Cyber-physical systems (CPS) integrate computing, networking and physical dynamics and are characterized by a high degree of heterogeneity and parallelism, with high dimensionality and complexity, including a variety of decision-making capabilities and control logic. Modeling and simulation of cyber-physical systems are considered important stages in the design, development and operation of CPS and their components. The main aim of the paper is to describe and analyze the evolution of agent based approach in the field of CPS and to define the basic requirements to the agent based systems regarding CPS. Based on O-MaSE methodology a software process model for agent based development of CPS is proposed. The approach includes the creation of 10 models reflecting various aspects and functionality of the CPS. The suggested approach is analyzed in terms of meeting the basic requirements for agent-based systems, imposed by the peculiarities of cyber-physical systems and fundamental requirements for their introducing, such as flexibility/changeability, reliability, reconfigurability, adaptability/agility and dependability.
Journal section: THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
A study of convergence of ξ approximations transform by region depended given as determined by () Functions on entire complex planepg(s) 104-105
In this study, the convergence behavior of the ξ approximants transform given as determined by () functions for the exponential operators is investigated on the entire complex plain. An algorithm is developed to observe how to transform a initial region on the complex plane defined by ξ approximants.
The electron beam technological processes like electron beam welding, electron beam additive technologies, etc. depend strongly on the characteristics of the electron beam, generated by the electron gun. In this work the estimation of the 3D radial current density distribution using training, testing and validation of different artificial neural networks is considered. The model estimation is based on experimental measurements of the electron beam current distribution in three cross-sections of the beam at different distances from the magnetic lens of the electron gun. The estimated neural models with different structures are compared. Graphical user interface for the evaluation of the radial electron beam distribution in any cross-sections of the beam is developed.
The problem of convective stability in a medium containing settling heavy solid particles are discussed. A study is made of the stability of steady convective flow of a medium containing an additive between vertical plates heated to different temperatures. It is shown that the presence of settling solid particles has a significant stabilizing effect on convective stability.
This article discusses the problems of teaching non-standard tasks at school. Currently, one of the main tasks of secondary schools is to identify creative thinking abilities of students and solve problems of their development. The report was identified as the main tool for developing students ‘ mental and thinking abilities. Problem solving is the most productive form of learning mathematics, and this process should be a necessary component of all extracurricular activities conducted in mathematics. Problems at the mathematical Olympiad are non-standard problems. Olympic tasks will usually help you learn a lot, find independent non-standard methods of solving problems. The high school curriculum provides for the use of the definition of inequality, proving using known inequalities, using the relationship between the arithmetic mean and geometric mean of positive numbers, and proving them using methods other than reverse-trip methods
Comparative analysis of pseudorandom sequences using modified Barker codes and M – sequences of the same lengthpg(s) 45-50
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  and graphs of changes in the rotation angles of a cylindrical body were constructed for various cases.