Usually, for the numerical solution of elastoplastic boundary value problems based on deformation theory of plasticity is used an elastic solutions method proposed by A.A. Ilyushin. In literatures the method of elastic solutions relative to boundary value problems of the theory of plastic flow is called the method of initial stresses or the method of initial deformations. In this paper, to solve the boundary value problems of the deformation theory of plasticity of transversally isotropic bodies, it is used relatively “simple” finite-difference method considered in combination with the iterative method, that is, the elastic solution method. The essence of the method is to construct symmetric finite-difference equations, separately for internal and boundary nodes of the area under consideration, and to solve them with respect to “central” or boundary node displacements and the organization of the iterative process. Elastoplastic problems are solved numerically for isotropic and transversely isotropic parallelepipeds under various boundary and boundary conditions. The obtained results are consistent with the known solutions, which shows the validity of the applied methodology. It is explored the spreading of the zone of plasticity and the effect of anisotropy on their distribution.

Keywords: deformation theory, elastic solutions method, plasticity, displacements, strain, stress, numerical method, iterative process, elastoplastic boundary value problems, transversely isotropic material.

Abduvali A. Khaldjigitov (Samarkand, Uzbekistan) – Dr. Habil. in Physics and Mathematics, Professor, Director of Samarkand branch of Tashkent University of Information Technologies (140100, Samarkand, Shohruh Mirzo st., 47а, e-mail: akhald@mail.ru).

Uchkunbek E. Adambaev (Tashkent, Uzbekistan) – Ph.D. in Physics and Mathematics, Doctoral Student, National University of Uzbekistan (100174, Tashkent, Universitet st., 4, e-mail: a_uchqun@mail.ru).

Mumin R. Babadjanov (Tashkent, Uzbekistan) – Doctoral student (Ph.D.), Tashkent University of Information Technologies (100200, Tashkent, Amir Temur st., 108, e-mail: mum1975@mail.ru).

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The problem of control of indicators of quality of oil products on technological installations is considered. The review of methods of quality control of oil products is carried out, models for forecasting of temperatures of the beginning and the end of boiling of light oil products on oil refineries are considered. Mathematical models of indicators of quality of light oil products (temperatures of the beginning and the end of boiling) in the form of autoregressive models with external factors are received. The factors are the measured technological parameters of the refinery: temperature, flow, pressure. Models of such a structure can be used to predict the quality of light petroleum products in oil refineries. The application of clustering methods for the analysis of the range and production of petroleum products in the Federal districts is proposed. Hierarchical and iterative methods of cluster analysis are briefly described. An example of the application of cluster analysis methods for the evaluation of production and assortment is given. The article studies the task of monitoring the quality of petroleum products at process units. Review of controlling methods quality of mineral oil has been performed, models for forecast temperatures of starting and ending boiling of light oil products at refineries have been considered. Mathematical models of indicators quality of light oil products (temperatures of starting and ending boiling) in the form of autoregressive models with external factors have been obtained. Factors are measured technological parameters of oil refinery including: temperature, consumption, pressure. Models of a similar structure can be applied to forecasting quality indicators of light oil product at refineries. The application of clustering methods have been proposed for analyzing the range and production of petroleum products by federal districts. Iterative and hierarchical cluster analysis methods are briefly described. An example of application of cluster analysis methods to assess the production and range of petroleum products in federal districts over 2 years is given. Research results have been conducted using the MATLAB software package are presented. The obtained results can be used in the analysis of the range of petroleum products of primary and destructive refining within large territorial units. The possibility of forecasting the production of petroleum products using multiplicative models has been considered. Models with different seasonal components and trend types have been proposed. The stages of building a mathematical model have been given. According to statistical data on the development of motor gasoline over 5 years, mathematical models of a time series have been built using the example of the Russian Federation. The quality of modeling has been assessed using the obtained models according to the average relative error. According to the obtained model of production of automobile gasoline, a post-forecast has been built with a forecasting horizon of 1 year. The average relative error of post-prognosis of the Russian Federation does not exceed 5 %, in federal districts – 12 %. Models can be used to predict the production of light petroleum products in the federal districts of the Russian Federation.

Keywords: petroleum product, autoregressive model, cluster analysis, production, time series, seasonality index, trend, quality indicators.

Andrey V. Zatonskiy (Berezniki, Russian Federation) – Dr. Habil in Engineering, Professor, Department of Automation of Technological Processes, Berezniki branch of Perm National Research Polytechnic University (618404, Perm region, Berezniki, Telman st., 7, e-mail: anaserg2008@mail.ru).

