卷 59, 编号 5 (2018)
- 年: 2018
- 文章: 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
摘要
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.
Σ-Definability in Hereditarily Finite Superstructures and Computable Analysis
摘要
We construct a computable real function not Σ-definable in hereditarily finite superstructures over the extensions with decidable theory of the reals.
Generalized Angles in Ptolemaic Möbius Structures. II
摘要
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.
The Local Approximation Theorem in Various Coordinate Systems
摘要
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.
Asymptotic Behavior at Infinity of Solutions to the Nonhomogeneous Sobolev Equation
摘要
Under study is the asymptotic behavior at infinity of solutions to the Cauchy problem to the nonhomogeneous Sobolev equation. We obtain the form of the limit function and the convergence rate.
Characterization of Locally Finite Simple Groups of the Type 3D4 Over Fields of Odd Characteristic in the Class of Periodic Groups
摘要
We prove that a periodic group is locally finite, given that each finite subgroup of the group lies in a subgroup isomorphic to a finite simple group of Lie type 3D4 over a field of odd characteristic.
Basics of the Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings
摘要
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.
The Fourier–Faber–Schauder Series Unconditionally Divergent in Measure
摘要
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.
Study of Solvability of a Thermoviscoelastic Model Describing the Motion of Weakly Concentrated Water Solutions of Polymers
摘要
We study the problem of existence of a weak solution to the initial-boundary value thermoviscoelasticity problem for the model describing the motion of weakly concentrated water solutions of polymers.
Polynomial Sub-Riemannian Differentiability on Carnot–Carathéodory Spaces
摘要
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.
Boundary Value Problems for Odd Order Forward-Backward-Type Differential Equations with Two Time Variables
摘要
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.
Automorphisms of Formal Matrix Algebras
摘要
We consider the automorphisms of formal matrix algebras over a given commutative ring. In some cases the automorphism group of these algebras is a semidirect product of certain subgroups whose structure is known.
Universality of the Periodic Hurwitz Zeta-Function with Rational Parameter
摘要
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.
The Dressing Chain and One-Point Commuting Difference Operators of Rank 1
摘要
We construct solutions to the difference-differential equation that are associated with onepoint commuting difference operators of rank 1 in the case of spectral curves of genus 1.
Homogenization of the Equations of Filtration of a Viscous Fluid in Two Porous Media
摘要
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.
Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups
摘要
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.
On Hamiltonian-Minimal Isotropic Homogeneous Tori in ℂn and ℂPn
摘要
We study isotropic homogeneous tori in ℂn and ℂPn. We find necessary and sufficient conditions for their Hamiltonian minimality.
On Groups with a Frobenius Element
摘要
We study groups with an H-Frobenius element and the nilpotent kernels of the corresponding Frobenius subgroups. We prove the two theorems that solve Question 10.61 of The Kourovka Notebook in this case.