The propulsive motion of a multimass system, vibration-driven robot (VR), in a viscous incompressible fluid was studied. The VR consisted of a round cylindrical body submerged in the fluid and an internal mass (IM) performing small-amplitude pendulum-like oscillations inside the body. Using the method of asymptotic expansions, the combined mechanical and hydrodynamic problems that describe the self-propulsion of the system in the fluid were solved. The hydrodynamic problem was formulated on the basis of the complete non-stationary Navier–Stokes equation. An analytical solution was derived to describe the cruising regime of the VR motion in the fluid. The non-stationary hydrodynamic influence on the VR was determined. The efficiency of the propulsive system’s motion was assessed.

This article explores the generalized Cauchy–Riemann system on the entire complex plane. The coefficient for the conjugation of the desired function belongs to the Hölder space and, for |z| > 1 , equals e^imϕ , where m is an integer. For m ≤ 0 , the system was shown to have no nonzero solutions that grow no faster than a polynomial. For m ≥ 0 , the complete set of regular solutions, i.e., those without singularities in the finite part of the plane, was constructed. The obtained solutions were expressed as series of Bessel functions of an imaginary argument. From the resulting set, the solutions bounded on the entire plane were distinguished, and the dimension of the real linear space of these solutions, which equals m , was determined.

The influence of the number of phase quantization levels L on the capacity C_M,L of a communication channel with additive white Gaussian noise (AWGN) was studied in a communication system using QPSK (4-PSK).

This article explores elements of the theory of a new scientific field – associative protection of information during storage and transmission. The approach under study is shown to enhance the level of protection and noise immunity in scene analysis.

The propagation of a pressure wave in a porous medium with a fractured porous zone was numerically investigated. The study used a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. The problem was examined in a twodimensional formulation, considering cases when a porous medium has a free surface or is unbounded. The fractured porous zone was shown to have either an ellipseor rectangle-shaped boundary. The influence of such inhomogeneities on the propagation of pressure perturbations was analyzed.

The problem of thermal stability of a cylindrical sample with nonlinear heat generation placed in a medium with the ambient temperature random walk was studied. The behavior of this system was examined depending on the parameters of the problem (heat generation intensity, random walk variance). A numerical algorithm based on averaging multiple random trajectories of the ambient temperature was proposed. A numerical method was developed for solving the heat transfer problem with the heat source and stochastic boundary which combines both explicit and implicit schemes for linearized transfer equations and the Euler–Maruyama method. The distributions of ignition characteristics and their moments were obtained. Their dependencies on the parameters of the problem were investigated.

Constitutive relations and a method for analyzing the behavior of fiberglass during longitudinal bending under the combined influence of force factors and an alkaline medium were proposed. Both natural and numerical experimental designs were outlined. A new approach to solving the problem of longitudinal bending of a fiberglass beam with initial failure was introduced, without involving geometrically nonlinear relations. This approach proved to be applicable when the resulting beam configuration is a flat curve. The results of numerical calculations were presented. In the first case, the beam with initial failure was studied using the new approach along with the finite element method (FEM). In the second case, for verification, the problem was solved in a geometrically nonlinear formulation. The results obtained showed a strong agreement.

For a nonstrictly hyperbolic mildly quasilinear biwave equation in the first quadrant, an initial-boundary value problem with the Cauchy conditions specified on the spatial half-line and the Dirichlet and Wentzell conditions applied on the time half-line was examined. The solution was constructed in an implicit analytical form as a solution of some integro-differential equations. The solvability of these equations was investigated using the parameter continuation method. For the problem under study, the uniqueness of the solution was proved, and the conditions under which its classical solution exists were established. In the case when the data were not smooth enough, a mild solution was constructed.

This study aims to solve the inverse problem for determining the heterogeneity of an object. The scattered field was measured outside its boundaries at a set of observation points. Both the radiation source and observation points were assumed to be located outside the object. The scattered field was modeled by solving the direct problem. The inverse problem was solved using a two-step method. Nonlinearities of various types were considered. When introducing the computational grid, the generalized grid method was applied. A numerical method for solving the problem was proposed and implemented. The numerical results obtained illustrate how the problem is solved for specified experimental data.

The simplest transformation model of the dynamic deformation along the length of a rod-strip consisting of two segments was constructed. The model is based on the classical geometrically linear Kirchhoff–Love model for the unfixed segment, while the fixed segment of finite length is assumed to be connected to a rigid and immovable support element through elastic interlayers. On the fixed segment, the deflections of the rod and interlayers were considered zero. For axial displacements within the thicknesses of the rod and interlayers, approximations were adopted according to S.P. Timoshenko’s shear model, subject to the conditions of continuity at the points where they connect to each other and immobility at the points where the interlayers connect to the support element. The conditions for kinematic coupling of the unfixed and fixed segments of the rod were formulated. Taking them into account and using the D’Alembert–Lagrange variational principle, the equations of motion and boundary conditions for the considered segments were derived, and the conditions for force coupling of the segments were obtained. With the help of the derived equations, exact analytical solutions of the problems of free and forced harmonic vibrations of the rod of the studied type were found. These solutions were employed in the numerical experiments to determine the natural modes and frequencies of bending vibrations, as well as the dynamic response during the resonant vibrations of the rod-strip made of a unidirectional fibrous composite based on ELUR-P carbon tape and XT-118 binder. The findings show a significant transformation of transverse shear stresses when passing through the boundary from the unfixed segment of the rod to the fixed one, as well as their pronounced localization in the region of the fixed segment near this boundary.

The problem of vibrations of plates and shells with a mass attached to the point was solved. A mathematical model was developed based on the hypothesis of nondeformable normals. The latter was used to derive a system of resolvable dynamic equations for the shell with a mass, where the unknowns are the dynamic deflection and stress function. The problem was solved numerically and analytically. In accordance with the boundary conditions, the shell deflection was expressed as double trigonometric series. The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. For time integration, the finite difference method was used.

Positive fixed points of the Hammerstein integral operators with a degenerate kernel in the space of continuous functions C [0, 1] were explored. The problem of determining the number of positive fixed points of the Hammerstein integral operator was reduced to analyzing the positive roots of polynomials with real coefficients. A model on a Cayley tree with nearestneighbor interactions and with the set [0, 1] of spin values was considered. It was proved that a unique translation-invariant Gibbs measure exists for this model.