The paper describes the main scientific results obtained under the guidance of Professor O. G. Pensky from Perm. The results are devoted to mathematical modeling of the behavior of the so-called digital twins, which are psychological analogs of a person. The paper formulates theorems describing the dangers of artificial intelligence to humans from a psychological point of view and proposes general models of dialectical development of the virtual world for digital twins. The paper describes the research of mathematical models developed together with the Israeli scientist O. L. Figovsky. These models are designed to calculate the coefficients of the influence of one person on another and make it possible to determine the degree of their mutual influence during their communication. It also reports on research into algorithms for intuition, insight, and hypnosis of digital twins. The article describes the difference between the studies carried out by the group of Professor O. G. Pensky and the research of its predecessors.

Keywords: psychology of robots, human digital twin, psychological characteristics, mathematical models, dialectics, human society, artificial intelligence, robot safety, mutual influence of robots, temperament of digital twins

The main maintenance of a diversification of production as activity of subjects of managing is considered. being shown in purchase of the operating enterprises, the organizations of the new enterprises, redistribution of investments in interests of the organization and development of new production on available floor spaces. The most important organizational economic targets of a diversification of management are presented by innovative activity of the industrial enterprise.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The article describes use of a PDF printout as the complementary source of unique spatial data in addition to the data from interchange format files. Predate methodic already published by author is proposed to be supplied with the original algorithm for automatical spatial alignment of the two vector maps with similar origin and purpose. Some of the existing methods and their drawbacks are briefly mentioned. General description of the method, it's limitations and possibilities are described; algorithmycal solution provided with some schemas. The practical mean of existing technology and it's possible approaches with the use of the new algorithm are pointed out.

Keywords: geographic information system, data integration, vector map, interchange format, PDF, coordinate transformation, spatial alignment, similarity transformation, least squares' method, algorythmic solution

The article provides a brief analysis of the starting processes of electrical devices. The mathematical formulation of the problem of synthesis of starting rheostats is formulated and its solution is proposed. The main condition for optimal starting of electric motors using thermistor rheostats is presented. Optimal diagrams of the starting current and set of revolutions are given. and also, the change in heat losses in the anchor chain. Recommendations on the layout of starting rheostats are given.

Keywords: thermistor rheostat, optimal start-up, thermal start-up characteristic, optimal control problem, DC motor, boundary conditions, speed

The paper discusses the use of threshold data separation schemes, as one of the promising areas of protection of both private and commercial information. In such schemes, parts of information are distributed among spatially distributed data storages, and information recovery is possible using at least one of the parts. The main disadvantage of such schemes is that they can be easily compromised, for example, if any part of the data is lost, or if the data is falsified by an intruder, it is impossible to localize the error, and, therefore, restore the original information. To solve this disadvantage, it is proposed to use schemes based on the system of residual classes [1] (RNS). The use of data separation algorithms based on the RNS will lead to a decrease in computational complexity, and, consequently, to a decrease in the load on data transmission media. Another advantage of SOCs is that they have corrective properties. A proportional increase in the number of information and redundant modules when using classical data separation schemes will lead to a sharp decrease in the reliability of the entire data exchange scheme. To solve this disadvantage, it is proposed to divide the information into groups, and then distribute it among the participants in the data exchange scheme.

Keywords: threshold separation of data, System of residual classes, reliability of data exchange schemes

The work is based on experimental results obtained by a survey among students of Grozny and Rostov-on-Don. The affective component of students ' attitudes towards friendship was determined by the technology of semantic differential Ch. Osgood. The distribution functions of the respondents ' emotional attitude to virtual and real friendship, calculated in the framework of a previously developed nonlinear stochastic model, are presented. The results of the comparative analysis show that in the group as a whole, the difference in the perception of real friendship between the respondents of both cities is small. On average, Grozny residents are a little more positive about real friendship. Students of both studied samples perceive virtual friendship in general more negatively than real friendship. But here the difference in relations is more significant. Subgroups with a positive perception in Grozny are about 10% less. On average, Grozny residents are more negative about virtual friendship than Rostov residents. Most likely, this is due to a difference in mentality.

Keywords: friendship, virtual friendship, affective component of attitudes, semantic differential technology, nonlinear phenomenological model, comparative analysis

In July and August 2019, the Grott ground penetrating radar was used as part of the field work of the Russian Arctic National Park, a federally funded institution, to survey areas polluted by oil products on Alexandra Island in the Franz Josef Land Archipelago. The results obtained are discussed and conclusions are drawn about the prospects of using the method of ultra-wideband electromagnetic sounding to solve environmental problems in the permafrost zone in the Arctic region.