Larisa G. Tugashova (Almetyevsk, Russian Federation) – Senior Lecturer, Department of Information Technologies and Automation Systems, Almetyevsk State Oil Institute (423458, Respublica Тatarstan, Almetyevsk, Lenin st., 2, e-mail: tugashowa.agni@yandex.ru).

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3. Tugashova L.G. Prognozirovanie pokazatelei kachestva nefteproduktov na ustanovkakh pervichnoi pererabotki nefti [Forecasting of indicators of quality petroleum products for the installation of primary oil processing]. Uchenye zapiski Al'met'evskogo gosudarstvennogo neftianogo instituta, 2015, vol. 14, pp. 99-103.

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An physicomechanical properties experimental study of the modern antifriction materials number was performed as part of the work. The 6 polymers and composites based on them having the greatest prospects for use as antifrictional coatings and interlayers in contact nodes are selected. The materials showed a nonlinear deformation behavior model in experimental study of samples. Therefore, the deformation theory of elastic-plasticity for the active loading case is chosen to describe the material behavior model in the framework of the first approximation. A numerical model of deformation of cylindrical samples under constrained compressionan experiment has been constructed. The optimal finite element mesh with a gradient decrease in the element size to the contact area of the cylindrical samples with the press plates has been selected. As part of the numerical experiments series, it was established: samples deformations from modern antifriction composite materials by 25–30 % more than other polymers considered, with one level of contact parameters; the modulus of the maximum contact tangential stress of all the materials examined is on average 25 times lower than the contact pressure.

Keywords: antifriction polymers, material properties, experiment, material behavior model, elastic-plasticity, modeling, numerical experiment.

Anatoliy A. Adamov (Perm, Russian Federation) – Dr. Habil. in Physics and Mathematics, Senior Researcher of the Institute of Continuum Mechanics, Ural Branch of RAS (614990, Perm, Academician Korolev st., 1, e-mail: adamov.aa@ya.ru).

Anna А. Kamenskih (Perm, Russian Federation) – Ph.D. in Engineering, Associate Professor, Department of Computational Mathematics, Mechanics and Biomechanics, Perm National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, e-mail: anna_kamenskih@mail.ru).

Yuriy O. Nosov (Perm, Russian Federation) – Master Student, Department of Computational Mathematics, Mechanics and Biomechanics, Perm National
Research Polytechnic University (614990, Perm, Komsomolsky av., 29, e-mail: ura.4132@yandex.ru).

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This article describes a method for applying an encoded digital steganographic watermark to a digital image and its subsequent extraction using Haar wavelets. The method of applying a digital steganographic watermark by key, and highlighting this sign with a key, is considered. The relevance of this method of applying and highlighting a digital steganographic watermark is considered. A few words describe the method of splitting a signal into sub-signals using the Haar algorithm and how it is applicable in the context of digital images. The results of checking the application of a digital watermark for resistance to various transformations are presented, such as: blurring with a 3×3, 5×5 core, jpeg compression with a compression ratio of 50 and 70 %, deleting the 1 LSB, 2 and 4 LSBs. Corresponding images are presented that illustrate the results of tests for resistance to conversion of a digital steganographic watermark. A small, illustrative and easy to implement example of applying a digital steganographic watermark, as well as its extraction using a previously created key using simple coding, which consists in the fact that the columns of pixels of the original image are shifted by a certain number of positions, is presented. Also, the article provides a brief description of the LSB algorithm and considers the main advantages and disadvantages of the algorithm developed and presented in this article with the standard LSB algorithm. In conclusion, the corresponding conclusions were drawn about the applicability of the developed algorithm, about its shortcomings and advantages, described in this article.

Keywords: Haar transform, steganography watermarks, digital watermarks, steganography algorithms, coding, Internet.

Elena L. Krotova (Perm, Russian Federation) – Ph.D. in Physics and Ma­thematics, Associate Professor, Department of the Higher Mathematics, Perm
National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, Russian Federation, e-mail: lenkakrotova@yandex.ru).

Andrey V. Chekmenev (Perm, Russian Federation) – Student, Electrical engineering faculty, Perm National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, Russian Federation, e-mail: spiritofice@yandex.ru).

Aleksandr O. Bolgov (Perm, Russian Federation) – Student, Electrical engineering faculty, Perm National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, Russian Federation, e-mail: aleksynderbolgov@gmail.com).

