The development of the construction industry leads to an increase in small businesses both in construction and in the sale of building materials. Besides, small business fills the market with various goods, solves various social and economic issues such as unemployment, industry monopoly. However, its activity can't exist without sufficient financial support. A two-level mathematical model of interaction between a retail enterprise and a commercial bank as a funding structure is considered. To research the proposed model, the method of simulation modeling based on numerical search was used. A computer program was created to build a Stackelberg equilibrium algorithm with hierarchical control as an impulsion. The algorithm can be used to find the optimal values of the control parameters of an individual entrepreneur and a commercial bank. These values maximize the objective functions and profit of the system participants. The identification of the proposed model was carried out on the basis of data obtained from the Internet. Finally, the results were obtained using numerical examples.A number of conclusions could be made about the functioning of the entire system.

Keywords: hierarchy,two-level system, credit, Stackelberg, small business, bank

In the automation of production, the use of robots is an important direction. When developing algorithms for controlling the movement of such a machine, multidirectional problems arise. In a critical situation, the robot must not harm workers or collide with its fellow robot. At the same time, the car must move along the optimal route. The article analyzes the methods of finding optimal paths on square navigation grids. The wave method on undirected planar graphs, the A* algorithm (an extension of Dijkstra's algorithm), and the D* Lite algorithm for graphs with non-constant or previously unknown structure were chosen for the analysis. A visualization and testing system in C#has been developed for the research and testing of algorithms. The system is implemented using the Microsoft Visual Studio 2019 IDE software tools and external GraphX and Emgu CV libraries. A unique feature of the system is the ability to directly read images of shop floor maps in widely used graphic formats and automatically convert them to a format that is understandable to the system. First, the user uploads the shop floor plan. For easier processing, the image is converted to two colors: black and white. Then the image is processed by the Emgu CV library, at the output we get all the contours of stationary obstacles. Then, depending on the size of the robot, an orthogonal navigation grid is superimposed. The analysis of the obtained results allows us to conclude that it is better to use a method (the D* Lite algorithm) that allows for a non-constant or unknown grid structure in advance.

Keywords: visualization, program, graphic format, work, shop, map, square, grid, cell, navigation, optimal route, planar graph

The article is devoted to the development of a software product that analyzes the concentration of gases (H2; CO; C2H4; C2H2) measured in transformer oil and set as a function of time. Product development consists of two stages. The first step is the task of classifying transformers. The second stage is predicting reliable operation before a possible failure based on the concentrations of dissolved gases in the transformer oil set as the initial data. During the development of the software product, the frameworks for creating web applications Flask and ReactJS were used, the models were trained on the frameworks H2O.ai, LightGBM, Sklearn.

Keywords: machine learning, regression, power transformers, gas concentration, web-service

The work is devoted to the development of 3D models of the territory with buildings and other objects placed on it for subsequent analysis of insolation. The work describes the requirements for solar insulation of buildings, analyzed the regulatory requirements for solar insulation of premises, a schedule of monthly sundials is presented using the example of the city of Volgograd, a substrate is formed with applied contours of buildings and objects for a more convenient implementation 3D which was formed in third-party software, presents a brief analysis of the Energy software product 3D which describes the positive and negative aspects of the software, on the example of the design project of the scientific and educational center, an analysis of the insolation of the territory according to the formed 3D model was carried out. Based on the results of the analysis, the placement of objects was corrected to achieve the required illumination.

Keywords: 3D model, modeling, Energy3D, SaSplanet, reference coordinates, 3-dimensional projection, 2-dimensional projection, 24-hour sun trajectory, solar analysis, monthly solar clock plot

The problem of searching over encrypted data using homomorphic encryption in distributed software systems is addressed. The paper considers the application of the approach developed by the authors for the implementation of a distributed system prototypes for issuing digital diplomas and certificates for obtaining competencies with recording in IPFS and an Ethereum smart contract and a search engine for recruiting personnel. The prototype of the system presented in the article demonstrates the use of homomorphic encryption, which allows the search engine and users to interact with the directly transformed data in public blockchain networks without performing the reverse transformation, ensuring their security.

