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The Bulletin of the Adyghe State University, the series “Natural-Mathematical and Technical Sciences” |
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#2 / 2021MathematicsShumafov M.M.Second-order stochastic differential equations: stability, dissipativity, periodicity. IV. – A survey
This paper is a continuation of the previous papers and presents the fourth part of the author’s work. The paper reviews results concerning qualitative properties of second-order stochastic differential equations and systems. In the first part we gave a short overview on stability of solutions of the second-order stochastic differential equations and systems by Lyapunov functions techniques and introduced some mathematical preliminaries from probability theory and stochastic processes. In the second part the construction of Ito’s and Stratonovich’s stochastic integrals is given. In the third part, analog of the chain rule for stochastic differentials (Ito’s formula) is presented. The stochastic differential equations in the sense of Ito and in the sense of Stratonovich are introduced. The existence and uniqueness theorem for solutions of stochastic differential equations is formulated. In the present fourth part of the work basic facts from the theory of stability of stochastic differential equations are briefly given. The basic definitions of stability in different senses of stochastic differential systems are presented, the basic general theorems on stability are formulated in terms of the existence of Lyapunov functions, which are stochastic analogs of the classical Lyapunov’s theorems on stability. The concept of stochastic dissipative systems is given. A theorem is formulated which gives conditions for existence of periodic and stationary solutions in terms of auxiliary functions for differential equations with a random periodic in time right-hand side, which is a periodic or stationary process.
Planar vector fields with central symmetry: roughness and first degree of non-roughness
We consider the space of smooth vector fields defined in a closed domain D on the plane, invariant under the central symmetry and transversal to the boundary D. The set of vector fields that are rough with respect to this space is described; it is shown that it is open and everywhere dense. In the set of all non-rough vector fields, an open everywhere dense subset consisting of vector fields of the first degree of non-roughness is distinguished.
On acyclicity of quadratic system with two non-rough foci
It is proved that a system of differential equations, the right-hand sides of which are second-order polynomials, has no limit cycles if it has only two equilibrium states in the bounded part of the phase plane, and they are the equilibrium states of the second group.
Technical SciencesCherkasov A.N., Sivenko A.V.Development of a model for ensuring the security of a social network account based on a neural network algorithm
An analysis is made of the current statistics of hacking accounts in social networks. The ar-chitecture of a neural network has been built, which makes it possible to classify user accounts into “safe” and “at risk”. Software has been developed to assess the reliability of a user's account on the “VKontakte” social network.
Development and research of software and methods for constructing quantum algorithms for solving NP class problems
In modern science and technology, there is a constant need to solve such strategically important tasks as predicting the weather and calculating climatic changes, creating cancer drugs, processing signals from the Universe to search for extraterrestrial civilizations, processing symbolic information, cryptanalysis, and anticipatory calculation of the trajectories of moving air and space objects, etc. The practical implementation of the listed tasks on modern, even supercomputer systems requires an unacceptably long period of time or is impossible at all. The scientific novelty of this direction is expressed in the development of a methodology for constructing a modular modeling system of quantum computing with an open architecture, as well as a modeling system for executing quantum algorithms. The aim of the work is to consider techniques for modeling quantum computations and implementing algorithms for solving NP class problems.
Data mining in the construction of individual educational trajectories
Currently, the changing model of education requires the personalization of training. The con-sequence of this trend is the need for individual educational trajectories that contribute to the acquisition of competencies other than the main training track. The work presents approaches to the construction of individual educational trajectories of learning, the possibility of using data mining in the construction of individual educational trajectories.
Organization of secure remote access for an employee of a commercial company working outside the office
The article discusses the methods and features of organizing remote access by employees of a commercial company who perform their official duties while out of the office, which is relevant due to the need for isolation in a pandemic. The use of public data transmission channels re-quires the use of effective information security systems. Based on the consideration of data transmission threats inherent in remote access and ways to neutralize them, this paper suggests options for replacing foreign software used in Russian commercial companies with similar domestic functions in terms of the import substitution trend.
Photogrammetric measurement system generating algorithm by primary input data
the process of automating the solution of applied measurement tasks, including on the basis of photogrammetric methods, there is a problem of compliance of the measurement system with the object and measurement conditions. In order for the measuring system to assess in advance the possibility of obtaining reliable results, as well as to best adapt to the conditions of measurement, it is necessary to have specialized algorithms and models. In general, such models are aimed at qualified technicians with the necessary knowledge in the field of information technology. A feature of the application of photogrammetric measurement systems in the forestry and metallurgical industry is the low qualification of users in the field of information technology, which is determined by the nature of the work performed and the conditions of attraction. This factor does not solve the problem of adjusting the system by traditional methods in which the user controls the configuration process. In this regard, the article proposes a model and algorithm for forming a measuring system from primary input data, in which the system itself controls the adjustment process.
Development of the malware detection model based on an analysis of API request sequences
An analysis of the relevance of existing works on the study of neural network algorithms for detecting malicious software made it possible to determine the optimal approach to solving the problem of virus recognition. A dataset has been generated containing sequences of system re-quests for 2083 executable files. Training the recurrent neural network model on the generated dataset made it possible to obtain a classifier with a malware recognition accuracy of 97.6%. The key aspect of the significance of the work lies in the practical orientation of the research – the resulting model will be applied as a component of a system for complex analysis of malicious software.
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