517.925We study the problem of the existence of periodic solutions of two-dimensional linear inhomogeneous periodic systems of differential equations for which the corresponding homogeneous system is Hamiltonian. We propose a new numerical-analytic algorithm for the investigation of the problem of the existence of periodic solutions of two-dimensional nonlinear differential systems with Hamiltonian linear part and their construction. The results obtained are generalized to systems of higher orders.The analysis of various processes in mechanics, physics, biology, celestial mechanics, and other branches of science and engineering requires the investigation of periodic solutions of differential equations of various types and their systems. In particular, there are many works devoted to the problem of the existence of periodic solutions and their construction, and numerous methods for their study have been developed [1 -4]. Among them, one should especially mention the numerical-analytic method of successive periodic approximations [5, 6], the idea of which was later extended to a broad class of problems [7 -10].The present work continues the investigations in this direction. We study periodic solutions of linear inhomogeneous systems and develop a new algorithm for the investigation of periodic solutions of systems of second-order differential equations with Hamiltonian linear part on the basis of the Samoilenko numerical-analytic method. Linear Two-Dimensional SystemsConsider a linear inhomogeneous two-dimensional ω-periodic systemfor which the corresponding homogeneous system is Hamiltonian, i.e.,here, x, f ∈ R 2 , t ∈ R, and f ( t ) and p ( t ) are continuous ω-periodic functions.It is known [11, p. 77] that a solution of system (1) that passes through a point ξ = ( ξ 1 , ξ 2 ) at t = 0 has the form

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The new numerical-analytic method for investigation of the nonlinear periodical impulsive systems of differential equations is substantiated. The problems of existing and approximate construction of the solutions are studied and the error estimates are obtained.

Convenient and accurate verification of the user of a car sharing system is one of the key components of the successful functioning of the car sharing system as a whole. The machine learning-based KYC (Know your customer) process algorithm makes it possible to improve the accuracy of customer data validation and verification. This makes it possible to eliminate possible losses and reputational losses of the company in case of unforeseen situations while using the client's car sharing services. The object of this study is to find a solution to the problem of user verification in a car sharing system based on the KYC process using deep learning methods with a combination of OCR (Optical Character Recognition) methods. The statement of the user verification problem in the car sharing system was formalized and the key parameters for the KYC process have been determined. The algorithm of the KYC process was constructed. The algorithm includes six successive stages: separating a face in the photograph, comparing faces, checking documents and their validity period, establishing and recognizing ROI (region of interest), formulating a verification decision. To separate the face in the client's photograph and compare faces, methods based on deep learning, as well as the quick HoG method (Histogram of oriented gradients), were considered and implemented. Verification of these methods on a test dataset, which includes images of documents of two thousand clients, showed that the recognition accuracy was 91 % according to Jaccard's metric. The average time of face separation using the HoG method was 0.2 seconds and when using trained models – 3.3 seconds. Using a combination of ROI and ORC separation methods makes it possible to significantly improve the accuracy of verification. The proposed client verification algorithm is implemented as an API on an ML server and integrated into the car sharing system.

Research on the development of methods for identifying signs of hidden manipulation (destructive information and psychological impact) in text messages that are published on Internet sites and distributed among users of social networks is relevant. One of the main problems in the development of these methods is the difficulty of formalizing the process of identifying signs of manipulation in text messages of social network agents. To do this, based on morphological synthesis, it is necessary to determine relevant indicators for analyzing text messages and criteria for making a decision about the presence of signs of manipulation in text messages. Based on morphological synthesis, a method for determining manipulation indicators in text messages was developed, taking into account the achievements of modern technologies of intelligent content analysis of text messages, machine learning methods, fuzzy logic and computational linguistics, which made it possible to reasonably determine a group of indicators for evaluating text messages for signs of manipulation. The stages of the method include evaluating the text message at the level of perception by the indicator of text readability, at the phonetic level by the indicator of emotional impact on the subconscious, at the graphic level by the indicator of text marking intensity, and calculating the integral indicator for making a decision about the presence of manipulation in the text message. Based on the proposed method, specialized software was developed that provided 13 % greater accuracy in evaluating messages for manipulative impact compared to the known method of expert evaluations, which reduced the influence of the subjective factor on the evaluation result