2017
Том 69
№ 7

Volume 66, № 1, 2014

Article (English)

Fixed-Point Theorems for Multivalued Generalized Nonlinear Contractive Maps in Partial Metric Spaces

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 3–16

We prove some fixed-point results for multivalued generalized nonlinear contractive mappings in partial metric spaces, which generalize and improve the corresponding recent fixed-point results due to Ćirić [L. B. Ćirić, “Multivalued nonlinear contraction mappings,” Nonlin. Anal., 71, 2716–2723 (2009)] and Klim and Wardowski [D. Klim and D. Wardowski, “Fixed-point theorems for set-valued contractions in complete metric spaces,” J. Math. Anal. Appl., 334, 132–139 (2007)].

Article (Russian)

On the Boundary Behavior of One Class of Mappings in Metric Spaces

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 17–29

We study the problem of extension to the boundary of continually ring Q-homeomorphisms relative to a p-module between continual domains in metric spaces with measures and formulate the conditions for the function Q and the boundaries of domains under which every continually ring Q-homeomorphism admits a continuous or homeomorphic extension to the boundary. The accumulated results yield, in particular, important applications to fractals in ℝ n , n ≥ 2.

Article (Ukrainian)

Queueing Systems with Resume Level

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 30–40

A new approach is proposed for the investigation of the characteristics of queueing systems of the M/G/1/b-type with finite waiting rooms and a resume level of the input flow. A convenient algorithm is proposed for the numerical evaluation of stationary parameters of the system. Its efficiency is demonstrated for a specific system.

Article (English)

Classification of the Regular Components of Two-Dimensional Inner Maps

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 41–48

We propose a topological classification of dynamical systems generated by two-dimensional inner maps on the fully invariant regular components of a wandering set with special attracting boundary (to within the topological conjugacy).

Article (Ukrainian)

Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 49–62

We establish two-sided estimates for the exact upper bounds of approximations by the interpolation analogs of the de-la-Vallée-Poussin sums on the classes of 2π -periodic functions C β,s ψ specified by the sequences ψ(k) and shifts of the argument β , β ∈, under the condition that the sequences ψ(k) satisfy the d’Alembert D q , q ∈ (0, 1), condition. Similar estimates are obtained for the classes C β ψ H ω generated by convex moduli of continuity ω(t). Under the conditions n − p → ∞ and p → ∞, the indicated estimates turn into asymptotic equalities.

Article (English)

On Nearly ℳ-Supplemented Subgroups of Finite Groups

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 63–70

A subgroup H is called nearly -supplemented in a finite group G if there exists a normal subgroup K of G such that HKG and TK < HK for every maximal subgroup T of H. We obtain some new results on supersoluble groups and their formation by using nearly -supplemented subgroups and study the structure of finite groups.

Article (Russian)

Kolmogorov-Type Inequalities for Fractional Derivatives on the Half Line

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 71–78

We obtain new sharp Kolmogorov-type inequalities for the fractional derivatives of functions defined on the half line.

Article (Ukrainian)

Distribution of Random Variable Represented by a Binary Fraction with Three Identically Distributed Redundant Digits

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 79–88

We present the complete solution of the problem of pure Lebesgue type of the distribution of random variable χ represented by a binary fraction with three identically distributed redundant digits.

Article (Russian)

Decay of the Solutions of Parabolic Equations with Double Nonlinearity and the Degenerate Absorption Potential

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 89–107

We study the behavior of solutions for the parabolic equation of nonstationary diffusion with double nonlinearity and a degenerate absorption term: $${\left({\left| u\right|}^{q-1} u\right)}_t-{\displaystyle \sum_{i=1}^N\frac{\partial }{\partial {x}_i}\left({\left|{\nabla}_x u\right|}^{q-1}\frac{\partial u}{\partial {x}_i}\right)+{a}_0(x){\left| u\right|}^{\lambda -1} u=0,}$$ where ${a}_0(x)\ge {d}_0\; \exp \left(-\frac{\omega \left(\left| x\right|\right)}{{\left| x\right|}^{q+1}}\right)$ , d 0 = const > 0, 0 ≤ λ < q, ω(⋅) ϵ C([0, + ∞)), ω(0) = 0, ω(τ) > 0 for τ > 0, and ${\displaystyle {\int}_{0+}\frac{\omega \left(\tau \right)}{\tau} d\tau <\infty }$ . By the local energy method, we show that a Dini-type condition imposed on the function ω(·) guarantees the decay of an arbitrary solution for a finite period of time.

Article (English)

On Two-Dimensional Model Representations of One Class of Commuting Operators

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 108–127

In the work by V. A. Zolotarev, Dokl. Akad. Nauk Arm. SSR, 63, No. 3, 136–140 (1976), a triangular model is constructed for a system of twice-commuting linear bounded completely nonself-adjoint operators {A 1, A 2} ([A 1, A 2] = 0, [A 1 , A 2] = 0) such that rank (A 1) I (A 2) I  = 1 (2i(A k ) I  = A k  − A k k = 1, 2) and the spectrum of each operator A k k = 1, 2, is concentrated at zero. The indicated triangular model has the form of a system of operators of integration over the independent variable in L Ω 2 where the domain Ω = [0, a] × [0, b] is a compact set in ℝ2 bounded by the lines x = a and y = b and a decreasing smooth curve L connecting the points (0, b) and (a, 0).

Brief Communications (Russian)

On Generalized Regularized Trace of a Fourth-Order Differential Operator with Operator Coefficient

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 128–134

We deduce a formula for the trace of a boundary-value problem with unbounded operator coefficient and boundary conditions depending on the parameter.

Brief Communications (English)

A Ring of Pythagorean Triples over Quadratic Fields

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 135–139

Let K be a quadratic field and let R be the ring of integers of K such that R is a unique factorization domain. The set P of all Pythagorean triples in R is partitioned into P η , sets of triples 〈αβγ〉 in P where η = γ − β. We show the ring structures of each P η and P from the ring structure of R.

Brief Communications (English)

On Kropina Change for mth Root Finsler Metrics

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 140–144

We study the Kropina change for mth root Finsler metrics and establish necessary and sufficient condition under which the Kropina change of an mth root Finsler metric is locally dually flat. Then we prove that the Kropina change of an mth root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.