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Том 59, № 5 (2018)
- Жылы: 2018
- Мақалалар: 18
- URL: https://journals.rcsi.science/0037-4466/issue/view/10477
Article
Construction of the Lyapunov–Krasovskii Functionals for some Classes of Positive Delay Systems
Аннотация
A criterion is established for the diagonal stability of positive linear difference-differential systems with discrete and distributed delay. The problem is studied of existence of a common diagonal Lyapunov–Krasovskii functional for a family of these systems. The approach developed is used to obtain conditions of the absolute stability and estimates of the time of transient processes for nonlinear difference-differential systems with sector type nonlinearities.
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Generalized Angles in Ptolemaic Möbius Structures. II
Аннотация
We continue studying the BAD class of multivalued mappings of Ptolemaic Möbius structures in the sense of Buyalo with controlled distortion of generalized angles. In Möbius structures we introduce a Möbius-invariant version of the HTB property (homogeneous total boundedness) of metric spaces which is qualitatively equivalent to the doubling property. We show that in the presence of this property and the uniform perfectness property, a single-valued mapping is of the BAD class iff it is quasimöbius.
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The Local Approximation Theorem in Various Coordinate Systems
Аннотация
We find some sufficient conditions on the local coordinate system of a Carnot–Carathéodory space of low smoothness that ensure Gromov-type estimates on the divergence of local (quasi)metrics. We also obtain these estimates for the canonical coordinate system of the second kind and various mixed coordinate systems.
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Basics of the Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings
Аннотация
We define a scale of mappings that depends on two real parameters p and q, n−1 ≤ q ≤ p < ∞ and a weight function θ. In the case of q = p = n, θ ≡ 1, we obtain the well-known mappings with bounded distortion. Mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used for solving a few problems of global analysis and applied problems.
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The Fourier–Faber–Schauder Series Unconditionally Divergent in Measure
Аннотация
We prove that, for every ε ∈ (0, 1), there is a measurable set E ⊂ [0, 1] whose measure |E| satisfies the estimate |E| > 1−ε and, for every function f ∈ C[0,1], there is ˜ f ∈ C[0,1] coinciding with f on E whose expansion in the Faber–Schauder system diverges in measure after a rearrangement.
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Polynomial Sub-Riemannian Differentiability on Carnot–Carathéodory Spaces
Аннотация
We show that the classes of Hölder mappings of Carnot–Carathéodory spaces are polynomially differentiable in the sub-Riemannian sense. Moreover, we prove the existence of intrinsic (or adapted) bases, which enable us to match the nonholonomic structures of the images of mappings and target spaces.
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Boundary Value Problems for Odd Order Forward-Backward-Type Differential Equations with Two Time Variables
Аннотация
We study solvability of boundary value problems for odd order differential equations in time variables. The presence of a discontinuous alternating coefficient is a peculiarity of these equations. We prove existence and uniqueness theorems for the regular solutions of such an equation, i.e. those that have all Sobolev generalized derivatives entering the equation under study.
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Universality of the Periodic Hurwitz Zeta-Function with Rational Parameter
Аннотация
The periodic Hurwitz zeta-function, a generalization of the classical Hurwitz zeta-function, is defined by a Dirichlet series with periodic coefficients and depends on a fixed parameter. We show that a wide class of analytic functions is approximated by shifts of a periodic zeta-function with rational parameter.
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Homogenization of the Equations of Filtration of a Viscous Fluid in Two Porous Media
Аннотация
A homogenized model of filtration of a viscous fluid in two domains with common boundary is deduced on the basis of the method of two-scale convergence. The domains represent an elastic medium with perforated pores. The fluid, filling the pores, is the same in both domains, and the properties of the solid skeleton are distinct.
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Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups
Аннотация
Let P be a subgroup of a Sylow subgroup of a finite group G. If P is a Sylow subgroup of some normal subgroup of G then P is called normally embedded in G. We establish tests for a finite group G to be p-supersoluble provided that every maximal subgroup of a Sylow p-subgroup of X is normally embedded in G. We study the cases when X is a normal subgroup of G, X = Op',p(H), and X = F*(H) where H is a normal subgroup of G.
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