Mathematics

Exact Orders of Errors in Smooth Functions Approximations

Authors: Shishkova E. V.

In this paper exact order estimations of errors in uniform metric approximation of smooth function and its derivatives over several classes are obtained in cases when the function is defined precisely or using its  δ-approximation  fδ(x) in  L2[a,b] metric. Integral operators with polynomial finite kernels are considered as approximate one.

Multivariate q-integral p-modules and Criterion of the Generalized Differentiability

Authors: Sakhno L. V.

In the  article in terms of Lq-norm the performance of anisotropic spaces of S.L.Sobolev in space Lp is given. As by one part of numbers probably inequality pi>1, and on another – pi=1 the analog of the theorem of F.Rissa and Hardy–Littlwood is represented in a combined  aspect. More common derivation, regular by Schwarz which only in part of variables is Sobolev’s also is considered.

Overtones of Oscillatory Boolean Matrices

Authors: Poplavskii V. B.

We consider a functioning property of a system with a finite set of elements and with different kinds of Boolean binary relations on it. We also construct the square matrices over arbitrary Boolean algebra which determine some Boolean binary relation and generate a cyclic semigroup with the maximum index and period. The looping of the system with a finite set of elements called an oscillator, is accompanied by appearing of subsequences (overtones) in a sequence of elements on the main diagonal of powers of a relevant Boolean matrix.

About the only Solution in the Problem of the Best Plural Reflection’s Approximation by Algebraic Polynomial

Authors: Vygodchikova I. Y.

This paper is devoted to the proof of the theorem including necessary and sufficient conditions in the problem of the best plural reflection’s ap-proximation by algebraic polynomial. In the proof is used several author’s were published results and two auxiliary lemmas. The proof is based on the minim ax’s problems theory, the approximation’s theory by algebraic polynomials of the P.L. Chebyshev and the plural’s analysis.

Inverse Spectral Problem of Reconstructing One-dimensional Perturbation of Integral Volterra Operator

Authors: Buterin S. A.

An integral operator representable as the sum of a Volterra operator and one-dimensional one is considered, when the inverse operator for Volterra one is an integro-differential operator of second order. The inverse problem of reconstruction of the one-dimensional item from spectral data provided that the Volterra component is known a priori is investigated. The uniqueness of the solution of the inverse problem is proved and conditions are obtained that are necessary and sufficient for its solvability.