Keywords: blockchain, distributed software systems, cloud computing, homomorphic encryption, mathematical model, transactions, smart contracts, digital diploma, recruiting

Currently, there are general mathematical models that allow calculating the simplest emotional education of a robot. Using these models, computer programs are implemented, for example, VibraImage by Elsys, which сalculates the simplest emotional upbringing based on the microvibrations of a person's head placed in front of a computer's webcam. However, it is not always possible to use the VibraImage program in specific situations. The purpose of this article is to describe an algorithm and software application for calculating the parameters of the simplest emotional upbringing of a robot according to the amplitude of a sound incentives acting on the robot. A formula is obtained for the simplest emotional education of a robot using the amplitude of the sound signal affecting the robot, as well as the ratio for evaluating the parameters of the simplest education of work. A computer program is described that allows one to calculate elementary education, memory coefficient and ultimate education of a robot using an audio file, which is a sound signal affecting the robot. The nature of the relationship between the parameters of the simplest upbringing and the length of the sampling step is determined. Identified the most suitable value for the sampling step length.

Keywords: robot, education, memory coefficients, amplitude of a sound signal, mathematical model, psychology of robots, limiting education, elementary education, computer program, sampling frequency

The article discusses the opportunities that arise when using data mining methods in construction. A numerical experiment is carried out to create an algorithm for making design decisions in the production of zero-cycle works, namely, when installing the enclosing structures of the pit edge. Comparison of the data obtained in the Deductor Studio software product with those actually used in the construction of a residential building is performed.

Keywords: construction, earthworks, information technology, decision tree, design decision making, data analysis, machine learning, Data Mining, Deductor.

Symmetry detection is an important task that arises in MRI analysis, TEM microscopy and other scientific and industrial problems. Current methods of symmetry detection usually analyse SIFT invariants or use voting schemas. The article proposes and analyses an optimization problem that can be used to describe the image symmetry detection pipeline in terms of correlation and similarity. The article also describes an algorithm that solves the aforementioned optimization problem using a ransom sample consensus voting scheme, thus bringing the proposed method closer to other RANSAC-based methods. It is shown that an implementation based on the proposed model outperforms SIFT-based detectors, and stays in row with other voting-based methods; it is also shown that the algorithm's parameters could be adjusted for specific tasks to improve the detection quality. The article also compares the proposed method with other existing solutions in terms of accuracy and precision; visualizations are also included.

Keywords: RANSAC, random sample consensus, reflection symmetry, computer vision, image processing

The choice of the installation location of compensating devices is determined by various factors that must be taken into account when performing calculations. The location of reactive power compensation devices is determined based on the results of mathematical modeling and the optimal operating mode of individual sections of electrical networks. The paper presents the results of modeling, considers the uncertainties encountered in solving the problem of placement of compensating devices.

Keywords: compensating devices, electric power industry, active power losses, minimum reduced costs, uncertainty, power gain, optimization criteria, electrical node, damage vector, optimization

In the given article a regression model of the labor productivity index from the investment dynamics into the fixed capital for the Central Federal District is build. The time series regression model is constructed by means of the trend deviation method. According to the obtained econometric model, a forecast of the labor productivity index for subsequent periods is made.

Keywords: econometric model, forecasting, labor productivity index, investment, regression, time series, trend

The results of the study of fluctuations of the center of mass of the car UAZ "Hunter" during its movement on the support surface with different height of road irregularities: asphalt-concrete surface and off-road are given. The study uses Simulink simulation.