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This article describes the main problems of natural language text analysis of user requests in the technical support department at the enterprise. The aims and objectives are defined and set, the relevance of this research is substantiated. The analysis of existing software products is conducted, its advantages and disadvantages are identified. The complex method of semantic analysis of the natural language text and formation of natural language knowledge bases with the use of a morphological Russian language analyzer is proposed.

A software that implements such features as importing data from the existing system; keyword searching by table fields for learning; keywords, negative words and stop-words selecting; building a links-tree between keywords and requests for identifying problematic requests; adding problems and areas of concern with keywords gridded for its further analysis by comparing the number of requests for different periods of time and the opportunity of sending the results to those responsible for the areas, and obtaining data on completed requests through the formation of requests in terms of implementers, problems and areas is developed.

Keywords: data mining, text mining, mystem, suffix tree clustering, text analyses, helpdesk.

Yulia I. Volodina (Berezniki, Russian Federation) – Ph.D. in Engineering, Associate Professor, Department of Automation of Technological Processes, Berezniki branch of Perm National Research Polytechnic University (618404, Berezniki, Telmana st., 7, e-mail: julia_volodina@mail.ru).

Marsel Ya. Zekirjaev (Berezniki, Russian Federation) – Master Student, Berezniki branch of Perm National Research Polytechnic University (618404, Berezniki, Telmana st., 7, e-mail: atp@bf.pstu.ru).

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We propose a mathematical model of the labor market situation of the enterprise, which is a General finite-dimensional case of a system of nonlinear differential equations. A technique is found to represent its exact analytical solution in the form of quadratures. The obtained results are applied to the study of a mathematical model suitable for describing and predicting the labor market conditions of an enterprise consisting of several structural units.

Keywords: industrial companies, personnel management, mathematical model of labor market conditions. system of nonlinear differential equations, integrability in quadratures.

Daniil L. Gorbunov (Perm, Russian Federation) – Ph.D. Student, Department of Computational Mathematics, Mechanics and Biomechanics, Perm National Research Polytechnic University (614990, 29, Komsomolsky av., Perm, e-mail: call-of-monolit@yandex.ru).

Sergey A. Fedoseev (Perm, Russian Federation) – Dr. Habil. in Engineering, Professor, Department of Computational Mathematics, Mechanics and Biomechanics, Perm National Research Polytechnic University (614990, 29, Komsomolsky av., Perm, e-mail: fsa@gelicon.biz).

1. Gorbunov D.L. Modeling of a closed mono-branch labor market conditions. Perm. University Herald.Economy, 2018, vol. 13, no.3. pp. 357 – 371. doi: 10.17072/1994-9960-2018-3-357-371

2. Gorbunov D.L. Ob odnoj sisteme nelinejnyh differencialnyh uravnenij, integriruemoj v kvadraturah [On a system of nonlinear differential equations integrable in quadratures]. Applied Mathematics and Control Sciences, 2018, no. 2, pp. 30-39, DOI: 10.15593/2499-9873/2018.2.02

3. Demidovich B.P. Lekcii po matematicheskoj teorii ustojchivosti [Lectures on the mathematical theory of stability]. Moscow, Izdatel'stvo Moskovskogo gosudarstvennogo universiteta, 1998, 480 p.

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The article investigates the combinatorial problem of the formation of coordinated work schedules, ensuring the continuous loading of the allocated labor resources for the construction of a group of wells. A parametric mathematical model of continuous scheduling, taking into account a number of restrictions on the organization of the well construction process, is proposed. The model is supplemented with a simple formula for calculating the time characteristics of the well construction depending on the drilling conditions and the drilling crew qualification. The universal nature of the basic model of continuous scheduling allows you to easily transform the model for many practical applications. A multi-criteria algorithm for finding the best planning options based on the methods of dynamic programming and aggregation of the initial planning task taking into account the flow rate of wells under construction is developed. For the selection of alternative solutions, a system of performance indicators and a number of criteria are proposed, taking into account not only the construction procedure and routes of drilling equipment, but also important economic factors, including the time risks of performing planned tasks. The novelty of the work lies in the fact that instead of the "manual" approach to the preparation of a single suitable calendar plan, a methodology for solving calendar planning problems is proposed, based on the development of adequate combinatorial search algorithms.

Keywords: continuous scheduling, well construction, combinatorial search, dynamic programming, aggregation, multi-alternative solutions, optimization of resource allocation.

Georgiy N. Kalanov (Moscow, Russian Federation) – Dr. Habil. in Engineering, Professor, Chief researcher, V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences (117997, Moscow, Profsoyuznaya st., 65, e-mail: kalyanov@mail.ru).