Keywords: national park, Arctic, pollution, waste, soil, rock, georadar, ecosystem, sounding, radarogram, infiltrate

The article considers the dynamics of an ion beam in a laser mass – EMAL-2 spectrometer.a numerical model based on the "large - particle" method is Implemented, taking into account the influence of spatial charge fields and the interaction of charged particles with the field of an electrodynamic system. The software package that implements the mathematical model of ion beam motion consists of two parts. The first part is a program written in C++, in which initial conditions are set, the Coulomb interaction between large particles is calculated using the "particle-particle" method, the system of differential equations (1) is integrated using the fourth-order Runge-Kutta method, and the results are recorded and processed. The second part is a script for the FreeFem++ package, which implements the solution of partial differential equations using the finite element method. A series of numerical experiments and their comparison with the data obtained experimentally are carried out.

Keywords: large particle method, laser mass spectrometer, particle-particle method, electrodynamic system, Runge-Kutta method, laser plasma, magnetic analyzer, ion beam, focusing system, triangulation

The article proposes a thermodynamic approach that allows us to more accurately represent the flow modes of quasi-stationary gas through a long step gas pipeline . It takes into account the peculiarities of the operation of side gas venting devices of small-caliber automatic guns on the principle of automatic operation. We use a combination of the main characteristics that represent the operation of such systems under difficult loading conditions and high temperatures. These are mainly gas consumption, heat transfer losses, gas flow rate, improvement of the approach to the solution of ensuring the appropriate parameters to ensure the reliable operation of the relevant technical systems with the possibility of recommendations after appropriate tests of such products.

Keywords: step gas pipeline, side gas outlet device, gas flow, thermodynamic parameters, heat loss, filling period, gas consumption, automatic weapons systems

Rail transport plays a key role in the transport of passengers and goods. The high demand for effective means of flaw detection of high-speed rails, which is an important component of railway safety, is justified by the constantly growing number of vehicles and their speed [2]. Failure of elements of the railway infrastructure entails huge losses. In this regard, the analysis and forecasting of the state of elements of the railway infrastructure is an urgent task. This article analyzes modern methods for diagnosing the state of a rail track from a mobile bogie or a conventional locomotive. A method for diagnostics of a rail track is proposed, based on registration of vibrations near the rolling surface of rails and processing these signals using neural networks.

Keywords: rail flaw detection, wheel surface, algorithm, IMM, MEMS, control system, inertial sensor, rail defect, contactless measurement

The article describes a device for simulating a control object for automated temperature control systems, a mathematical model of the heating and cooling processes of an isolated room, modeling temperature effects on the control object, and a method for implementing a control object simulation on a microcontroller. The device will allow debugging and testing of automated temperature control systems under laboratory conditions, which will improve the quality of temperature control systems being developed.

Keywords: temperature control, automation of temperature control process, mathematical modeling

The goal of the paper is to consider the major ways of word formation in the modern English language and to analyse some of the word-building models, which have emerged relatively recently. As the material for the paper we have collected modern cognitive-semantic studies, Russian and foreign research works devoted to brand new words in English, lexical data from native speakers and the authors’ observation as well as the notes made during the visits of Great Britain in 2010-2020.

Keywords: word-building, word-building models, word formation, modern English, lexical item, lexical unit, tendency, neologism, etymology, modern English-speaking community

The work consists of two parts and is devoted to a comparative analysis of the declared cognitive and actually perceived affective relations to friendship. In the second part, the distribution functions for the entire hierarchical system of factors identified in the first part and reflecting the structure of the cognitive perception of friendship by DSTU students are presented. It was found that the overall cognitive attitude of the group is positive. For two indicators of the second level and the integral factor of all cognitive perception, about 80% of all respondents are characterized by positive values of these indicators. For the third factor of the second level, the subgroup with a positive perception (60%) is also larger than with a negative one (40%), but not so much. The affective component of students ' attitudes towards friendship gives a completely different picture. Here, 57% of respondents are characterized by an almost neutral emotional attitude to it, while only 29% are positive. All this suggests that in the group as a whole, students position a more positive relationship to friendship on a cognitive level than they actually feel emotionally. We associate this with the influence of society (both the immediate environment in direct communication, and through literature, art, mass media, etc.). The paper also analyzes the relationship between cognitive and affective attitudes to friendship at the individual level. In General, there is no such connection for the studied audience, even statistically (the correlation coefficient is only 0.17). But if we divide the entire audience into two subgroups, characterized by both the excess of cognitive perception over affective, and with the opposite ratio, then for them separately there is already a positive statistical relationship.

