Mathematics

The Mixed Problem for the Differential Equation with Involution and Potential of the Special Kind

Authors: Khromov A. P.

For the solution of some mixed problem with involution and real symmetrical potential, explicit analytical formula has been found with the use of the Fourier method. Techniques allowing to avoid term-byterm differentiation of the functional series and impose the minimum conditions for initial problem data, are used.

On a Approximate Solution of the Problem of Aspherical Convex Compact Set

Authors: Dudov S. I., Mesheryakova Е. А.

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution.

The Inverse Problem of Spectral Analysis for the Matrix Sturm – Liouville Equation

Authors: Bondarenko N. P.

The inverse spectral problem is investigated for the matrix Sturm - Liouville equation on a finite interval. The article provides properties of spectral characteristics, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability has been obtained.