## No 4 (2019)

FINITE DIFFERENCE METHOD FOR SOLVING THE ELASTOPLASTIC PROBLEMS OF ANISOTROPIC BODIES

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):9-25
MODELLING THE QUALITY AND PRODUCTION OF PETROLEUM PRODUCTS WITH MATLAB
Zatonskiy A.V., Tugashova L.G.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):26-42
MATHEMATICAL MODELING OF MODERN ANTIFRICTION POLYMERS BEHAVIOR
Adamov A.A., Kamenskikh A.A., Nosov Y.O.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):43-56
THE METHOD OF EXTRACTING THE STEGANOGRAPHY WATERMARKS BY KEY USING HAAR WAVELETS
Krotova E.L., Chekmenev A.V., Bolgov A.O.

#### Abstract

Applied Mathematics and Control Sciences. 2019;(4):59-70
TEXT ANALYSIS METHODS AND TOOLS IN THE USER SUPPORT SYSTEM
Volodina Y.I., Zekiryaev M.Y.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):71-86
THE MODEL OF CONTROL LABOR MARKET CONDITIONS COMPANY AS A INTEGRABILITY IN QUADRATURES SYSTEM OF NONLINEAR DIFFERENCIAL EQUATIONS
Gorbunov D.L., Fedoseev S.A.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):89-102
CONTINUOUS SCHEDULING IN CONDITIONS OF MASS WELL CONSTRUCTION. PART 1
Kalyanov G.N., Titov N.N., Shibeko V.N.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):103-123
ATTAINABLE VALUES OF ON-TARGET FUNCTIONALS IN ECONOMIC DYNAMICS PROBLEMS
Maksimov V.P.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):124-135
STABILITY ANALYSIS OF THE RATING AND CONTROL MECHANISM TO AGENT’S STRATEGIC BEHAVIOR (ON EXAMPLE OF THE RISK MANAGEMENT POLICY COORDINATION)
Alekseev A.O.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):136-154
PRICES FORECASTING IN THE PRIMARY HOUSING MARKET IN SAINT-PETERSBURG BASED ON REGRESSION- DIFFERENTIAL MODELING
Sergeeva A.O., Izmaylova E.V.

#### Abstract

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.
Applied Mathematics and Control Sciences. 2019;(4):157-167