Mathematics

On Recovering Differential Pencils on a Bush-type Graph

Authors: Yurko V. A.

We study the inverse problem of spectral analysis for differential pencils on a bush-type graph, which is an arbitrary compact graph with one cycle. We pay the main attention to the most important nonlinear inverse problem of recovering coefficients of differential equations provided that the structure of the graph is known a priori. We use the standard matching conditions in the interior vertices and Dirichlet and Neumann boundary conditions in the boundary vertices.

On Solvability of One Class of Urysohn Type Nonlinear Integral Equation on the Whole Line

Authors: Khachatryan K. A., Sardaryan T. H.

In present work one class of Urysohn type nonlinear integral equation on whole line is studied. Equations observed have applications in various fields of mathematical physics. It is assumed that Hammerstein type nonlinear integral operator with a difference kernel serves local minorant in terms of M. A. Krasnoselskii for the Urysohn initial operator.

A Minimal Non-extendable Partial Semigroup

Authors: Petrikov A. O.

This article discusses partial semigroups with a finite number of elements. Any partial semigroup can be extended to a full semigroup by adding elements to it, for example, a zero semigroup, in an external semigroup way. The author of the article is interested in the question of continuation of a partial semigroup without adding any elements to it in an internal semigroup way. The aim of this work is to find an internally non-extendable partial semigroup with a minimal number of elements.

CMS Operators Type B(1, 1) and Lie Superalgebra osp(3, 2)

Authors: Movsisyan G. S., Sergeev A. N.

The main purpose of this article is to study the realation between the representations theory of Lie superalgebras osp(3, 2) and the Calogero –Moser – Sutherland (CMS) B(1, 1) type differential operator. The differential operator depends polynomially on three parameters. The corresponding polynomial eigenfunctions also depend on three parameters; but in the general case, the coefficients of these eigenfunctions have a rational dependence on the parameters.

Multipoint Differential Operators: „Splitting“ of the Multiple in Main Eigenvalues

Authors: Mitrokhin S. I.

We study the boundary value problem for the differential operator of the eighth order with a summable potential. The boundary conditions of the boundary value problem are multipoint. We derived the integral equation for solutions of differential equation which define the studied differential operator. The asymptotic formulas and estimates for the solutions of the corresponding differential equation for large values of the spectral parameter are obtained.