The banking system occupies a dominant position in the modern market economy. The banking system is directly related to risks, one way or another, affecting the entire asset distribution system. The specificity of resource management in a bank requires the synthesis of methods of financial and economic analysis, the use of accounting methods, strategic planning, budgeting. This article describes a two-level mathematical model of interaction between the Central Bank of the Russian Federation and a commercial bank. For the research, the method of simulation was chosen, the algorithm for constructing the Stackelberg equilibrium was implemented in software.

Keywords: two-level hierarchical model, Stackelberg equilibrium, Central Bank of the Russian Federation, commercial bank, refinancing rate, management parameters, subjects of management

he article provides a comparative analysis of the experimental data obtained as a result of field tests (excavation), with the data of numerical calculations. Mathematical modeling of the experiment was carried out using the Plaxis software package, according to the model of plastically hardening soil. The main task was to compare the obtained data on the decompaction of the soils of the foundation pit with the calculated deformations and analyze the results. The problem was solved in accordance with the experimental data in two settings: in the first case, the variant with inclined slopes of the pit sides was considered; in the second, the problem with vertical slopes was solved. As a result of the calculation, data on the deformations of the soil massif were obtained and analyzed according to the two selected schemes. The best possible convergence of the calculation results with the experimental data was obtained for a pit with inclined slopes, which corresponded to the experimental formulation of the problem. For the case with vertical slopes, the results of deformations of the decompaction of the bottom of the pit turned out to be two times less, which corresponds to the conclusion that the quantitative results of deformation of both the foundation of the pit and its upper side part directly depend on the angle of the slope.

Keywords: experimental pit, experimental data, numerical calculation, deformations of decompression, pit slopes, calculation results

The theme of secure applications is considered, using various techniques and the proposal of a graph calculation model of testograms

Keywords: application security testing, testograms, test trees

The article discusses an optical vector analyzer with high resolution and high accuracy based on optical double-sideband modulation and stimulated Brillouin scattering. A model of an optical vector analyzer is presented.

Keywords: optical vector analyzer, double-sideband modulation, stimulated Brillouin scattering, fiber Bragg grating with phase shift, simulation, Optisystem

Methods of mathematical modeling of complex systems are considered. To construct mathematical models of changes in the electrical capacity of microlayers of magnetic nanofluids, the universal statistical package IBM SPSS Statistics was reasonably adopted. To optimize the construction of models, a database of the electric capacity of a cell with a microlayer of magnetic nanofluid and a program for generating a calculated model of the electric capacity of a capacitor with a magnetic nanofluid for IBM SPSS Statistics and Microsoft Excel were developed.

Keywords: magnetic nanofluid, concentration, microlayer, polarization, electric field, mathematical model, regression model

The article discusses the use of algorithms based on artificial neural networks when working with non-stationary signals, in particular biomedical ones, such as an electroencephalograph signal, to identify and process local signal features. The use of conventional patch electrodes for EEG recording leads to the appearance of noise and requires special signal processing. For this, bandpass wavelet filtering is used. The obtained data are further processed using an artificial neural network to identify information contained in a limited interval in the biomedical signal. To train the neural network, the Levenberg-Marquardt method was used, as the optimal one and meeting the requirements.

Keywords: artificial neural network, electroencephalography, wavelet filtration, biomedicine, non-stationary signal, system analysis

The paper is devoted to cellular automaton modeling based on the class of cellular automata with the Margolus neighborhood. A simulation of the kinetics of gas emission in the final volume of coal, including: convection, diffusion, sorption, is performed. To organize this kind of evolutionary process, the cell-automaton modeling method was supplemented with the Monte Carlo method.

Keywords: cellular automaton, Margolus neighborhood, Monte Carlo method, diffusion, convection, sorption, porous medium, coal

For the long-term operation of a power oil transformer, it is necessary to comply with all regulated checks of its technical condition, prescribed in the instructions. The current regulations provide for daily routine inspection and technical examination at least once a week. Famously, the heating of a power transformer during its operation is linked to the presence of active losses in the windings and core. High power transformers have impressive heat losses. Oil cooling systems are used to prevent that overheating of the transformer and damage to the insulation of the coil windings. The deterioration of the quality of the transformer oil causes an increase in active losses, due to which the efficiency of the power device decreases. This negatively affects the process of converting electrical en-ergy. The conclusion is that the quality of the oil directly affects the longevity of the power transformer. Thus, the most important functional elements from a control point of view are the transformer oil and the coil of the power device. Based on the foregoing, the urgent problem of technical control of electrical substations’ transformers is the development of methods and devices for express monitoring of the functional state of power oil transformers, which allow quick diagnostic information receiving, sufficient for a timely decision on the need for unscheduled repairs or maintenance.

