In this article, for a specific class of conditionally well-posed integro-differential equations in a novel pair of weighted Sobolev spaces, an alternative method for constructing approximations (particularly finite-dimensional ones) to the solution of the corresponding boundary value problem is proposed, and its theoretical justification is provided for minimal differential properties of the coefficients of the equation.

Heat transfer in a vibrating cylindrical air-filled cavity, where the heat flux on the walls is defined by the Newton–Richmann law, was studied numerically. To describe the process in an axisymmetric formulation, the full system of Navier–Stokes equations with constant values of the viscosity and thermal conductivity coefficients was used. Three characteristic vibration frequencies were considered. The influence of the heat transfer coefficient on the temperature distribution in the cavity was investigated. The findings show that when the heat transfer occurs through the cavity walls, vibration can reduce the period average temperature in the central part of the cavity. For each of the considered vibration frequencies, the values of the heat transfer coefficient were determined at which the overall average temperature in the cavity increases. The influence of the heat transfer coefficient on the direction of the heat flux through the side surface of the cavity at different vibration frequencies was analyzed.

A comparative analysis of the thermal stability of 𝑀𝑔/𝑁 𝑏 diboride solid solution and pure 𝑀𝑔𝐵₂ was carried out. The specific heat capacity of these materials below the critical temperature of 𝑀𝑔𝐵₂ , which is an essential characteristic for assessing their thermal stability, was evaluated. Based on the 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 calculations of the phonon density of states for both compounds, it was demonstrated that 𝑀𝑔𝑁 𝑏𝐵₄ is characterized by a higher phonon density of states in the frequency range of 5–7.5 THz compared with 𝑀𝑔𝐵₂ . 𝑀𝑔𝑁 𝑏𝐵₄ was also found to exhibit a higher heat absorbing capacity at low temperatures. The specific heat capacity of 𝑀𝑔𝑁 𝑏𝐵₄ at low temperatures exceeds that of 𝑀𝑔𝐵₂ by 50 %, thus indicating its better thermal stability. The potential of 𝑀𝑔𝑁 𝑏𝐵₄ solid solution for practical application in superconducting wires made of 𝑀𝑔𝐵₂ was outlined.

BUG algorithms are effective strategies for local path planning in unknown environments. This article presents a practical implementation of the InsertBug algorithm using the Robot Operating System (ROS) and highlights its challenges. The algorithm relies on laser sensor and odometry data to construct a locally optimal path in an unknown terrain. Its evaluation was performed in the Gazebo 3D virtual environment, employing the TurtleBot 3 Burger robot. The evaluation spanned three types of environments: mazes, settings with simple convex and concave obstacles, and office spaces. The algorithm was assessed based on the robot’s overall traveled distance and accumulated turns in yaw rotations measured in radians. The findings demonstrate the effectiveness of the algorithm in diverse layouts. The implementation serves as a valuable resource to further advance autonomous navigation systems.

This article reviews a large body of research on the hydrodynamics of oscillatory motion of bodies, covering three different, yet closely related, classes of problems: the oscillations of solid cylindrical bodies in a still fluid, the elastic oscillations of elongated bodies in a fluid, and the propulsive motion of oscillating bodies (oscillatory propulsors). The findings available so far are summarized. Some key challenges are identified, and their potential solutions are proposed.

Vortex particle methods of computational hydrodynamics are widely employed by engineers to solve the problems of flow simulation and estimation of unsteady hydrodynamic loads acting on bodies. The main advantage of such methods is a relatively low computational cost, but their applicability is limited to subsonic incompressible single-phase non-heat-conducting flows. If high order discretization is required, the usage of direct algorithms leads to a significant increase in computational complexity and memory demand. To overcome this limitation, approximate fast algorithms of quasilinear computational complexity were developed and implemented for the most time consuming operations, such as the computation of convective velocities and the solution of the boundary integral equation. The general principles of fast algorithms were described. Their modifications for the problems mentioned above were discussed, and their efficiency was evaluated. The results obtained show that the application of fast algorithms enables a computational speedup of up to several hundred times for around a million vortex particles.

