the Bochner space L p ( T ; X ) {\displaystyle L^{p}(T;X)} is defined to be the Kolmogorov quotient (by equality almost...

equation describing the evolution of the probability distribution p ( t , x ) {\displaystyle p(t,x)} is: ∂ p ∂ t + ν ∂ p ∂ x = 1 2 σ 2 ∂ 2 p ∂ x 2 , { p ( 0 ...

z t = y ∗ − p t ( x ) 2 p t ( x ) ( 1 − p t ( x ) ) , {\displaystyle z_{t}={\frac {y^{*}-p_{t}(x)}{2p_{t}(x)(1-p_{t}(x))}},} where p t ( x ) = e F t −...

mathematically represented as: F ( t ) = f ( P t , X t , H t , C t ) {\displaystyle \displaystyle F(t)=f(P_{t},X_{t},H_{t},C_{t})} where: F ( t ) {\displaystyle...

conditional distribution p ( t | x ) {\displaystyle p(t|x)} : inf p ( t | x ) ( I ( X ; T ) − β I ( T ; Y ) ) , {\displaystyle \inf _{p(t|x)}\,\,{\Big (}I(X;T)-\beta...

given by p T x {\displaystyle p^{T}x} . Together, these requirements give rise to the associated linear programming problem: min x , s p T x , s.t. F...

{\begin{aligned}b_{-1}&=p(t_{x},f_{(-1,-1)},f_{(0,-1)},f_{(1,-1)},f_{(2,-1)}),\\[1ex]b_{0}&=p(t_{x},f_{(-1,0)},f_{(0,0)},f_{(1,0)},f_{(2,0)}),\\[1ex]b_{1}&=p(t_{x},f_{(-1...

and x to represent the mole fraction; K p = p T 2 ( x NO 2 ) 2 p T ⋅ x N 2 O 4 = p T ( x NO 2 ) 2 x N 2 O 4 {\displaystyle K_{p}={\frac {p_{T}^{2}{\bigl...

The Poisson kernel for Hn+1 is given by P ( t , x ) = c n t ( t 2 + ‖ x ‖ 2 ) ( n + 1 ) / 2 {\displaystyle P(t,x)=c_{n}{\frac {t}{\left(t^{2}+\left\|x\...

∂ x 1 | p , … , ∂ ∂ x n | p } T p Y = R { ∂ ∂ x 1 | p , … , ∂ ∂ x k | p } T X / Y p = R { ∂ ∂ x k + 1 | p , … , ∂ ∂ x n | p } {\displaystyle...

) = ( 1 − γ ) p t ( X i ) + ( γ / λ ) ∑ x ∈ S ( P ( t ) ) x i ,   ∀ i ∈ 1 , 2 , … , N , {\displaystyle p_{t+1}(X_{i})=(1-\gamma )p_{t}(X_{i})+(\gamma /\lambda...

semigroup on X, i.e. Pr [ X t ∈ A | X 0 = x ] = P t ( x , A ) . {\displaystyle \Pr[X_{t}\in A|X_{0}=x]=P_{t}(x,A).} Theorem (Krylov–Bogolyubov). If there exists...

alphabets are used, and with their Cyrillic meaning (A, B, C, E, H, K, M, P, T, X, Y). Its current design derives from Moldovan plates of 1992 design, but...

g. pressure, that varies with time and position: p = p ( t , x , y , z ) {\displaystyle p=p(t,x,y,z)\;} . If the bug during the time interval from t {\displaystyle...

" Ъ ° ' 6x → ← ? ↓ ∅ ± ∇ 7x DEL   Cyrillic and Latin letters with identical (A, B, C, E, H, K, M, O, P, T, X) and similar (Y/У) glyphs were unified....

x\neq y} and there exists a 0 < t < 1 {\displaystyle 0<t<1} such that p = t x + ( 1 − t ) y . {\displaystyle p=tx+(1-t)y.} If K {\displaystyle K} is...

of the system at time t (namely a probability distribution p t ( x ) {\displaystyle p_{t}(x)} ); we want to know the probability distribution of the state...

charge and parity, one then has ψ ( t , x → ) ↦ ψ c p ( t , x → ) = ( ψ L c p ( t , x → ) ψ R c p ( t , x → ) ) = η c ( − i σ 2 ψ L ∗ ( t , − x → ) i σ 2...

x j {\displaystyle x_{j}} in t time steps is given by P t ( x i , x j ) {\displaystyle P^{t}(x_{i},x_{j})} . Here P t {\displaystyle P^{t}} is the matrix...

{\displaystyle L_{x}\in T_{\star x}M} belongs to the image of   K ⋆ x : R ⋆ p → T ⋆ x M   . {\displaystyle \ K_{\star x}:\mathbb {R} _{\star }^{p}\to T_{\star...