Authors: E. H. KHALILOV

Keywords: quadrature formulas, simple-layer potential, double-layer potential, Hankel function, curvilinear integral, Lyapunov curve

DOI:  https://doi.org/10.32010/j.bmj.2022.02

Authors: V. M. ABDULLAYEV, S. S. JAFARLI, Y. M. MEHDIYEV

Abstract. In this work, a class of optimal control problems for a rod (plate) heating process with feedback, when the incoming information about the state of the process is continuously received only from its individual points, at which some temperature sensors are placed, is investigated. The heating process itself takes place in a stove at the expense of controlling the temperature inside the stove. The mathematical model of the controlled process is in both cases described by a punctual loaded parabolic type equation. In the work, we derive formulae for the gradient of the functional. Algorithms of numerical solutions to the considered problems are proposed.

Keywords: optimal control, principle of maximum, loade differential equations, non-separated conditions

DOI:  https://doi.org/10.32010/j.bmj.2022.03

Authors: J. J. HASANOV, Z. V. SAFAROV

Abstract. The aim of this paper is to prove the Hardy-Littlewood-Stein-Weiss theorems for Riesz potentials in modified Morrey spaces

Keywords: maximal operator, fractional maximal operator, Riesz potential, weighted modified Morrey space

DOI:  https://doi.org/10.32010/j.bmj.2022.04

Authors: L. I. MAMMADOVA, I. M. NABIEV

Abstract. In the article we consider the  Sturm-Liouville operator with semiseparated boundary conditions, one of which contains a spectral parameter. An asymptotic formula for the eigenvalues of the operator under consideration is given and a uniqueness theorem for the solution of the inverse problem of recovering the corresponding boundary value problems is proved.

Keywords: Sturm-Liouville operator, eigenvalues, inverse problem, uniqueness theorem

DOI:  https://doi.org/10.32010/j.bmj.2022.05