This paper is devoted to study the inverse boundary value problem for a third-order partial differential equation with nonlocal boundary conditions, including integral conditions. Using variable separation method and analytical methods is proved the existence and uniqueness of the classical solution of the considered problem .

In this paper a boundary value problem is considered generated by the diffusion equation and non-separated boundary conditions, one of which contains a spectral parameter. Some spectral properties of the boundary value problem are studied. It is proved that the eigenvalues are real and nonzero and that there are no associated functions to the eigenfunctions.

In this paper, we consider the boundary value problem which describes the small bending vibrations of homogeneous beam in cross-sections of which the longitudinal force acts, the left end of which is fixed, and the mass is concentrated on the right end. The oscillatory properties of eigenfunctions are studied and the basis property in of the system of root functions without one arbitrary remote function is established.

In the article, the comparison of the capabilities of 5G networks, which are planned to be widely used, in the management of UAVs, with the currently widely used 4G mobile network technologies was considered. Since both 5G technology and UAVs are new applications of information technology, and especially the recent wide application of UAVs, the secure management of UAVs and 5G networks is one of the most pressing issues. Considering this point of view, it is actually to publish this article.

In this paper we consider the certain nonlinear boundary value problem for ordinary differential equations of fourth order which contain some parameter. The values of this parameter are determined at which nodal solutions to the problem under consideration exist.

The Riesz transform has been well studied on classical Lebesgue, Morrey, Sobolev, Besov, Campanato, etc. spaces. But its discrete version has not been well studied. In this paper, we find a necessary condition and a sufficient condition for the summability of the discrete Riesz transform.

In this paper we consider global bifurcation from zero and infinity of nontrivial solutions of some nonlinear Dirac problems. We show the existence of two families of global continua of nontrivial solutions of this problem emanating from bifurcation points with respect to the line of trivial solutions that contain asymptotic bifurcation points and are contained in classes of vector-functions with fixed oscillation count.

This study addresses the application of different kernel sizes and shapes to optimize morphological operations in the process of background subtraction in video. In this approach, a multi-kernel strategy is employed to adapt to various environmental conditions, such as illumination and object sizes. In this way, the accuracy of object detection is enhanced by adaptively adjusting the morphological operations using a multi-kernel strategy to refine the results of background subtraction.