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The Bulletin of the Adyghe State University, the series “Natural-Mathematical and Technical Sciences” |
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#3 / 2021MathematicsShumafov M.M.Second-order stochastic differential equations: stability, dissipativity, periodicity. V. – A survey
This paper is a continuation of the previous papers and presents the fifth final part of the author’s work. The paper surveys the results concerning stability, dissipativity and periodicity properties of the second-order stochastic differential equations and systems. Some new de-velopments in the theory of stability of stochastic differential equations based on the use of the modifying Lyapunov’s second method are presented. The work consists of five parts. In the first two parts we have introduced mathematical preliminaries from probability theory and stochastic processes including the construction of Ito and Stratonovich stochastic integrals. In the third part, some facts from the theory of stochastic differential equations are presented. The existence and uniqueness theorems for stochastic systems are formulated. In the fourth part, definitions are provided and basic facts from the theory of stability of stochastic differential equations are given. The basic general Lyapunov-like theorems on stochastic stability, dissipativity and periodicity for solutions of systems considered are formulated in the terms of the existence of Lyapunov functions. Here in the present fifth part, effective sufficient conditions of stability in probability, exponential stability in mean square for the second-order stochastic differential equations and systems are given. Also we give sufficient conditions for dissipativity and periodicity of random processes defined by nonlinear second-order differential equations with random right-hand sides. As an example the harmonic oscillator disturbed by white noise is considered. In the final section of the present paper, we briefly review some new publications related to stochastic stability that characterizes the state - of - the - art of the theory.
The acyclicity of a quadratic differential system We now give a brief overview of some of the main publications devoted to the study of the question of limit cycles and separatrices of quadratic differential systems. In this paper, we con-sider the existence of closed trajectories for a certain class of autonomous quadratic systems on the plane. The proof is based on the application of the theory of straight line isoclines, Dulac and Bendixon criteria of the qualitative theory of differential equations. The proposed proof covers the results of the well-known work of L.A. Cherkas and L.S. Zhilevich.
Technical SciencesSimankov1 V.S., Buchatskiy P.Yu.Methodological foundations of innovative solutions in renewable energy engineering
We deal with the approach that makes it possible to investigate the energy system with renewable energy sources (RES) by methods of system analysis. We propose to use multi-criterion optimization, analysis and decision-making techniques in the development of a system of input and potential models for renewable energy sources that took into account the characteristics of energy conversion technology.
Methods for building a high-performance fault-tolerant distributed database for the task of perimeter security
The paper discusses the methods for constructing a high-performance fault-tolerant distributed database for the perimeter security problem. The architecture of the fault tolerance subsystem, the architecture of the backup subsystem, and approaches to achieving the specified key indica-tors are described. The study of the system performance was carried out, the values of the key performance indicators achieved by the fault tolerance subsystem were determined.
Software and hardware subsystems of intelligent situational center
The paper discusses hardware and software for creating a unified software and hardware platform for a situation center as a heterogeneous environment – an environment whose computing nodes are controlled by incompatible software that supports the possibility of organizing interaction. The method of organizing the interaction of the subsystems of the situation center through a universal list of requests is also considered.
On the question of a method for researching user requirements for software
The User Story methods (user stories) increasingly are used as the basis of requirements design artifacts in software development. In practice, it is proved that the User Story method is more effective for describing the main goals of the system. But continuous management of software operation can be particularly time-consuming and error-prone, especially when evaluating the quality or volume of user stories and observing the overall picture of the system. On the other hand, these models were recognized as effective tools for communication and goal analysis. Within the framework of this work, methods for identifying and presenting requirements for software development are considered and analyzed. In the article, we propose a generative approach for creating reliability diagrams based on automated analysis of user stories. Stories are converted into diagrams, which allow requirements developers and users to check the basic concepts and functional stages underlying the stories, and detect distorted or redundant stories. Such models also open the door for automated systematic analysis.
Model of the functioning of the active security system of a social network user account
The analysis of the development of neural network algorithms in social networks is carried out. The algorithm of functioning of the system for ensuring the active security of the user account is presented. The software has been developed to assess the reliability and propose recommendations for protecting a user's account on the «ÂÊîíòàêòå» (“In Contact”) social network.
Cybersecurity and information security: similarities and differences
The concepts of “cybersecurity” and “information security” are analyzed, the differences between them are explained, their evolution is described, important areas of overlap are considered, and various theoretical justifications – concepts and possible uses – are given. Assessing the current state of these concepts and matching them with world trends, the main directions of the necessary changes are determined in the terms considered.
Overview of topical issues in basic spam filtering methods and analysis of their effectiveness
An analysis of the main problems of filtering mail spam, modern methods of filtering unwanted letters and methods of bypassing security systems is presented. The concept of “legitimate spam” is being introduced – a new problem that email users face. Methods of text presentation are considered: bag-of-words and Embedding-space, as well as classification methods: artificial neural networks, the method of reference vectors, naive Bayesian classifier. The work identifies effective methods based on text analysis, for solving the problems of detecting various types of spam: a typical (known to system), compiled using methods of bypassing spam detection systems, and legitimate.
On International Scientific Conferences
Information on international scientific conferences of PUTS-2021 (On Management Problems in Technical Systems, St. Petersburg) and “Remote Educational Technologies” (Yalta) is presented, in which co-employees of the Department of Automated Information Processing and Management Systems of Adyghe State University participated.
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