## No 2 (2021)

MODELING OF THERMODYNAMIC PARAMETERS OF SOLIDS BY THE ASYMPTOTIC METHOD

#### Abstract

In this work to solve the differential equation of heat conduction we use the separation method taking into account the boundary conditions. The solution of the problem is reduced to the Sturm-Liouville theory. There are other well-known methods for solving the differential equation of heat conduction: the operator method, the solution of the heat equation using the Green's function. We propose a method for solving the differential equation of heat conduction by the asymptotic method using the Laplace transform and furtherLaurent expansion of a function for a solid plate. A theoretical dependence of the temperature on time is obtained which has two sections: the initial one is linearand at large times it is nonlinear. Using the asymptotic expansion we propose expressions for determining the coefficient of thermal conductivity of a solid and the coefficient of heat transfer of a solid to the environmentas well as a method for determining the thermodynamic parameters of a solid. An experiment was carried out where a preheated solid is immersed in a calorimetric chamber filled with water of lower temperature. The heated solid gives off heat to the water. With the help of thermocouples the dependence of water temperature on time is obtained, linear and nonlinear sections of temperature changes are determined. Furtherusing the obtained theoretical expressionthe values of the thermal conductivity coefficient of a solid and the heat transfer coefficient of a solid to water are found. It is shown that, according to the model proposed in the work, the experimentally determined values of the thermal conductivity coefficient and specific heat capacity for a copper plate are close to the known tabular values. At the same time, the calculated and tabulated values of the heat transfer coefficient of copper to water have a significant difference, which requires additional research.

**Applied Mathematics and Control Sciences**. 2021;(2):9-22

DEFORMATION BEHAVIOR MATHEMATICAL MODELING OF A POLYMER MATERIAL LAYER WITH TECHNOLOGICAL hole FOR A LUBRICANT

#### Abstract

Mathematical modeling of the flat layer of a polymeric material deformation behavior with a polished steel plate within the framework frictional contact was carried out of this work. The influence of the technological groove geometric configuration for the lubricant on the contact unit deformation is considered. The lubricant volume in the calculation scheme does not take into account that does not correspond to the favorable occasion of lack of lubrication in the recess. The parameterized model creation of a polymer layer portion with one technological recess with a different base rounding radius from 0.5 to 2 mm with a step of 0.25 mm is done. The technological recess geometrical influence on the deformation of its profile at loads from 5 to 90 MPa was established within the framework of the study. Changes in the cross-sectional area of the recess, the maximum level of the plastic deformations intensity, contact pressure, contact tangential stress and the contact interaction area from the load and the rounding radius are established. The contact zone parameters redistribution due to an increase in the contact interaction area for all rounding versions for the technological recess base for the lubricant occurs at loads of more than 40-50 MPa. The design with a rounding radius of 2 mm has a number of advantages: minimum deformation of the technological recess area, the minimum level of the maximum plastic deformations intensity, the maximum contact interaction area, etc.

**Applied Mathematics and Control Sciences**. 2021;(2):23-40

SOME RESULTS OF SOLVING THE NON-STATIONARY PROBLEM OF GAS DIFFUSION IN POLYETHYLENE

#### Abstract

The problems of diffusion of molecular oxygen and ethylene in amorphous-crystalline polyethylene are considered. The temperature of the medium is assumed to be constant, and the diffusion process is described by the classical Fick partial differential equations. It is assumed that the material obtained from the polyethylene granules using the thermomechanical extrusion process is located in a limited sealed container. The impermeability of the container shell leads to the need to take into account the parameters of the gas in the free volume. The problem is nonlinear and non-stationary, and it is assumed that the rate of interphase processes at the gas-polyethylene interface significantly exceeds the rate of diffusion. Using the finite element method, numerical results are obtained describing the process of oxygen evacuation from polyethylene and the process of ethylene diffusion into the material, at different values of the external pressure of the penetrant gas. The main characteristics of these processes are determined. An effective variant of double vacuuming is considered, which makes it possible to obtain a significantly lower concentration of oxygen in polyethylene. The results are of practical significance for evaluating the parameters of the production of high-quality heat-shrinkable polyethylene pipes produced by the technology of gamma-ray radiation exposure in the protective environment of an inert gas.

