problem (1), (2) the (weak approximation τ) in unknown method [1] is used. Let us consider an auxiliary split problem with time shift t − 3 functions and non-linear terms ) ( 1 uτt (t, x) = 3a(t)uτxx (t, x), nτ < t 6 n + τ; (7) 3 ( ) ( ) ( ) ( τ τ ) τ( τ...
) τ 1 2 τ τ ut (t, x) = 3b t − , x, u t − , x , ω t − ux (t, x), n+ τ <t6 n+ τ ; (8) 3 3 3 3 3 ( ) ( ( ( τ τ ) τ )) 2 uτt (t, x) = 3f t − , x, uτ t − , x , ω τ t − , n+ τ < t 6 (n + 1)τ ; (9) 3 3 3 3 � uτ (t, x)�t60 = u0 (x). (10) Let us prove a priori...

on temperature and concentration on the interface σ(θ1, C) = σ0 − κ1θ1 − κ2C with constants σ0 > 0, κ1 > 0, and κ2. We introduce the dimensionless independent variables ξ = x/l10, η = y/l10, and τ = ν1t/l210, as well as velocities, modified pressures...
ξξ = 0, and the interface can only be a straight line. In what follows, we consider it parallel to the solid walls η = 0 and η = l2/l10, so that in the dimensionless variables its equation is η = 1. We seek a solution of (1) in the form uj = Uj(η, τ...

единицам, сделав в (2) следующую замену: tτ ω= , g l α = , 2A l ωβ = , 2kl J γ = . (3) В итоге имеем следующую систему: ( )( ) ( ) ( ) 1 1 2 1 2 2 2 1 1 11 1 12 2 21 2 22 sign sin 0 (0) (0) (0) (0) ϕ α β τ ϕ γ ϕ ϕ ϕ αϕ γ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ...
⎧ = + + −⎪⎨ = − − =⎪⎩ = = = = && && & & ,,,. (4) Перепишем (4) в виде системы дифференциальных уравнений первого порядка: ( ) 1 2 2 1 3 3 4 4 3 1 1 11 1 12 2 21 2 22 ( ) (0) (0) (0) (0) z z z p z z z z z z z τ γ α γ γ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ =⎧ ⎪ = +⎪⎨ =⎪ ⎪ = − +⎩ = = = = & & & & & & ,,, (5...

] a joint statistical dynamics for DTS and PLL can be viewed in the coordinates ˆφ φ φ= − ; ˆτ τ τp = − , where  is the phase difference; p is the difference of the time position of the base and input signals; ˆ ˆφ,τ are their values...
. The characteristics of tracking failure are determined using differential equations: ( ) ( ) ( ) ( ) ( )1 2 1 2 32 2 2 0 0 0 φ 4cosφ 4sinφ 8 αφ φ sin 2φ ; | τ | | τ | | τ | 1 1 1 τ τ τ p p p э э э d n t n t n t n t n t dt AT AT A...

. . . The following notations are introduced z χ ; τ = 2 t; a∗ = max(| aj (t) |, | cj (t) |), j = 1, 2, u∗ = βa∗ lχ; l l χ ∗ a(z, t) = a A(ξ, τ ); c(z, t) = a∗ C(ξ, τ ); θ(z, t) = a∗ Θ(ξ, τ ); f (z, t) = 2 ReF (ξ, τ ); l χ χ2 h(z, t) = 2 ReH(ξ, τ ); nj (t) = 4 Nj (τ...
P = ν/χ is the Prandtl number. After substituting (8) into system (6), (7), the initial boundary value problem in dimensionless form is obtained ∫ ξ Aτ + 2ReA(F + H) − 2ReAξ F (ξ, τ )dξ = Aξξ , 0 ∫ Cτ + 2ReC(F − H) − 2ReAξ ∫ Θτ − 2ReΘξ F (ξ, τ )dξ...

phthfphthf τ ξ n t λ n t λ;ttt = ∂ ∂ − ∂ ∂ == , d d Q n t n t ttt phthfphthf τ ξ λλ; = ∂ ∂ − ∂ ∂ == =ξ⋅=′ f.ss ~ h A 0,20 м 2 =ξ⋅=′ f.ss h Г 0,20 м 1 , не A, а Г; не показатель степени м 2 , а сноска [2] (сноска «Физич-е вел- ны …» внизу) () 2 h...
τa Fo ⋅ = () 2 τ Fo h a⋅ = τ0,01τ h τ 2 ⋅= ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ξ ′ =′ f.s s τ0,01ττ 2 ⋅= ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ξ ′ =′ f.s s h ; y t λ τ t С, y t λ τ t С 2 2 2 2 ∂ ∂ = ∂ ∂ ∂ ∂ = ∂ ∂ ththff ;λ τ ,λ τ 2 2 2 2 y tt С y tt С ththff...