Keywords: power transformer; transformer oil; impedance; diagnostics; functional state; dielectric loss tangent; equivalent circuit; MathCad

The article deals with the priority passage of regulated intersections by public transport using the method of extending the permitting signal. The relevance of the problem under consideration is due to insufficient study of the issue of choosing the optimal control parameters for the method of extending the resolving signal. Using simulation modeling, a study was carried out of the priority passage control process on two- and three-lane road sections. In the course of the experiment, the dependences between the extension time of the allowed signal and the cycle duration were determined at different ratios of the phase coefficients, as well as the optimal distance of the priority activation detectors. The obtained results of the research work can be used in the design of the urban intelligent transport system and when adjusting the control modes in the automated traffic control system of the urban agglomeration.

Keywords: priority movement of urban passenger transport, transport detectors, intelligent transport systems, simulation, traffic light control parameters

The trend to miniaturize and reduce the material consumption of modern electrical products of alternating current, places increased demands on the quality of their individual elements. All electrical products of alternating current (electromagnets, electromagnetic relays, motors) have a moving and fixed parts of the magnetic circuit and at least one working coil. During the operation of electrical products of alternating current, a current flows in the working coil, a working magnetic flux is created in the fixed part of the magnetic circuit, which sets in motion its movable part. The magnitude of the magnetic flux is determined by the design, the mutual arrangement of the parts of the magnetic circuit and the working coil, as well as the number of turns in it and the magnitude of the flowing current. During the working cycle of electrical products of alternating current, the moving part of the magnetic circuit moves relatively stationary, which also leads to a change in the magnetic flux. It is required to know their mechanical, electrical and magnetic properties. Each group of indicators requires the use of its own methods and means of testing electrical products of alternating current. This situation stimulates the search for the integral characteristics of electrical products of alternating current, which allow to draw conclusions about the quality of individual parts and operational properties of the entire product. The article proposes to use the web-ampere characteristic of the operating cycle as an integral characteristic of an electromagnet. To obtain the weber - ampere characteristic of electrical products of alternating current, it is necessary to influence the magnetic circuit with an external varying magnetic field and measure the magnetic flux arising in its cross section with a special sensor. When determining the weber - ampere characteristic of the working cycle, the electrotechnical product of alternating current in assembled form is subjected to testing, which makes it impossible to use magnetic flux sensors. Therefore, the use of existing measurement methods is not possible and therefore it is necessary to develop a method for determining the weber - ampere characteristic of the operating cycle of AC electrical products, which has acceptable accuracy and does not require the use of additional sensors.

Keywords: electromagnets, integral characteristics, functional state assessment, magnetic measurements

The article deals with building a seasonal model with a linear growth of the Winter’s statistic value, on the basis of which the parameters are calculated: the customs value index and the weighted average rate, which are the composition of the calculation formula of customs payments. To build the model, the monthly data of the customs statistics on imports of 28 commodity group “Products of inorganic chemistry; inorganic or organic compounds of precious metals, rare earth metals, radioactive elements or isotopes” of the Customs Nomenclature of the external economic activity of EAEU from 01.01. 2018 up to 31.12.2020 are used in the region of activity of the Southern Customs Administration.

Keywords: time series, econometric modeling, forecasting, adaptation parameter, seasonality coefficients, adaptive model

The article deals with the forecasting of direct material damage to urban areas depending on the number of fires based on official data of the Ministry of Civil Defense, Emergencies and Elimination of Consequences of Natural Disasters, presented in state reports on the state of protection of the population and territories of the Russian Federation from natural and man-made emergencies for five years, based on the model of correlation analysis, which allows us to determine the degree of mutual influence of the parameters under consideration and the linear regression responsible for determining trends for subsequent years. The analysis of the reasons associated with the lack of the possibility of assessing the damage resulting from the fire of the structures of the building or its premises and its subsequent extinguishing in order to increase the economic efficiency of the cost examination during the restoration of real estate is an auxiliary basis for the construction of a correlation-regressive forecasting model.