**Applied Mathematics and Control Sciences**. 2021;(2):41-51

USING THE ALGORITHM OF CONDITIONAL ALTERNATING MATHEMATICAL EXPECTATIONS TO MATHEMATICAL MODELS DESIGN TO ESTIMATE THE QUALITY INDICATORS OF OUTPUT PRODUCTS

#### Abstract

In order to increase production efficiency and improve the quality of an output product, the problem of mathematical models designs for estimating the quality indicators of output products in conditions of nonlinearity of the technological process is considered. The use of existing parametric approaches in the design of such models is limited by the need to obtain an analytically specified functional dependence (known the model structure) with a sequential refinement of the values of its coefficients. In turn, this leads to obtaining a mathematical model for estimating the quality indicators of output products of low-accuracy. In the case of nonlinearity of the technological process, the most promising are nonparametric methods such as the algorithm of alternating conditional mathematical expectations. It is proposed to use an algorithm of conditional alternating mathematical expectations to determine the structure of relationships between variables, the form of which is initially unknown and to identify nonlinear functional dependencies based on transformations of the variables used. The effectiveness of the proposed approach in designing a mathematical model using a synthetic example is shown. The proposed approach was tested on a mass-transfer technological object of the production process of a high-octane gasoline additive - methyl-tert-butyl ether. It was possible to improve the accuracy of the mathematical model for estimating the concentration of methanol in the output product up to 67.2 % MAE in comparison with the model obtained by the neural network.

**Applied Mathematics and Control Sciences**. 2021;(2):52-70

APPLYING NEURAL NETWORK MODELS TO THE CONSTRUCTION OF PRODUCTION RULES EXPERT SYSTEMS

#### Abstract

The development of urbanization, the dramatic increase in the population of large cities and, as a consequence, the increased tempo of life, have had a direct impact on the number of vehicles. That is why intelligent methods of traffic flow control to optimize traffic capacity are growing in popularity. The application of these methods makes it possible to use existing roads and highways with high efficiency without the need to build additional lanes, interchanges, ring roads and so on, which in particular is postulated by the strategy of the National Technological Initiative of the Russian Federation. The purpose of this study is to develop an algorithm, the idea of which is to form productive rules for the traffic flow control by directing the impact on its parameters. In this way, experts can assess the impact of certain characteristics on those that can be manipulated. The construction of the algorithm is done by forming neural network models followed by using the method of the most dominant rule and Garson's algorithm. Since the use of the algorithm involves expert group evaluation, it must have a logical (verbal) rule output in the following form, e.g: "if the slope is minimum, the width of the roadway is maximum, ... then the percentage of heavy vehicles is minimum". This transformation is carried out through the use of the membership function, which allows to fully describe the degree to which a certain parameter belongs to a certain fuzzy subset. In the problems of traffic flow control, it is recommended to use a triangular-shaped membership function. The study contains the results of computational experiments to determine the optimal partitioning of input parameters into fuzzy values to generate satisfying real-world conditions rules. When constructing the algorithm, special attention should be paid to assessing the quality of the neural network model. For this purpose such methods of estimation as root mean square error (RMSE) and logistic error function (LogLoss) are used. Data from loop and radar detectors describing the capacity in long-term operating areas on sections of transportation corridors were used as the initial data set for the numerical study. Sensitivity analysis based on the application of the finite increment formula was used to determine the most significant traffic flow parameters.

