Mathematics

Basis Conditions for Systems of Translates and Dilates of Functions in Lp-Spaces

Authors: Terekhin P. A.

We consider a family of translates and dilates of function (or in other words family of wavelets on finite interval) in Lebesgue spaces. The explicit expressions for biorthogonal family are given. The theorem of equiconvergence for biorthogonal wavelets series and Fourier–Haar series is established.

Shape-Preserving Linear n-width of Unit Balls in C[0, 1]

Authors: Sidorov S. P.

Let Dk, k is a natural number or zero, be the k-th differential operator, defined in Ck(X), X = [0, 1], and let C be a cone in Ck(X). Let us denote δnk (A, C)C(X) := Dkf − DkLnfC(X) linear relative n-width of set A ⊂ Ck(X) in C(X) for Dk with constraint C. In this paper we estimate linear relative n-width of some balls in C(X) for Dk with constraint C = {f ∈ Ck(X) : Dkf ≥ 0}.

An Analysis of Queueing Networks with Dynamic Routing Control

Authors: Mitrophanov Y. I., Fokina N. P.

A method for analysis of closed exponential queueing networks with one class of customers and central dynamic routing control is proposed. The method of control is based on a use of different routing matrices during fixed time intervals in the network operation process. The method for analysis is based on a description of the network operation process with model Markov chains. An example of analysis of this type network is given.

Method of Hermite Interpolation by Polynomials of the Third Degree on a Triangle Using Mixed Derivatives

Authors: Matveeva J. V.

There is a sine of the minimum angle of the triangle in the denominator of estimation of inaccuracy of interpolation for derivative of function in building of triangular finite elements. The way of method of Hermite interpolation by polynomials of the third degree on a triangle suggested by N.V. Baidakova is free of minimum angle condition for approximation of any derivatives. There is two-dimenetional cubic element in finite element method equal to element of N.V. Baidakova in this paper.

Convergence of Multiple Vilenkin–Fourier Series in Lorentz Spaces

Authors: Lukyanenko O. A.

Let Λψ,p[0, 1)d be a near to L∞[0, 1)d Lorentz space. We find the function ψ˜ for which the multiple Vilenkin–Fourier of any f ∈ Λψ,p[0, 1)d converge to f in the norm of Lorentz space Λ ˜ [0, 1)d.

About Dirichle’s Rows whith Finite-Valued Multiplicative Coefficients, Satisfy the Riman’s Type Functional Equation

Authors: Krivobok V. V.

In this paper the class of absolutely convergent on the half-plane σ > 1 Dirichlet series with multiplicative finite-valued coefficients is considered. We prove that only Dirichlet L-functions are solutions of a functional Riemann type equation.

On the Binary Additive Problem

Authors: Zinchenko N. A.

Let c be a number lying in the interval (1, 2]. The binary additive problem with semiprimes p1p2 such that { 1/2(p1p2)^(1/c)}<1/2 solved in this paper.

On Convergence of Riesz Means of the Expansions in Eigenfunctions of a Functional-Differential Operator on a Cycle-Graph

Authors: Burlutskaya M. S., Khromov A. P.

The paper deals with necessary and sufficient conditions of uniform convergence of generalized Riesz means for the expansions in eigen and associated functions of the 1-st order functional-differential operator on the graph with three ribs forming a cycle.