Keywords: friendship, pilot survey, cognitive component, hierarchical factorization method, distribution functions, affective component, comparative analysis

An overview of modern tools for computer-aided design of technical systems is given. Using the method of comparing systems by the criterion of functional completeness, their main functionality, compliance with standards, and additional specialized applications are analyzed. It is shown how much computer-aided design systems accepted for comparison have differences or similarities in terms of functional completeness. Using the method of formalized functional completeness analysis allows us to assess the level of compliance of systems with the requirements at the stage of preliminary analysis, form a group of systems that have the same functional completeness and analyze them by other criteria. Based on the formalized analysis of functional completeness, the choice of the Autodesk Inventor system for the development and research of a new design of the mechanism for moving a tunneling explosive-bulk complex was made. It was used to generate the shape of the support frame of the complex in conjunction with the movement mechanism and made a preliminary analysis of the safety margin of the metal structure. The value of the coefficient of safety margin, taking into account the gravity of the structure with a different combination of influencing factors, ranges from 20.11 to 43.2. This makes it possible to conduct research under load in critical operating modes.

Keywords: computer-aided design systems, functional completeness analysis, formalized analysis, three-dimensional modeling, animation, superiority graph, similarity graph, absorption graph

The article deals with current methods of evaluating the organization and management in construction under conditions of uncertainty. The typology of the failure process is given, which determines the scenario of the crisis development at the enterprise. A model of forecasting and management in a crisis is proposed, and the conceptual aspects of building this model are considered. It is proposed to improve the enterprise management system based on the analysis of the economic component as a temporary function. Recommendations are given for improving the existing organizational forms of enterprise management.

Keywords: construction organization, organizational and technological solutions, reliability assessment, construction quality assessment

The article discusses the problems that arise in pattern recognition related to clustering and data abstraction. Detailed typical data clustering options. The problem of data transformation by vector quantization with the least error is given. A competitive training system for an artificial neural network based on a growing neural gas is described. Using the method of growing neural gas, an improved algorithm of a self-learning artificial neural network of competitive training is proposed. The criteria for completing clustering using the adaptation criterion as a stop criterion are defined. Examples of data clustering by an artificial neural network using the method of growing neural gas are given.

Keywords: clustering, artificial neural network, computer modeling, pattern recognition, self-learning intelligent systems

The article considers the problem of economic forecasting of the volume of federal taxes and fees by the example of the Southern Federal District. To make a forecast, an econometric model was constructed with the introduction of dummy variables.The main objective of the study is the implementation of a short-term forecast using an econometric model. According to data from 01/01/2018 to 03/31/2020. an economic forecast of federal tax revenues was made and for the next two months.In conclusion, the proposed forecasting technique has such advantages as efficiency and simplicity.

Keywords: taxes, fees, forecasting, federal budget revenues, budget system, multiplicative model, dummy variables

This article describes the developed tool for creating a report on the effectiveness of sales channels for the hierarchical structure of sales channels. The developed model for the report on sales channels takes into account the type of source, the criterion for the freeness of the sales channel, the source of traffic and the source of customers themselves. The ROI is estimated and customer conversion activity data is tracked. The article also describes the results of the implementation of the model and its use.

Keywords: sales channel, meta-information, contextual advertising, call tracking, ROI, Google AdWords, Yandex.Direct

In this paper we consider various dynamics of opinions in social communities. The purpose of this work is to show all the variety of patterns of changes in opinions in teams. An important aspect is the specific application of dynamics. The process depends on the type of social community. This research is very important.The study of patterns of change and formation of opinions in any team is the basis for two main goals. The first important goal is to find consensus in the team.The second important goal is to determine the ratings of all participants.The following dynamics are considered in the paper: De Groot, Friedkin-Jones, Hegselmann-Krause, model of dynamics with centers of influence, Deffuant - .Weisbuch, Zaller-Deffuant .

Keywords: reputation, social community, game theory, opinion dynamics, influence, opinion, consensus, game-theoretic models, principal, player, agents, principal, player, agents

The article is devoted to the study of the interaction violations of electric locomotives current collectors with a contact wire, accompanied by the appearance of an electric arc. In order to further develop the system of technical diagnostics of current collection disruptions, accompanied by arcing, it is necessary to study the nature and parameters of the processes that occur with these disruptions. The main part of the article is devoted to the determination of the geometric parameters of the heating zone of the contact wire material by a movable electric arc, followed by an analysis of the applicability of the obtained dependences and their normalization. The description of the research area, the essence of the problem and the main statements of the technical diagnosis of current collection disruptions is given. The nature of the distribution of heat in the cross-section of the contact wire is shown. Based on the nature of the process and plane geometry, the parameters of the heating zone of the contact wire material are obtained: the area of the heating zone and the depth of the heating zone. Limitations in the application of the obtained dependencies are given.

