International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The paper discusses the correlation properties of pseudo-random sequences (PRS) used to form noise-like signals in high-speed data transmission systems. The most frequently used pseudo-random sequences are considered: modified Barker codes, M-sequences having the same length. In the Matlab medium a comparative analysis of the correlation properties of the PRS is done. It is shown, that modified Barker codes have unsatisfactory correlation properties. It is proved, that the use of M – sequences allows to obtain signals with the required correlation properties for communication systems, including systems with code division of channels. The directions of further research are determined.

The present paper describes the fact that revised and pedagogically justifiable implementation of CAS systems (e.g. Matlab system) is a great contribution to teaching higher mathematics. It brings practical applications to mathematics teaching and thus enhances motivation and students’ interest in the discussed topic. The Computer Algebra System, popularly known as CAS, is a modern computing technology that provides great learning and teaching opportunities to both students as well as instructors. MATLAB is one of the most popular CAS programs that is widely used in mathematics classrooms especially at the university level. As more and more universities are adopting its use in education, it is necessary to study and analyze how the software could be used in teaching and learning of mathematics. It has been shown to be a technology that could be used for developing mathematical thinking, concepts and skills, and a source of motivating students for learning mathematics. It is also a very useful tool in demonstrating connections in various underlying mathematical concepts in the teaching and learning processes.

This paper describes a finite volume contact algorithm with surface smoothing using the Nagata patch interpolation. Nagata interpolation is derived from existing discretisation, using the mesh points positions and their calculated normal vectors. The contact between a deformable and a rigid body is analysed, whereas the rigid body is described with Nagata patch interpolation. Such approach allows a more accurate evaluation of the resulting contact stresses and forces

In this paper a method of construction of a generator for address sequences with given values of switching activity, based on the Idea of Antonov and Saleev and with use of Toeplitz and Hankel matrices, was proposed. The broad possibilities of this approach and the limitations associated with conflicting requirements for the values of the rows of the matrix and their linear independence are shown. Examples of the formation of standard address sequences used for self-testing of storage devices are described

This paper examines the possibility to use neural networks for approximately solving the MiniSum problem, a classic facility location problem. For this we first create a set of realistic MiniSum instances, based on the Bulgarian road network. Two standard neural network approaches – Hopfield networks and Boltzmann machines, are then applied to the instances. Since the quality of solutions is not satisfactory, the reasons for the poor performance are discussed. An improved neural network approach is then proposed. This approach has excellent performance on the MiniSum instances. It always finds solutions just several percent worse than the optimum, and is often able to find the exact optimum.

In this paper we introduce, analyze and apply persistent homology, one of the main algorithms of TDA, on some real data sets from the bio-medical field. Topological data analysis (TDA) is a field which is a synergy between mathematics, data science and computer science. The main goal of TDA is studying the shape of data using topological techniques. TDA proposes new algorithms that deal with these problems based on tools or concepts from algebraic topology and pure mathematics. We analyze the results and give a topological characterization of the dataset and propose to use them in future work.

The problems of continuous motion of a cylindrical body with a displaced center of mass along vibrating horizontal and inclined surfaces are considered.
The analytical solutions of the motion equations were obtained by the method of partial discretization of nonlinear differential equations [1] and graphs of changes in the rotation angles of a cylindrical body were constructed for various cases.

In this paper we analyze and apply one of the main algorithms of TDA (Topological Data Analysis), Mapper, on some real data sets. We use Mapper for visualization of a data sets, and we tend to get some insights if some key characteristics of the data are captured by the visualization and how they are connected with human perception of the data. Also, we will discuss if the visualization can make progress in further work.

The results of a solution of the problem of the stability of steady convective flow in a vertical layer with thermally insulated boundaries and a comparison with the opposite limiting case of ideally thermally conducting boundaries are presented. Study is made of the effect of thermal properties of boundaries on the convective flow stability in a closed vertical layer. The numerical solution of a spectral amplitude problem for normal disturbance is presented for thermally insulated boundaries. The critical Grashof numbers are determined. A comparison with the case of ideal conducting walls shows that there is a slight effect of thermal properties on the instability criterion.

The work is devoted to the mathematical problems of the analysis of asymptotic time behavior of solutions of the nonstationary Boltzmann equation. The proof of the fundamental difference between such behavior for the cases of “hard” and “soft” (in the sense of H. Grad) potentials of intermolecular interaction is given

The application of a rigorous CFD method and an all-encompassing algorithmic performance optimization method can make possible the CFD simulation of the extremely large-scale problems, which allows simulation of either larger systems, or more detailed simulation of systems that are already simulated. The CFD code has to show both efficient one-node performance and excellent parallel scaling. The record breaking performance on one node has been achieved before with application of the LRnLA algorithm and making use of many core parallelism as well as the vectorization. In the current work, the algorithm is extended for many-node parallelism. The algorithms is characterized by high parallelization degree, small number of node communication events, and may be concisely described and programmed on the base of the previously implemented one-node solution, which is a rare feature among the algorithms with temporal blocking in all four of the spatial and time dimensions.

In this paper we are consider a problem of nonlinear heat conduction with double nonlinearity under action of a strong absorption. For which an exact analytical solution is found, analysis of which makes it possible to reveal a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects are established: an inertial effect of a finite velocity of propagation of thermal disturbances, spatial heat localization and finite time effect i.e. existence of a thermal structure in a medium with strong absorption.