Baku Mathematical Journal

Journal Information
ISSN / EISSN: 27908410 / 27908429
Total articles ≅ 21

Latest articles in this journal

Alekber K. Mekhdiev, Rafail K. Mekhtiev
Baku Mathematical Journal, Volume 1, pp 125-144; https://doi.org/10.32010/j.bmj.2022.13

Abstract:
An elastic medium is considered, weakened by a doubly periodic system of round holes, filled with absolutely rigid inclusions, soldered along the bypass and has a crack initiation. The medium (binder) is weakened by two periodic systems of rectilinear crack initiation directed collinear to the abscissa and ordinate axes, and their sizes are not the same. General representations are constructed that describe a class of problems with a doubly periodic stress distribution outside circular holes and cracks under transverse shear. The analysis of the limiting equilibrium of cracks in the framework of the end zone model is carried out on the basis of a nonlocal fracture criterion with a force condition for the propagation of the crack tip and a deformation condition for determining the advancement of the edge of the end zone of the crack. Basic resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations. The equations in each approximation were solved by the Gaussian method with the choice of the principal element for different values of the order of M, depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing the growth of cracks.
Azamat M. Akhtyamov, Khanlar R. Mamedov
Baku Mathematical Journal, Volume 1, pp 179-194; https://doi.org/10.32010/j.bmj.2022.19

Abstract:
An nonself-adjoint Sturm–Liouville problem with two polynomials in nonseparated boundary conditions are considered. It is shown that this problem have an infinite countable spectrum. The corresponding inverse problems is solved. Criterions for unique reconstruction of the nonself-adjoint Sturm-Liouville problem by eigenvalues of this problem and the spectral data of an additional problem with separated boundary conditions are proved. Schemes for unique reconstruction of the Sturm-Liouville problems with polynomials in nonseparated boundary conditions and corresponding examples are given
Aigul R. Sagitova, Anfisa V. Shakirova, Yaudat T. Sultanaev
Baku Mathematical Journal, Volume 1, pp 150-154; https://doi.org/10.32010/j.bmj.2022.15

Abstract:
In the article we consider the Sturm-Liouville equation −y ′′+(q(x)+h(x))y = 0, 0 ≤ x < +∞, where q(x) satisfies the conditions of regularity of growth at infinity and h(x) is a fast-oscillating function. Sufficient conditions are found under which the asymptotics of solutions of the equation is determined only by the function q(x). A new method for obtaining asymptotic formulas for solutions is proposed, consisting in the standard replacement of the equation by a system of first-order equations followed by the application of the Hausdorff identity [1]
Togrul R. Muradov, Seadet A. Nurieva, Valid F. Salmanov
Baku Mathematical Journal, Volume 1, pp 172-178; https://doi.org/10.32010/j.bmj.2022.18

Abstract:
In this work systems of sines 1∪ {sin (n − β)t}n≥1 and 1∪ {cos (n − β)t}n≥1 cosines are considered, where β is real parameter. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter β in one subspace of grand-Sobolev space are found.
Matlab Yu. Salimov, Afarim A. Salimova
Baku Mathematical Journal, Volume 1, pp 195-204; https://doi.org/10.32010/j.bmj.2022.20

Abstract:
This work deals with the solvability of inverse boundary value problem with time-dependent unknown coefficient for nonlinear diffusion equation. Definition of classical solution for the considered inverse boundary value problem is introduced. By the Fourier method, the problem is reduced to the system of integral equations. Using the contraction mappings method, the existence and uniqueness of the solution of the system of integral equations are proved. Finally, the existence and uniqueness of the classical solution of original problem are proved.
Mahbuba E. Kerimova, Mahir M. Sabzaliyev
Baku Mathematical Journal, Volume 1, pp 145-149; https://doi.org/10.32010/j.bmj.2022.14

Abstract:
A boundary value problem stated in an infinite semi-strip for a third order non-classic type differential equation degenerated into a hyperbolic equation, is considered. The complete expansion of the solution of the problem with respect to a small parameter as constructed and the residual term is estimated.
Abdullah Karakuş, Manaf Dzh. Manafov
Baku Mathematical Journal, Volume 1, pp 164-171; https://doi.org/10.32010/j.bmj.2022.17

Abstract:
The regularized trace formula of first order for the ”weighted” Sturm-Liouville equation with point δ-interaction is obtained.
Orkhan Z. Namazov, Rashad M. Tagiyev
Baku Mathematical Journal, Volume 1, pp 155-163; https://doi.org/10.32010/j.bmj.2022.16

Abstract:
Using the relation method for the system of first order, two-dimensional hyperbolic type partial differential equations describing the motion of gas liquid gas mixture corresponding to gas-lift process of oil production in an annular and lifting pipe, we consider a boundary condition problem. In this problem the existence a boundary condition problem. In this problem the existence of the solution with respect to the equations of motion is studied and it is shown that when constructing the solution of this problem by means of boundary conditions, it is impossible to determine the coefficients of positive degrees of the parameter ε. For this reason, the solution is sought in the form of a series using negative degrees of the parameter ε.
Shaban T. Gurbuz, Anar A. Nabiev, Suna Saltan
Baku Mathematical Journal, Volume 1, pp 205-229; https://doi.org/10.32010/j.bmj.2022.21

Abstract:
In the present work, we obtain some integral representations for special solutions, which play an important role in solving direct and inverse problems for secondorder and fourth-order matrix Sturm-Liouville pencils. We also investigate some useful properties of the special solutions.
R.S. Mammadov, Azerbaijan State Oil and Industry University, S.Y. Qasimov
Baku Mathematical Journal, Volume 1, pp 106-110; https://doi.org/10.32010/j.bmj.2022.11

Abstract:
In the paper, optimal control problem for cooling process with minimum energy in materials with heat conducting viscosity is considered. To solve approximately the considered problem, a finite-dimensional approximation for the solution of the corresponding boundary value problem in the form of truncated Fourier series is constructed and an integral representation for the coefficients of this series is obtained. This yields a system of integral equations with respect to control parameters. So, the problem is reduced to finding a minimum norm function from these moment relations. Applying the theorem on orthogonal decomposition of a normalized space, every approximation of control parameter and the corresponding value of a functional in analytic form is finded.
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