Keywords: fires, cost assessment, cost of restoration repairs, real estate objects, economic efficiency, statistics, direct material damage, correlation and regression analysis

The article discusses transfer learning methods of convolutional neural network VGG16 for solving the problem of object recognition in images from UAVs (unmanned aerial vehicles). In the absence of the required amount of initial information, it is proposed to work on the augmented dataset. The article presents the architecture of a neural network and considered its action on a specific example. When developing a service, loading the image and displaying the results of the model, was used Flask framework, training of models took place using a cloud service Google Colab based on Jupyter Notebook.

Keywords: deep learning, neural networks, object recognition, data augmentation

The continually increasing rate of human economic activity leads to changes in many natural systems. Their restoration is one of the most important tasks today. For this purpose, protected areas have been created, such as natural reserves, national parks, and wildlife sanctuaries. National parks are of particular interest, as they are the only protected areas listed above where tourism is allowed and organized. However, their activities cannot exist without sufficient financial support. This article describes a two-level optimal control model of the national park activity. For the purpose of exploring and analysing the proposed model, an algorithm that can be used to find the Stackelberg equilibrium guaranteeing the sustainable development of the national park is proposed and implemented in software.

Keywords: two-level hierarchical model, Stackelberg equilibrium, national park, leader, follower,subjects of management ,control parameters

Mathematical modeling and optimization of the process of controlling the sulfate regime when the apatite load changes on the phosphoric acid extractor is considered. It is shown that the preservation of the "sulfuric acid/apatite" ratio with a sharp change in the apatite consumption leads to a violation of the technological regulations for SO3. The algorithm of correction of this ratio in the transition mode is developed, which minimizes the probability of violation of the regulatory indicators. A variant of implementing the optimal apatite load correction procedure using stand-alone scenarios is proposed. The results were confirmed during the simulation.

Keywords: algorithm, mathematical model, stabilization of the sulfate regime, extraction phosphoric acid, change in the load on the extractor, phosphorus yield coefficient from apatite, optimization, autonomous scripts

In modern times due to the growth of mass production of electronic devices, it becomes necessary to quickly and accurately verify their characteristics. At the same time, device testing, as a rule, includes a set of different types of checks performed at different stages of the production process. In particular, the analog signature analysis method is used for these purposes. It allows you to quickly detect faults at the component level, which makes it useful in various stages of production, such as incoming inspection, testing printed circuit boards or repairing faulty devices. This article discusses the basic principles of the method, as well as the features of its application.

Keywords: analog signature analysis, component level testing, current-voltage characteristic, fault localization

The purpose of this research is analysis of the possibility of using classical neural networks for the malignant neoplasms recognition on skin digital images. In this study was used International Skin Imaging Collaboration database including 6594 dermatoscopic images. At the first stage of the study, digital skin images were classified into malignant and benign neoplasms using the IBM SPSS Statistic tool to automatically select the architecture for artificial neural network. At the second stage was built architecture of artificial neural network, which include one hidden layer. At the third stage was used architecture of an artificial neural network with two hidden layers. In the course of the study digital skin images classified with the highest value of the accuracy indicator (0,752 [0,736 ; 0,768]) during classification using the architecture of an artificial neural network, which includes two hidden layers. The sigmoid was used as the activation function for the hidden layers. The hyperbolic tangent was used as activation function for output layer. With this value of the accuracy, the specificity of the diagnostic method was obtained – 0,813 [0,802 ; 0,824], as well as the value of the sensitivity – 0,665 [0,637 ; 0,691]. Thus, artificial neural networks can be used as a method for skin malignant neoplasms diagnostic on digital images.

Keywords: artificial neural networks, digital skin images, machine learning, image classification, skin cancer

When designing security systems for buildings and structures, the technical specification specifies the required characteristics of the equipment. On the basis of the technical specification, a certain number of solutions (projects) from different designers and suppliers can be formed. These projects may differ in equipment, method of installation and maintenance, different degrees of functional reserve and the possibility of expanding the system if necessary. At this stage of equipment selection, the engineer is faced with the problem of choosing one optimal option from the presented subset, since all projects (solutions) meet the requirements of the technical specification. The presented algorithm for selecting the elements of the security system of real estate objects is based on the construction of a complex assessment model. The characteristics by which the equipment will be compared are determined. The degree of importance of each characteristic is determined. A comprehensive assessment of each alternative is calculated. The proposed approach avoids the negative consequences of subjectivism arising from the influence of the external environment.