The problem of searching for an element within a dictionary was considered. Over the past decades, various approaches, including classical and quantum algorithms, have been proposed to solve it. One possible solution is the method of quantum amplitude amplification, which underpins the well-known Grover algorithm and enables a quadratic speedup in the search process.

In this article, a new approach to searching for an element w of length m in a dictionary V of size n with the use of the quantum fingerprinting function was introduced. The developed algorithm has a query complexity of O(√n) and requires O(logn+logm) qubits.

The problem of the motion of a hydro-mechanical system consisting of a viscous liquid and solid bodies, a wall and a plate, bordering it is formulated and solved. The wall undergoes a prescribed translational motion, and its boundary is permeable to the liquid. The hydro-mechanical system is subjected to time-periodic influences. The problem formulation includes the equation of the plate motion, the Navier–Stokes equation, and the conditions at the solid–liquid interfaces. New hydro mechanical effects are revealed.

The existence of contact and almost contact metric structures invariant under the group of motions on the real extension of a two-dimensional sphere with a Riemannian direct product metric was examined. The basis vector fields of the Lie algebra associated with the Lie group of motions were found. The results obtained show that invariant contact structures do not exist, but there is an almost contact metric structure, which is integrable, normal, and has a closed fundamental form, thus making it quasi-Sasakian. The Lie group of automorphisms of this structure coincides with the group of motions and has the maximum possible dimension. All linear connections were found that are invariant under the automorphism group and in which the structural tensors of the quasi-Sasakian structure are covariantly constant. Each such connection is uniquely determined by the quasi-Sasakian structure and by fixing one constant. It was established that the contact distribution of the almost contact structure is completely geodesic. Therefore, the derived connections are consistent with this distribution.

The Neumann boundary value problem for the p-Laplace equation with a low order term that does not satisfy the Bernstein–Nagumo condition was studied. The solvability of the problem in the class of radially symmetric solutions was investigated. A class of gradient nonlinearities was defined, for which the existence of a weak Sobolev radially symmetric solution that has a H¨older continuous derivative with exponent ¹ _p−1 was proved.

Anew implicit scheme for solving 3D dynamic elasticity problems was considered. To approximate the elasticity equations by spatial coordinates, a rare mesh FEM scheme based on a four-node finite element with a linear approximation of displacements within the element was employed. The finite elements are located in the centers of hexahedral cells, with each cell containing a single element. As a result, for meshes with the same element size, this scheme uses five times fewer finite elements and half as many nodes as traditional schemes utilizing four-node linear finite elements, which makes it highly efficient. The equations were approximated in time based on the implicit unconditionally stable Crank–Nicolson numerical scheme (trapezoidal rule). The applicability of the scheme was discussed, with a focus on the class of problems for which it outperforms the explicit scheme. An example of a test model problem solved using this scheme was provided.

The use of fuzzy logic in the development of game mechanics was analyzed. The important role of fuzzy logic in the video game design process, which requires a balance between creativity and attention to detail, was emphasized. The shortcomings of current prototyping tools and methods were discussed. The growing need for a system effectively incorporating expert knowledge into decision-making was highlighted.

The results of previous research on this problem show that fuzzy logic, which mimics human reasoning, can be successfully used for selecting game mechanics in the early stages of game development. Hence, it appears to be a good alternative to resource-intensive neural networks. The design of the system proposed here does not require the construction of complex algorithms, offering a relatively simple refinement of the developed approach by enabling an expansion of the scope of input data. In addition, the possibility to easily improve the expert knowledge base used ensures the refinement of information and the adaptation of the system to changing requirements.

Various applications of fuzzy logic were covered, and its potential to improve game design by supporting the selection of game mechanics using expert systems was considered.

A mathematical model for calculating the stress-strain state (SSS) of a cyclic shell with a defect in the form of a local non-through depression on the inner surface was constructed using a three dimensional spline version of the finite element method (FEM). An approach was proposed that combines the parameterization of the region under consideration and the cubic approximation of the target variables. The findings on the stress distribution in the defective region were presented for different locations of the depression zone. The patterns of change in the SSS of a cyclic shell with variations in the geometric parameters of the depression were established.