**Applied Mathematics and Control Sciences**. 2021;(2):73-92

COMPARISON OF METHODS FOR IDENTIFYING USER ROLES IN ONLINE SOCIAL NETWORKS

#### Abstract

The development of social media has led to its use as a tool for propaganda and mobilising users to participate in protest movements and political actions aimed at undermining the foundations of society and overthrowing the current government. The impact on social media by the organisers of protest movements has become increasingly targeted and organised. In the context of ensuring public safety and countering destructive influences on social media, it is becoming increasingly important to identify the structure of purposeful impact on social media. Important elements of this structure are the roles played by social network users who participate in the protest movement. The paper presents the data of a survey of the social network VKontakte users in Perm region, who have published protest-related materials during the year 2020. Descriptions of the roles of social network users based on data on their publication activity are presented. Existing methods of identifying the roles of online social network users based on clustering and neural network classification are described. Problems associated with the preparation of datasets for qualitative training of neural networks are indicated. The authors have researched user roles using different clustering methods, and proposed original methods of numerical evaluation of user roles and expert neural network classification of user roles based on artificially synthesized datasets. The results of comparison of different clustering methods, numerical estimation method and expert neural network classification method are presented, their advantages and disadvantages are indicated. High correlation between numerical evaluation method and expert neural network classification method is shown. It is noted that the effectiveness of expert neural network classification of roles of users in social networks is higher than that of various clustering methods. In conclusion, the optimum areas of application of the proposed methods for classifying the roles of social network users are indicated and the directions for further research are outlined.

**Applied Mathematics and Control Sciences**. 2021;(2):93-111

CONTROL OF THE HEATING CABLE OPERATION BASED ON A MATHEMATICAL MODEL OF HEAT AND MASS TRANSFER PROCESSES IN AN OIL WELL

#### Abstract

The paper considers the problem of controlling the process of thermal dewaxing of oil and gas wells using a heating cable. An axisymmetric mathematical model of heat and mass transfer processes in an oil well is proposed, the implementation of which makes it possible to estimate the temperature distribution on the wall of a pumping compressor pipe, to determine the area of possible deposition of asphalt-resin-paraffin substances and the necessary conditions to prevent their formation. The mathematical model is a system of differential equations based on the laws of conservation of energy, mass and momentum. Considers the basic principles of heating cable control used in modern thermoelectric installations. The inefficiency of these methods is shown, which leads to increased energy consumption and accelerated aging of the heating cable. A fundamentally new algorithm for controlling the operation of a heating cable is proposed, based on modeling the processes of heat and mass transfer in an oil well. The use of this algorithm makes it possible to obtain with a sufficiently high accuracy the temperature distribution inside the well and determine the required heating time and power to prevent the deposition of asphalt-resin-paraffinic substances on the walls of the tubing. The control algorithm is implemented taking into account the technological parameters of production, which have a significant impact on the temperature distribution in the well, and adapts to their possible change caused by the heterogeneity of the oil and gas reservoir. The proposed heating cable control algorithm makes it possible to reduce energy consumption, which is the main disadvantage of thermal dewaxing of oil wells using resistive heating, and to prevent premature equipment failure caused by possible overheating of the heating cable line. The results presented in the work can be useful in the development and operation of oil and gas wells complicated by asphalt-resin-paraffin deposits. Application of the proposed mathematical model makes it possible to evaluate the efficiency of thermal dewaxing of wells with a heating cable at the stage of field development and draw conclusions about the effectiveness of this method of combating paraffin deposits. The control algorithm based on the proposed mathematical model makes it possible to effectively use the equipment and reduce capital costs for electricity and well turnaround.