Keywords: multi-criteria task, algorithm, selection task, security system, ranking, design, terms of reference, criterion, complex evaluation, model

This article proposes the development of a method for fixing changes in the galvanic skin response and human pulse, depending on the viewing of a video fragment, which presumably causes a certain emotional reaction of a person. The creation of a prototype device on the Arduino Leonardo platform and compatible with this platform sensors for fixing galvanic skin response and a human pulse sensor is described, with the help of which data is collected for further use in determining the emotional state of a person.

Keywords: galvanic skin reaction, pulse, emotional state, arduino, emotion

The paper deals with the issues of modeling the processes of laser radiation absorption in contact with a biological object, which leads to a significant increase in temperature in the interaction zone. For organic tissues, when the temperature rises above a certain value, their damage begins, and then the processes of destruction are observed. With an increase in the speed of movement of the laser beam on the surface, the width of the incision and the level of injury decrease, as the time of interaction of the radiation with the tissue decreases. In this paper, we consider various models for performing calculations: using complex ratios taking into account the thickness or using expressions for an object of semi-infinite thickness. The regularities of the growth of the average temperature and the process of establishing the thermal balance on the surface of the body, depending on the parameters of the laser radiation pulses, are also investigated.

Keywords: computer simulation, medical laser, laser incision, biological tissues, temperature field, level of injury, pulse packet, speed of movement

a study of a ventilation system with a local recirculating diffuser was carried out. A three-dimensional model of the office space has been built. Using the STAR-CCM + hydrodynamic computing complex, a numerical simulation of the ventilation system has been performed. The calculation results are analyzed, the advantages of the investigated system are given.

Keywords: ventilation systems, local recirculating diffuser, indoor air quality, energy saving, numerical simulation, STAR-CCM +

Bar structures are widespread in construction due to their economy, freedom of design shapes and sizes. As a result, automation of design and calculation of such structures is an urgent task. As part of the study, the task of developing a software module that generates output documents of a web application for calculating bar metal structures has been implemented. The software is developed on the .NET platform using the Spire.Doc and netDxf plug-in libraries. The developed module generates AutoCAD-compatible drawings and text reports in accordance with Russian standard SP 16.13330. The possibility of automated generation of reports allows more efficient use of the computing complex in production, cost reduction and calculation accuracy increase.

Keywords: Design in construction, bar structure, computing system, web development, report, drawing

Low-orbit satellite communication systems (LowSCS) are successfully used to organize stable communication in Northern latitudes. With the help of theLowSCS, effective management and monitoring of the process of production and transportation of hydrocarbon raw materials is provided. This approach allows us to ensure minimal costs for the extraction and delivery of oil and gas from fields located on the shelf of the Arctic Ocean. As the number of countries engaged in the development of Arctic Ocean deposits increases, so does the number of LowSCS groupings. To prevent the possibility of interception and imposition of a delayed command to control the intruder satellite, it is necessary to increase the information secrecy of the LowSCS with the help of "friend-foe" identification systems for the spacecraft. At the same time, to ensure high imitability in such systems, it is proposed to use zero-knowledge authentication protocols. To increase their efficiency, the article suggests using the codes of residual number system (RNS). The novelty of this idea is that the use of parallel SOC codes will reduce the time spent on performing arithmetic operations implemented in authentication protocols. And this, in turn, will lead to an increase in the information secrecy of the NSSS, so the probability of selecting the correct response signal by the intruder satellite decreases. Therefore, the purpose of the article is to develop authentication protocols for low-orbit spacecraft based on parallel codes of residual class systems, the use of which will reduce the time for satellite identification.

Keywords: satellite identification system, zero-knowledge authentication protocols, residue number system

This article discusses the algorithms used for the operation of the chatbot. Within the framework of these algorithms, a general approach to the operation of dialog systems is considered. And the algorithm of the dialog system is proposed, based on a general approach, which includes a natural language processing module. The algorithms that will be applied to the chatbot to search for products of interest to the user are also presented. Among the considered algorithms are such as the algorithm of interaction between the user and the chatbot, the processing of user requests and the algorithm of natural language processing. A modified algorithm for natural language processing is also presented, taking into account the necessary requirements.

Keywords: chatbot, natural language processing, user request processing, named entity recognition, dialog manager, dialog system

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