Mathematics

The M.A. Lavrentiev Inverse Problem on Mapping of Half-Plane Onto Polygon with Infinite Set of Vertices

Authors: Salimov R. B., Shabalin P. L.

The authors consider a generalization of the M.A.Lavrentiev inverse problem on a conformal mapping of half-plane onto interiority of a polygon for the case where the set of vertices of this polygon is infinite. We assume that the inner angles at unknown vertices and the image of the vertices under the conformal mapping on the real line are given. Under certain restrictions on values of the angles and on the sequence of points of the real line that are preimages of the vertices the formula for such a mapping is obtained.

The Approached Calculation of Eigenvalues of the Discrete Operator by Means of Spectral Traces of Resolvent Degree

Authors: Maleko Е. М.

Letadiscreteself-adjointoperatorT actsinaseparableHilbertspace and have the kernel resolvent, and eigenvalues and eigenfunctions of the operator T be known. In the paper the method of calculation of eigenvalues of the perturbed operator T + P is considered. Resolvent of this operator is presented as convergent Neumann series on eigenfunctions of the operator T. The point of the method is that at first is found a set of numbers which approximate traces of the resolvent degrees of the operator T + P.

About the Congruences of Two-Generated Monoid

Authors: Kudryavtseva L. A.

The congruences of two-generated monoid which generated by pair of words of length 2 are considered over two-letter alphabet. It is shown that number of equivalence classes for words of length n is equal to n + 1. The number of words in each class is found.

The Problem of Convergence in Point Trigonometric Interpolation Process of Lagrange

Authors: Borisova L. V., Shatalina A. V.

An analogue of the characteristic of R. Salem is obtained for a trigonometric Lagrange interpolation process on the matrix of equally spaced nodes.

On Inverse Problem for Sturm – Liouville Operator with Discontinuous Coefficients

Authors: Akhmedova E. N., Guseinov I. M.

In the paper uniqueness of reconstruction of the Sturm – Liouville operator with discontinuous coefficients by spectral data is proved and algorithm of construction of the potential is provided.