We consider the problem of identifying the constant parameters involved in the right-hand sides of a linear non-autonomous system of differential equations with first-order ordinary derivatives. The specificity of the problem lies in the fact that additional conditions for identifying the unknown parameters, firstly, are nonlocal, and secondly, they include derivatives of an unknown function. The work examines the conditions for existence and uniqueness of a solution to the problem, and proposes two different approaches to the numerical solution of the problem. The results of computer experiments are presented.

The rate of convergence of double rational Fourier series and, in particular, double trigonometric Fourier series of functions of generalized bounded variation is estimated.

Let $|\cdot|$ be the Euclidean norm in $\mathbb{R}^n$, $n\geq 2$. For $r>0$, weLet $|\cdot|$ be the Euclidean norm in $\mathbb{R}^n$, $n\geq 2$. For $r>0$, we denote by $V_r(\mathbb{R}^n)$ the set of functions $f\in L_{\mathrm{loc}}(\mathbb{R}^n)$ satisfying the condition \begin{equation*}\label{eq } \int_{|x|\leq r}f(x+y)dx=0\quad\text{for any}\quad y\in\mathbb{R}^n. \end{equation*} The paper investigates the interpolation of tempered growth functions of class $(V_r\cap C^{\infty})(\mathbb{R}^n)$ together with the derivatives of bounded order in a given direction. Let $d\in\mathbb{R}^n$, $\sigma\in\mathbb{R}^n\setminus\{0\}$ be fixed, $\{a_k\}_{k=1}^{\infty}$ be a sequence of points lying on the line $ \{x\in\mathbb{R}^n:\,x=d+t\sigma,\,t\in(-\infty,+\infty)\}$ and satisfying the conditions \begin{equation*}\label{equation} \underset{i\ne j}\inf\, |a_i-a_j|>0,\quad |a_k|\leq|a_{k+1}|\quad\text{for all}\quad k\in\mathbb{N}. \end{equation*} Let also $m\in\mathbb{Z}_+$ and $b_{k,j}\in\mathbb{C}$ ($k\in\mathbb{N}$, $j\in\{0,\ldots,m\}$) be a set of numbers satisfying the condition \begin{equation*}\label{eq} \underset{0\leq j\leq m}\max\, |b_{k,j}|\leq(k+1)^{\alpha} \end{equation*} for all $k\in\mathbb{N}$ and some $\alpha\geq 0$ independent of $k$. It is shown (Theorem) that, under the indicated conditions, the interpolation problem \begin{equation*}\label{ equation*} \left(\sigma_1\frac{\partial}{\partial x_1}+\ldots+\sigma_n\frac{\partial}{\partial x_n}\right)^jf(a_k)=b_{k,j},\quad k\in\mathbb{N},\quad j\in\{0,\ldots,m\}, \end{equation*} is solvable in a class of functions belonging to $(V_r\cap C^{\infty})(\mathbb{R}^n)$, which, together with all their derivatives, have growth no higher than a power-law at infinity. It is noted that the condition of separability of nodes $\{a_k\}_{k=1}^{\infty}$ in  the Theorem cannot be removed, and also that the solution of the considered interpolation problem is not the only one. In addition, it is stated that the one-dimensional analogue of the Theorem is not valid since every continuous function of class $V_r(\mathbb{R}^n)$ at $n=1$ is $2r$-periodic.

The concepts of chaotic systems and systems of differential equations with impulsive action are formulated. A method for stabilizing the zero solution of the chaotic Lorenz system by means of impulsive actions that occur on a certain set of the phase space is proposed.

The task of reducing the level of vibration of radio-electronic devices (REA) is an urgent task in mechanical engineering of aircraft industry. The purpose of the study is to investigate the vibrations of plate-like elements with attached masses under the influence of vibration loads. All deformable elements are viscoelastic. The viscoelastic properties obey the hereditary Boltzmann-Volterra integral relation. Linear oscillations of the considered mechanical system are investigated. For reduction of impulse perturbations of a radio-electronic unit with attached masses, a method and an algorithm for solving the problem are developed. The method of complex amplitudes, the methods of mathematical physics equations, the Gauss method, the Mueller method and the Godunov orthogonal run method were used in developing a method for solving the problem. An algorithm for determining the resonance frequency and amplitude of displacements of the considered mechanical system was proposed. Application of the proposed mathematical model taking into account viscous properties of the elements allows to reduce the total impulse loads of the REU up to 25%. It is established that the use of rubber shock absorbers reduces the amplitudes of vibrations of the equipment up to 30%. It is also established that the use of dissipative and inhomogeneous design allows maximal reduction (up to 40–50%) of resonant amplitudes of REU in low-frequency ranges.

On plane and space domains, we present several integral inequalities for functions with non-zero boundary trace. These new inequalities for functions are generalizations of the isoperimetric inequalities from the author’s recent paper (F.G. Avkhadiev. An analog of the Poincaré metric and isoperimetric constants, Russian Mathematics, 2024, Vol. 68, No. 9, pp. 79–85).

Our theorems are formulated using hyperbolic type domains, the distance from a point to the boundary of a domain and the hyperbolic radius. We give schemes of proofs using the Poincaré metric and its properties, some hyperbolic characteristics of plane domains as well as space domains of hyperbolic type in the sense of Loewner and Nirenberg.

In this paper, operator matrix ${\mathcal A}_\mu$ of order three with spectral parameter $\mu$ is considered. It corresponds to a system with non-conserved and no more than three particles on the one-dimensional lattice and is considered as a linear, bounded and self-adjoint operator in a cut subspace of the Fock space. Using the spectral properties of a family of generalized Friedrich models, the location and structure of the essential spectrum of the operator matrix ${\mathcal A}_\mu$ is investigated. The Fredholm determinant associated with the operator matrix ${\mathcal A}_\mu$ is found and its discrete spectrum is described by the zeros of the Fredholm determinant.