Mathematics

On the Distribution of the Numbers with Binary Expansions of a Special Type in Arithmetic Progressions

Authors: Naumenko A. P.

Let 2 be the primitive root mod p. Let N0 be a set of natural numbers whose binary expansions contain even numbers of 1. Numbers from N0 are uniformly distributed in arithmetic progressions with the difference p.

Operator Integration with an Involution Having a Power Singularity

Authors: Kornev V. V., Khromov A. P.

Spectral properties of the integral operator with an involution of special type in the upper limit are studied and an equiconvergence theorem for its generalized eigenfunction expansions is obtained.

Spectral Sequences of Fibre Tolerance Spaces

Authors: Klyaeva I. A.

The paper presents the theoretical base for the construction of spectral sequences of tolerant exfoliations. Namely, the authors give a number of important qualities of singular cubes in tolerant exfoliations. The fundamental base group operation on the group of fiber homology of tolerant exfoliation theorem is proved. According to the general theory of spectral sequences the first and the second terms of spectral sequence of tolerant exfoliations are got.

The Theorem on Equiconvergence for the Integral Operator on Simplest Graph with Cycle

Authors: Burlutskaya M. S.

The paper deals with integral operators on the simplest geometric two-edge graph containing the cycle. The class of integral operators with range of values satisfying continuity condition into internal node of graph is described. The equiconvergence of expansions in eigen and adjoint functions and trigonometric Fourier series is established.

Generalized Regular Systems of Differential Equations

Authors: Aldibekov T. M.

From the set of systems of differential equations we consider the class of systems with solutions asymptotic defined by generalized exponents. The generalization some known signs correct theorems are obtained.