Keywords: electric transport, overhead contact system, contact wire, current collection disruption, electric arc, current collection with arcing, thermal wear, softening, diagnostics

The paper discusses modern approaches to the mass valuation of real estate, automated systems for typical buildings assessment, and also provides the development of a method for the continuous assessment of real estate objects, which makes it possible to effectively evaluate groups of real estate objects and infrastructure. This research is aimed at studying the economic component of this process - modeling of a system for assessing the market valuation of real estate in typal development objects. The purpose of the study is to develop a system of continuous assessment (mass valuation) of real estate, taking into account the current methodological support of the process of assessing the market value of real estate, and should contribute to the improvement of the comparative approach to valuation in the framework of the practical activities of appraisers, as well as for state regulation of the real estate market.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The consideration and study of the process of functioning of the offices of the company were the following objectives. Determine the quantitative dependencies of the input flow of patients and unserved requests (refusals). To conduct the sensitivity analysis. Build a basic model of a dental company as a simulation model (input model) that provides targeted variation of input parameters, and a linear programming model (output model) that processes simulation results and provides data on the degree of sensitivity of the model to changes in its parameters. Compare two simulation models of a dental company with different numbers of doctors. Determine the most effective model. Determine a combination of management variables in the optimization model that takes into account the amount of estimated lost profits due to rejection of applications, and based on this, make a conclusion about the need to hire additional employees, thereby increasing the profitability of the dental company. To achieve these goals, the following tasks were solved. A simulation model of a dental company as a Queuing system in the GPSS language was developed and studied. It is determined under which parameters the model is most effective. An analysis of the sensitivity of the model to changes in its parameters is performed. Numerical Monte Carlo methods were used to investigate this issue. We have developed a custom application in the VBA object-oriented programming language that allows you to determine for a certain period of time, starting with how many failures, you should hire an additional doctor, so that the company's profit is maximized. The practical value of the proposed model lies in its flexibility, complex nature, and consistency in the organization and technological regulation of the company's main systems and business processes. The model of a dental company has a sufficient degree of universality, as it can be used in any branch of the service sector. more complicated when you add players. The term "truel" we understand the rivalry three players. They are assigned some values of accuracy the probabilities of eliminating the opponent in one shot. At each stage of the game is chosen by the active player (the selection rule active player either randomly or by prior agreement between the players about their participation). The active player chooses an opponent to eliminate or passes the course. Developed mathematical models for different formulations of the conditions of the game (random or fixed choice of the active player). For each model are analyzed based on the probability of winning in the "truly" of accuracy, based on randomly generated program values. Comparing analytical solution and simulation, we see that they have the same answers. For large dimensions similar games analytical method requires complex calculations, so an acceptable alternative is the simulation method. Data research nahegelegenen in political and judicial practices, as well as analytical tools for the study of the theory of evolution.

Keywords: simulation model, Queuing systems, GPSS World, linear programming model, Monte Carlo numerical methods, VBA

The article is devoted to the development of a mathematical model of a vulcanization boiler, namely, the temperature control loop inside the boiler. The mathematical model of the boiler was obtained by the Rotach method in the form of a transfer function. Simulation modeling was performed in the VisSim software tool. The adequacy and stability of the model is proved and the numerical values ​​of the quality criteria of the transient process are obtained. The resulting model is intended to determine the optimal settings of the regulator of the vulcanization process control system.

Keywords: transfer function, vulcanization boiler, transient, software, system order, vulcanization process, control, calculated transfer function, delay time, sleeve

A task flow scheduling procedure is proposed that sets the order between groups of equivalent tasks based on their comparison by a number of characteristics. The goal of task flow scheduling was to minimize the total time spent on idle tasks in queues while waiting for the release of sequentially used resources. In the proposed method, when selecting tasks to perform, priority is given to tasks that use the minimum resources. This algorithm allows you to avoid running tasks that use the same resources simultaneously. Recommendations for practical application of the scheduling procedure are given, and a scheme for its interaction with the built-in OS scheduler is developed. To get the greatest effect from controling task scheduling in various environments, options for changing the dispatching algorithm are proposed.

Keywords: multi-program information systems, real-time systems, algorithm, flowchart, task dispatching, process scheduling by structural criteria, task grouping, task control based on priorities, comparison of multi-criteria tasks, Pareto dominance rule

The article proposes a structure and algorithm for managing a software complex for analyzing the financial condition of an enterprise. The developed software package is designed to identify data patterns when conducting financial analysis taking into account the specifics of the enterprise.

Keywords: analytical platform, management algorithm, data warehouse, data processing scenario, balance sheet, key figure, information base, data visualization, efficiency