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The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary...
In this note we shall consider the following problem: which conditions should satisfy a function ℎ : (0, 1) → ℝ in order to guarantee the existence of a (regular) measure μ in with compact support and for some positive constants 𝑐 2 , and 𝑐 2 independent of γ ∈ Γ and 𝑟 ∈ (0,1)? The theory of...
A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.
L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿 𝑝 -deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛 α 𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.
The asymptotic behavior as 𝑡 → ∞ of solutions of a nonlinear integro-differential equation is studied. The equation arises as a model describing the penetration of the electromagnetic field in to a substance.
We prove that any surjective homomorphism of Maltsev algebras is a Kan fibration.
Two symmetric invariant probability measures μ 1 and μ 2 are constructed such that each of them possesses the strong uniqueness property but their product μ 1 × μ 2 turns out to be a symmetric invariant probability measure without the uniqueness property.
Problems of the Mackey-continuity of characteristic functionals and the localization of linear kernels of Radon probability measures in locally convex spaces are investigated. First the class of spaces is described, for which the continuity takes place. Then it is shown that in a non-complete...
Linear dynamical systems are introduced in a general axiomatic way, and their development is carried out in great simplicity. The approach is closely related both with the classical transfer function approach and with the Willems behavioral approach.
A Bochner mean square deviation for random elements of 2-convex Banach lattices is introduced and investigated. Results, analogous to the law of large numbers for squares of random elements are proved in some classes of Köthe function spaces.
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