Mathematics

On Riesz Basises of the Eigen and Associated Functions of the Functional-Differential Operator with a Variable Structure

Authors: Kurdyumov V. P., Khromov A. P.

For a functional-differential operator of a variable structure with integral boundary conditions the Riesz basisness of its eigen and associated functions in the space L32[0, 1] is proved.

Recovering of a Mapping Via Jacobi Matrix, Normalized Homogeneous Function

Authors: Egorov V. V.

Consider system of the differential equations f′(x) = Φ(f′(x))×M(x) with generalized partial derivatives, where f′(x) is a matrix Jacobi of sought mapping, M is a given n×n matrix-value function with integrable elements, Φ is a given function of matrices.

Expansions in Eigenfunctions of the n-th Order Differential Operator with Non-Regular Boundary Conditions

Authors: Dmitriev O. Y.

The paper deals with the expansions in eigenfunctions of the n-th order differential operator with non-regular boundary conditions of special type. Necessary and sufficient conditions for existing of such expansions either on the interval [0, 1] or inside it are derived.

Equiconvergence Theorem for Expansions in Eigenfunctions of Integral Operators with Discontinuous Involution

Authors: Golub A. V., Khromov A. P.

In the paper we consider the equiconvergence of expansions in trigonometric Fourier series and in eigen- and associated functions of integral operators with involution having discontinuities of the first type.

About Nonsingularity of One Boundary Value Problem of Forth Order with Derivatives by Measure

Authors: Golovaneva F. V.

In the work sufficient conditions for nonsingularity of boundary value problem of forth order with derivatives by measure are obtained.

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.

Pages