**Applied Mathematics and Control Sciences**. 2021;(2):115-132

THE METHOD FOR SELECTING THE BEST PERFORMER FOR SOLVING OPERATING TASK BASED ON A COMPETENCE APPROACH

#### Abstract

There are some problems regarding the interaction of various areas of human resource management, due to the development of information products in the field of obtaining corporate knowledge and monitoring competencies. The main issue is the formation of a close connection between corporate education and the employee's work activities. Presently, the formation of a competency base is associated with the existing positions and roles for employees in the organization. Thus, the control of competencies is primarily carried out at the initial stage of recruitment and adaptation of staff. Further development of employee competencies is associated with training. But as practice shows, the company is forced to apply radical methods to support the employee's motivation to acquire new knowledge and competencies. At the same time, the question of the organization's interest in training employees remains open. Nevertheless, employee training has a direct impact on improving the quality of work and the financial stability of any organization. This paper proposes a method to improve employee productivity, combined with support for motivation to develop and learn. The purpose of developing such a method is to ensure that both employees and the organization are motivated to learn and develop. In this case, it is advisable to combine this process with work activities. And the expansion of the competence base can be supported by the creation of intra-organizational competencies and a detailed analysis of work activities through the prism of a competence-based approach. The main activity of the method is aimed at finding a suitable performer for solving office problems. The development uses an ontological approach that allows a semantic analysis of the requirements for work tasks and projects and the selection of the most relevant criteria for choosing an executor. In this case, the candidate for the performance of the work task is selected primarily according to his existing competencies and conditions that he is ready to comply with. This approach also makes it possible to use the rating system to organize personalized training and find an approach to eliminating the lack of competencies in the company, as well as to ensure the interchangeability of performers and the continuity of the workflow. Individual trajectories of training can be formed to train personnel to perform specific work tasks in this case. And an analysis of the availability of competencies in an organization can identify weaknesses in work activities and provide targeted training for employees.

**Applied Mathematics and Control Sciences**. 2021;(2):133-144

THE METHOD OF AUTOMATICLY GENERATED EFFECTS OF EVENT-BASED GAME MECHANICS IN THE FRAMEWORK OF A CORPORATE E-LEARNING SYSTEM

#### Abstract

The article is devoted to the problem of the lack of a flexible unified approach to the corporate e-learning systems implementation using game mechanics. The aim of the work is to develop a new method for automatically generated effects of event-based game mechanics. The proposed method is based on a formal model for describing event-based game mechanics and production rules. This approach allows us to consider the impact of event-based game mechanics as a control object, providing the ability to unify the rules for generating impacts for the entire class of event-based game mechanics. The article describes an information model of an e-learning management system that meets the xAPI (Experience API) standard specification and allows implementing proposed method for automatically generated effects of event-driven game mechanics. The proposed information model provides with ability for using a blended learning approach and mobile technologies. The article also highlights the specificities of the learning management system software implementation, designed on the basis of the proposed information model that meets the xAPI standard, and that implements the developed method for automatically generated effects of event-based game mechanics. It is proposed to consider the subcomponents of the Activity Provider component as separate microservices, the exchange of messages between each other by REST API interfaces. Information of user actions is also sent to the Learning Record Store (LRS) via REST APIs. The library of production rules is a separate component. The rules for automatically triggering the game mechanics’ effects are written using the extended Gherkin notation language. Every rule effect associated with a specific program function those implements dispatching events of actions of event-based game mechanics. Experiments and approbation of the proposed method of automatically generated effects of event-based game mechanics have proven the effectiveness of the proposed method. Results analysis of corporate training using the proposed solutions according to the four-level Kirkpatrick model showed that each of the four levels of this model for assessing effectiveness was successfully achieved.

**Applied Mathematics and Control Sciences**. 2021;(2):145-167

APPLICATION OF THE LONG MEMORY MODELS FOR RETURNS FORECASTING IN THE FORMATION OF INVESTMENT PORTFOLIOS

#### Abstract

This paper continues research within the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics of the faculty of Economics of PSU. This paper describes the method of formation investment portfolios of four assets based on forecasted returns obtained using long memory econometric models and tests the hypotheses that the optimization of portfolio structure by forecasted returns obtained using such models (by the example of ARFIMA) allows to improve portfolio characteristics in comparison to the optimization by historical returns. Different variants of portfolios of four financial instruments were formed to test the method and test the hypotheses. The study obtained the following results. Portfolio parameters do not deteriorate, on average, when optimized by forecasted data and, in some cases, they improve because the optimizer identifies the most profitable assets more often and gives them more weight. The optimizer is better at identifying the most profitable assets based on the forecasted returns than the least risky ones because the autoregressive models predict the trend of the index rather than its volatility. Finally in the paper there are formulated the possible directions for further research: improving the methodology, namely, performing preliminary fractal analysis of series, imposing stricter restrictions on risk, using other forecasting models, rebalancing the portfolio; conducting research on data from the U.S. stock market, which is certainly more developed in comparison with Russia; using stock indices as a benchmark for assessing the effectiveness of portfolios.

**Applied Mathematics and Control Sciences**. 2021;(2):171-191