Applied Mathematics and Control Sciences

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.

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.

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.

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.

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.