= ∑ 𝜑𝑖 , 𝑖=1 𝑗 = 1, … , 𝑙, 𝑖=1 где 𝜑 𝑖 – вектор-функции размерности 𝑙; 𝜑𝑗 , 𝜑𝑗𝑖 – 𝑗-е компоненты векторов 𝜑 и 𝜑 𝑖 соответственно. Рассмотрим систему 𝑚 𝜕𝑢𝜏 = ∑ 𝛼𝑖,𝜏 (𝑡)𝜑𝑖 (𝑡, 𝑥, 𝑢̅𝜏 ), 𝜕𝑡 𝑖=1 где функции 𝛼𝑖,𝜏 (𝑡...
) определены соотношением 𝛼𝑖,𝜏 (𝑡) = { 𝑚, 𝑖−1 𝑖 ) 𝜏 < 𝑡 ≤ 𝑡0 + (𝑛 + ) 𝜏, 𝑚 𝑚 в противном случае, 𝑡0 + (𝑛 + 0, 𝑛 = 0,1, … , 𝑁 − 1; 𝜏𝑁 = 𝑡1 − 𝑡0 . Система (1.5) слабо аппроксимирует систему (1.4). 7 (1.5) �Далее, рассмотрим систему...

reduction of the set of parameters sufficient for characterization the E-distribution of the set of events X. The unit values of all multicovariances τ (X) of subsets of events X ⊆ X, in which the power is greater than some fixed value: |X| greaterorequalslant...
-truncated approximation hatwidep[N0], and [N0] any order N0 = 0,1,··· ,|X|, p[m] (X) = productdisplay Ym⊆X τ (Ym), X ⊆ X (3) emdash.cyr multiplicative-truncated projection of the order m of E-distribution p(X); {τ (Y ),Y ⊆ X} emdash.cyr multicovariances of E...

of the Cauchy problem for equation uxx − uyy + f2(x, y;u(x, 0)) = 0, at y < 0 with initial conditions u(x, 0) = τ(x), 0 6 x 6 1; uy(x,−0) = ,−(x), 0 < x < 1 can be represented as follows: u(x, y) = τ(x+ y) + τ(x− y) 2 − 1 2 x−y∫ x+y ,−(t)yt− 1 4 x−y∫ x+y yη η∫ x...
+y f2 ( ξ + η 2 , ξ − η 2 ; τ ( ξ + η 2 )) yξ. (8) If we set a1(x) = a2(x) = a3(x) = 0 and a4(x) = ψ′2(x) then Problem I is a special case of Problem II. Then we will study the existence and uniqueness of solutions of Problem II. Using condition (7...

∗ be a H-type norm so that x ∗ y > xy. Consider 0 < τ < 1 and 0 6 α, β, γ 6 1 so that α+β +γ 6 1. Consider (Ῡ, ϖ, ∗) be a complete SFMS and G : Ῡ× Ῡ× Ῡ → Ῡ and h : Ῡ → Ῡ be two functions so that G(Ῡ× Ῡ× Ῡ) ⊆ h(Ῡ) and h is continuous...
and commuting with G. Let for all ῑ, κ̄, λ̄, ē, f¯, ḡ ∈ Ῡ and ϱ > 0, (1) is satisfied, ϖ(G(ῑ, κ̄, λ̄), G(ē, f¯, ḡ), τ ϱ) > ϖ(hῑ, hē, ϱ)α ∗ ϖ(hκ̄, hf¯, ϱ)β ∗ ϖ(hλ̄, hḡ, ϱ)γ . (1) Then, G and h possess a unique soft tripled coincidence point. Moreover...