Nikolay N. Titov (Moscow, Russian Federation) – Ph.D. in Engineering, Executive director, LTD “NVP MODEM” (121108, Moscow, 29, Mozhaiskoe av., e-mail: nikoltit@yandex.ru).

Victor N. Shibeko (Gomel, Republic of Belarus) – Senior Lecturer, Department “Informatics”, Sukhoi State Technical University of Gomel (246746, Republic of Belarus, Gomel, Octyabrya av., 48, e-mail: svn20070809@gmail.com).

1. Kalyanov G.N., Titov N.N., Shibeko V.N. The search for effective solutions to the continuous task scheduling. Information technology and computer systems, 2018, no. 1, pp. 85-98.

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6. Anichkin A.S., Semenov V.A. Object-oriented framework for the software implementation of the application of the scheduling theory. The proceedings of ISP RAS, 2017, vol. 29, iss. 3, pp. 247-296, DOI: 10.15514/ISPRAS-2017-29(3)-14

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The problem of description of attainability sets is considered as applied to a control problem for an economic mathematical model with respect to a family of on-target functionals under some constraints according to control actions. The functionals are given in a general form covering a great many widely used cases. Dynamics of the system under control is governed by equations connecting state variables of continuous and discrete times with taking into account aftereffects. Some constructions and algorithms are proposed which allow to obtain external polyhedral estimates of the attainability sets.

Keywords: economic mathematical models, control problems, hybrid systems with aftereffect, on-target functional, attainability sets.

Vladimir P. Maksimov (Perm, Russian Federation) – Dr. Habil. in Physics and Mathematics, Professor, Department of Information Systems and Mathematical Methods in Economics, Perm State University (614990, Perm, Bukireva st., 15, e-mail: maksimov@econ.psu.ru).

1. Nikolskii M.S. Otsenivanie mnozhestva dostizhimosti sverkhu po vklyucheniyu dlya nekotorykh nelineinykh system upravleniya [Estimation of reachable sets from above with respect to inclusion for some nonlinear control systems]. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 163-170.

2. Kurzhanski A.B., Varaiya P. On ellipsoidal techniques for reachability analysis. Optimization methods and software, 2002, vol. 17, pp. 177-203.

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7. Patsko V.S., Fedotov A.A. Struktura mnozhestva dostizhimosti dlya mashiny Dubbinsa so strogo odnostoronnim povorotom [The structure of the reachable set for the Dubins car with a strictly one-sided turn]. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 171-187.

8. Gusev M.I., Osipov I.O. Asimptoticheskoe povedenie mnozhestv dostizhimosti na malykh vremennykh promezhutkakh [Asymptotic behavior of reachable sets on small time intervals]. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 86-99.

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10. Rodina L.I. Estimation of statistical characteristics of attainability sets of controllable systems. Russian Math. (Iz. VUZ), 2013, vol. 57, no. 11, pp. 17–27.

11. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Elementy sovre­mennoi teorii funktsional'no-differentsial'nykh uravnenii. Metody i prilozheniya [Elements of the Modern Theory of Functional Differential Equations: Methods and Applications]. Moscow, Institut kompjuternyh issledovanij, 2002. 384 p.

12. Maksimov V.P. On the -attainability sets of continuous discrete functional differential systems. IFAC PapersOnLine, 2018, vol. 51, no. 32, pp. 310-313.

13. Maksimov V.P. The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki, 2019, vol. 29, no. 1, pp. 40-51.

14. Maksimov V.P. K voprosu o postroenii i otsenkakh matritsy Koshi dlya system s posledeistviem [On the construction and estimates of the Cauchy matrix for systems with aftereffect]. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 153-162.

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The stability of the matrix rating and control mechanisms to the agent’s strategic behavior is investigated. The agents could to distort information about their capabilities and preferences to achieve their own purposes. It is shown that the results of complex assessment obtained using the additive-multiplicative approach of the mechanism based on the convolution matrix, the elements of which were determined using the matrix anonymous generalized mechanism, are resistant to the strategic behavior of agents, i.e. the agent's objective function, formalized as the difference between the complex estimate obtained by reporting the original convolution matrix and the complex estimate when the message is distorted, has a minimum. The task is considered on the example of the task of agreeing with the collegial management body a unified risk management policy of the organization in terms of creating a risk matrix that describes the response to the risks with all possible combinations of risk factors: the possibility (likelihood) of a risk event and consequences if it occurs (amount of risk). We consider a model example with three members of the board of directors, each of which has its own vision of the risk matrix, and shows the final risk map, which was obtained using the proposed approach.