Keywords: Center of mass fluctuations, vehicle, simulation, Simulink

The work is based on the results of a survey conducted among students of Grozny and Rostov-on-Don at the end of 20219. The cognitive component was measured by a test method, using 11 primary features. According to them, an integral indicator of the cognitive perception of friendship for each respondent was calculated using a modified method of analyzing hierarchies. The affective component of student attitudes towards friendship was determined by the semantic differential technology Ch. Osgood, using a special semantic scale with 20 bimodal features. Based on the results obtained, the individual level of emotional perception of friendship was calculated within the framework of the previously developed phenomenological semantic model. Statistical analysis of the obtained indicators of cognitive and affective perception showed that both in general for the study groups and for the general population, the correlation coefficients are small. For Rostov, about 0.17, for Grozny-0.273, and for the total population of respondents for these two cities-0.243.The scattering of experimental data is close to isotropic. All this indicates the statistical independence of these two components of attitudes in general for the studied samples. This confirms both the generally accepted opinion and the previously obtained results (for several thousand respondents) when studying other social attitudes. However, for certain subgroups of the studied audience, the statistical relationship between these two parameters is more significant. Thus, approximately 1/3 of the respondents, both in Rostov and Grozny, indicated a higher level of emotional perception, compared to cognitive. For these subgroups, the correlation coefficient for Rostov is 0.8, for Grozny-0.87, and for the two cities in total – 0.79. For the remaining 2/3 of the respondents (they are characterized by a higher level of cognitive perception compared to emotional perception), the correlation coefficients are slightly lower, but still exceed the results obtained without dividing into subgroups. For students of Rostov-on-Don-0.5, Grozny-0.44, and for the two cities in total-0.46. The revealed statistical relationship between the studied components of attitudes is associated with the influence on the formation of these components of the psychological type of respondents. And the subgroups we have identified differ precisely in their psychological type. But this hypothesis requires further testing.

Keywords: friendship, attitudes, cognitive component, test method, affective component, semantic differential technology, statistical analysis, correlation, subgroups, statistical relationship

The article presents a method for determining the dynamic characteristics (period and form of natural vibrations) of buildings and structures, taking into account the flexibility of the foundation under seismic impact. This also takes into account the uneven settlement during the construction of structures on various soils. The total displacement of the mass of the structure under seismic effects, taking into account the compliance of the base, is recorded as the sum of displacements from shear and rotation. In addition, a coefficient is introduced into the calculation, which is the mode of vibration of a rigidly embedded system. The formulas obtained can be used to create a mathematical model of the joint work of the "foundation - structure" system.

Keywords: structure, dynamics, natural oscillations, oscillation period, oscillation shape, base pliability, seismic impact

The work is based on the results of a survey conducted among students of Grozny and Rostov-on-Don at the end of 20219. The cognitive component was measured by a test method, using 11 primary features. According to them, an integral indicator of the cognitive perception of friendship for each respondent was calculated using a modified method of analyzing hierarchies. The affective component of student attitudes towards friendship was determined by the semantic differential technology Ch. Osgood, using a special semantic scale with 20 bimodal features. Based on the results obtained, the individual level of emotional perception of friendship was calculated within the framework of the previously developed phenomenological semantic model. Statistical analysis of the obtained indicators of cognitive and affective perception showed that both in general for the study groups and for the general population, the correlation coefficients are small. For Rostov, about 0.17, for Grozny-0.273, and for the total population of respondents for these two cities-0.243.The scattering of experimental data is close to isotropic. All this indicates the statistical independence of these two components of attitudes in general for the studied samples. This confirms both the generally accepted opinion and the previously obtained results (for several thousand respondents) when studying other social attitudes. However, for certain subgroups of the studied audience, the statistical relationship between these two parameters is more significant. Thus, approximately 1/3 of the respondents, both in Rostov and Grozny, indicated a higher level of emotional perception, compared to cognitive. For these subgroups, the correlation coefficient for Rostov is 0.8, for Grozny-0.87, and for the two cities in total – 0.79. For the remaining 2/3 of the respondents (they are characterized by a higher level of cognitive perception compared to emotional perception), the correlation coefficients are slightly lower, but still exceed the results obtained without dividing into subgroups. For students of Rostov-on-Don-0.5, Grozny-0.44, and for the two cities in total-0.46. The revealed statistical relationship between the studied components of attitudes is associated with the influence on the formation of these components of the psychological type of respondents. And the subgroups we have identified differ precisely in their psychological type. But this hypothesis requires further testing.