Keywords: control mechanism, rating and control mechanism, mechanism design, game uncertainty, strategical behavior, strategy-proof, median scheme, risk-management.

Alexander O. Alekseev (Perm, Russian Federation) – Ph.D. in Economics, Associate Professor, Department of Construction engineering and materials science, Perm National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, e-mail: alekseev@cems.pstu.ru).

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3. Alekseev A.O. Kompleksnoe otsenivanie slozhnykh ob"ektov v usloviiakh neopredelennosti [Rating and control of complex objects in uncertainty cases]. Applied Mathematics and Control Sciences, 2019, no. 2, pp. 103-131.
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7. Alekseev A.O., Korgin N.A. O primenenii obobshchennykh mediannykh skhem dlia matrichnoi aktivnoi ekspertizy [About the generalized median schemes application for the matrix active examination]. Prikladnaia matematika, mekhanika i protsessy upravleniia: materialy Vserossiiskoi nauchno-tekhnicheskoi internet-konferentsii studentov i molodykh uchenykh, 30 November – 5 December 2015. Perm, Izdatel'stvo Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. 2016, pp. 170-177.
8. Alekseev A.O. Matrichnye mekhanizmy kompleksnogo otsenivaniia, elementy matrits svertki kotorykh opredeleny v nechetkom vide [Integrated assessment matrix mechanisms, whose elements of convolution matrices are defined as fuzzy]. Upravlenie bol'shimi sistemami. UBS-2017 : materialy XIV Vserossiiskoi shkoly-konferentsii molodykh uchenykh, 4-8 September 2017, Perm, Moscow, 2017, pp. 219-233.
9. Alekseev A.O., Korgin N.A. Matrichnyi anonimnyi obobshchennyi mediannyi mekhanizm s pravom delegirovaniia soobshchenii [The matrix anonymous generalized median schemes with delegation]. Teoriia aktivnykh sistem. Moscow. 2016, pp. 85-91.
10. Alekseev A.O., Korgin N.A. Matrichnyi anonimnyi obobshchennyi mediannyi mekhanizm s pravom delegirovaniia soobshchenii [The matrix anonymous generalized median schemes with delegation]. Applied Mathematics and Control Sciences, 2016, no 4, pp. 137-156.
11. Alekseev A.O., Melekhin M.I., Shaidulin R.F., Spirina V.S., Korgin N.A., Korepanov V.O. Programmnyi modul' eksperimental'nogo issledovaniia ustoichi­vosti matrichnogo anonimnogo obobshchennogo mediannogo mekhanizma k strategicheskomu povedeniiu agentov [Program for experimental research of the matrix anonymous generalized median schemes stability to the agent’s strategical behavior]. Certificate of program for computer no. 2016660758 (2016).
12. Alekseev A.O., Korgin N.A. Delovaia igra «Matrichnaia aktivnaia ekspertiza» [Business game “Matrix active expertise”]. Upravlenie bol'shimi sistemami (UBS'2016): materialy XIII Vserossiiskoi shkoly-konferentsii molodykh uchenykh, 5-9 September 2016, Samara. Moscow, Institut problem upravleniia im. V.A. Trapeznikova Rossiiskoi akademii nauk, 2016, pp. 242-256.
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The relevance of the study of the real estate prices dynamics in the city of St. Petersburg is shown. The criterion and factors influencing the object of modeling are determined. Normalized values of the criterion and factors are calculated. The mutual correlation of factors is investigated. A linear multifactor model and a model in the state space are built, it was proved that they cannot be used due to its poor predictive properties. A regression-differential model of prices changing for primary real estate in St. Petersburg is built, taking into account the mutual influence of factors, the possibilities of influence on its dynamics are revealed. Based on the linear multifactor model and the regression-differential model, the forecast of price changes for the next three years is made.

Keywords: housing construction, mathematical model, regression-differential model, forecast, socio-economic system, correlation.

Anastasya O. Sergeeva (Berezniki, Russian Federation) – Master Student of the Departament of Information Technologies and Automation Systems, Berezniki branch of Perm National Research Polytechnic University (618404, Perm region, Berezniki, Thalmann st., 7, e-mail: anaserg2008@mail.ru).

Elena V. Izmaylova (Berezniki, Russian Federation) – Ph.D. in Engineering, Associate Professor, Berezniki branch of Perm National Research Polytechnic University (618404, Perm region, Berezniki, Thalmann st., 7, e-mail: loko87@inbox.ru).

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