Keywords: friendship, attitudes, cognitive component, test method, affective component, semantic differential technology, statistical analysis, correlation, subgroups, statistical relationship

The following object of research is considered: information processes in special-purpose automated systems with the application of resident type anti-virus protection mechanisms in conditions of the destructive influence of malicious software. The purpose of the study is to improve the efficiency of information processing in special-purpose automated systems in terms of mechanisms resident-type anti-virus protection and the destructive impact of malicious software. The research methods include methods of the theoretical foundations of information security, the methodological apparatus of system analysis, mathematical modeling, methods of probability theory, and mathematical statistics. In the course of the study, the following results were obtained: firstly, the assessment of information processes application in automated special-purpose systems effectiveness was substantiated; secondly, theoretical foundations and method for optimizing the time resources of special-purpose automated systems in the interests of implementing resident-type anti-virus protection mechanisms in conditions of the destructive impact of malicious software have been developed; thirdly, functional and mathematical models of mentioned above information processes have been developed; fourthly, an appropriate technique developed and a computational experiment has been carried out to assess the increase in the efficiency of information processing in special-purpose automated systems in conditions of resident-type anti-virus protection mechanisms usage and the destructive impact of malicious software. The obtained results have allowed improving the efficiency of information processing in special-purpose automated systems in terms of resident-type anti-virus protection mechanisms and destructive effect, through the optimal use of these systems time resource by antivirus mechanisms.

Keywords: special-purpose automated systems, anti-virus protection, anti-virus mechanisms, timeliness, information protection, information processing efficiency, computational experiment

The article presents the results of experimental studies of microclimate parameters (temperature, intensity of thermal radiation) at the area of an arc steelmaking furnace, on the basis of which the adequacy of mathematical models of heat transfer implemented in the ANSYS software package is confirmed. Mathematical models of heat transfer are represented by the discrete ordinate model (DO), which most accurately describes the transfer of radiative heat in space, and the Shear Stress Transport (SST) turbulence model. The use of these mathematical models will make it possible to pre-evaluate the thermal radiation situation at the projected or reconstructed objects, and also will allow you to choose effective means of thermal protection in advance.

Keywords: arc steelmaking furnace, mathematical models, experimental studies, heat transfer, temperature, intensity of thermal irradiation

The results of the development of a sensory subsystem of an ophthalmopneumatic gas tonometer designed to measure intraocular pressure, study the anterior ciliary arteries and measure indicators are presented. After identifying the design features of the device, a structural diagram, an electrical diagram of the subsystem was proposed, a three-dimensional model of the device was made, and the technical characteristics of individual elements were considered. Brief conclusions on the work done are given, as well as the prospects for the development of the project.

Keywords: ophthalmopneumovasotonometer, intraocular pressure, pneumatic system, sensors, range finders, video cameras

The methodology of numerical experiment of laying with closed method by methods of horizontal-directional drilling, brown-screw drilling, forcing, microtonneling has been developed. Some features of the construction of cases for penetration by collectors under existing highways, including general information about the used materials of the cases, are given. A selection of controlled factors and experiment planning, system stability check, results reliability analysis was performed.

Keywords: collector, numerical experiment methodology, microtonneling, horizontal directional drilling, brown-screw drilling, puncture, forcing, motorway, case, reinforced concrete, metal pipes

The article deals with the issue of production of electrode tapes. A mathematical model of the parameters of the electrode tape forming process is described. Mathematical calculations of the porosity, thickness and mass of the active layer are given. A conclusion is made about the composition of the impregnating rolls and the accuracy of dosing fractions. An example of calculating the molding parameters with an active CuO layer is given.

Keywords: electrode tapes, technologies, composite materials, thickness and porosity of the active layer

The calculation of efficiency indicators in the production of grain and leguminous crops is carried out on the example of the Irkutsk region. Given that the production of agricultural products occurs under conditions of uncertainty, the initial data for calculating these indicators are random variables, so the calculations are carried out using a probabilistic break-even analysis based on the Monte Carlo method. The break-even point, invested income, and operating profit are selected as performance indicators. Based on the given initial data of the Ministry of Agriculture of the Irkutsk Region and the Federal State Statistics Service for the Irkutsk Region, point and interval estimates were obtained during modeling. For the listed performance indicators, the models of their calculation, depending on the source data, are given. As initial data there are: the volume of production of grain and leguminous crops; expenses for a production unit; fixed costs; average price per unit of production; the size of the subsidies.

Keywords: operating profit, grain and pulses production, probabilistic break-even analysis, agricultural products, Monte Carlo method

This article discusses the theoretical order and practical solution of the problem of calculating the beam by the initial parameters method using the Mathcad calculation complex. The article describes in Detail and proposes the procedure for creating a universal calculation algorithm and program for any combination of vertical load. . Программа автоматизировано создает эпюры. The program automatically creates diagrams of internal force factors, displacements, rotation angles of beam sections.The article may be of interest to design engineers, specialists in calculating the dynamics and strength of structures, teachers and students of engineering Universities and the construction industry.

Keywords: method of initial parameters, beams, diagrams of internal force factors, beam movement, angles of rotation of sections

The article considers the geological features of the Karasan landslide. The result of mathematical simulation of landslide motion in time is also presented.

Keywords: landslide, landslide slope, mathematical modeling, geomechanical modeling, finite element method, Karasan landslide, anti-landslide protection

In contrast to the classical transport problem, according to the minimum total time criterion, it is assumed that resources are processed both at the source points and at the destination points, the duration of which depends linearly on the volume of the processed batch. This takes into account both the availability of the vehicles involved and their characteristics, such as load capacity. The use of the Hungarian method is justified for the distribution of resources along the available routes. To solve the problem of distribution of available vehicles by starting points, taking into account the load capacity of vehicles, it is proposed to use the method of dynamic programming. An illustrative example and distribution of delivery means using the "Search for a solution" command in MS Excel are considered.

Keywords: transport task, minimum time criterion, processing costs, load capacity

The article deals with modern problems in the field of coordination of working documentation, due to the lack of regulatory documentation that regulates the clear time allotted for the preparation and approval of the developed documentation. The main goal is to obtain averaged time indicators based on the data of standard projects of objects, as well as to determine the degree of mutual influence of factors on the considered terms, in order to apply them in the preparation of a consolidated calendar plan of the organization provided to the technical customer for the conclusion of the contract, as well as to predict and reduce time indicators for the removal of comments and repeated requests.

Keywords: matching, matching organizations, average labor intensity, repeated requests, correlation and regression analysis

It is indicated in the article that the study of the electron bunching process in the drift space of a transit klystron is an urgent task that allows one to establish general laws applicable to more complex models. In this connection, the behavior of the pre-modulated electron beam in the drift space of the transit klystron has been investigated. A numerical model has been implemented that takes into account the effect of space charge fields and the interaction of charged particles with elements of an electrodynamic system. A series of numerical experiments with different values ​​of the current and initial velocities of electrons, as well as their comparison with theoretical data, have been carried out. As a result of numerical experiments, data were obtained that characterize the dynamics of the electron flux in the drift space of the transit klystron at different values ​​of the initial velocity (0.5 s, 0.9 s) and cathode current (10 mA, 1A, 10A).

Keywords: flyby klystron, mathematical model, numerical simulation, large particle method, particle-particle method, drift space, convection current distribution, electron flow, multithreaded calculations, system of differential equations