The article considers modeling of nonlinear electrical conductivity of a biological cell using the equivalent circuit method. The paper proposes a nonlinear model of the electrical conductivity of a biological cell based on the use of nonlinear active and passive elements. The main mechanisms that determine the nonlinear nature of the electrical characteristics of a cell, including the phenomena of cell membrane polarization, are considered. To verify the model, a comparison of calculated and experimental data on the electrical parameters of biological cells is carried out. It is shown that the use of a nonlinear equivalent circuit allows more accurately reproducing the real behavior of cells in a wide range of applied voltages. The presented modeling technique can be applied to study the electrical properties of various types of biological cells, as well as to develop new electronic devices interacting with living systems. The article considers a complex nonlinear dependence of the electrical conductivity of a biological cell on voltage, which is caused by the interaction of two ion channels with different characteristics and resonance effects created by a series circuit. The method of equivalent circuits made it possible to create a single model that combines components responsible for ionic conductivity, capacitive properties of the membrane and resonance phenomena associated with the presence of electropores.

Keywords: mathematical modeling, equivalent circuit method, software, biological cell, computational research, electrical conductivity

In the modern world, it is increasingly necessary to process geographical information in a variety of forms. This paper discusses the concept of «tile», its purpose, features, as well as the process of retiling, which is a method of creating and updating tiles. This technology helps to increase the efficiency of modern cartographic services, reducing the loading time of maps. The main stages of the development of a microservice implementing the retiling logic are presented sequentially. The main data provider is the OpenStreetMap (OSM) open source project. The spatial data set is a core OSM product and contains up-to-date geographic data and information from around the world. The technology stack is based on the Python language, to which specialized modules for working with tiles are added, as well as a library for implementing a simple and high-quality API.

Keywords: Python, tile, retiling, OpenStreetMap, microservice, Flask-RESTX, mercantile

One of the most reliable methods of identity verification are biometric authentication methods. There are two types of methods: static and dynamic. Static methods include fingerprint scanning, 3D facial recognition, vein patterns, retina scanning, etc. Dynamic methods include voice verification, keyboard handwriting and signature recognition. As of today, static methods have the lowest type I and II error rates, because their primary principle of operation is based on capturing a person's biometric characteristics, which do not change throughout their lifetime. Unfortunately, this advantage, which accounts for such low type I and II error rates, is also a drawback when implementing this method for widespread use among internet services. If biometric data is compromised, user can no longer safely use method everywhere. Dynamic biometric authentication methods are based on a person's behavioral characteristics, allowing user to control information entered for authentication. However, behavioral characteristics are more vulnerable to changes than static, resulting in significantly different type I and II errors. The aim of this work is to analyze one of the dynamic methods of biometric authentication, which can be used in most internal and external information systems as a tool for authorization or confirmation of user intentions. Biometric user authentication based on their handwritten signature relies on comparing unique biometric features that can be extracted from signature image. These unique features are divided into two categories: static and dynamic. Static features are extracted from signature image, based on characteristics such as point coordinates, total length, and width of the signature. Dynamic features are based on coordinate dependency of the signature points over time. More unique features are identified and more accurately each is weighted, the better type I and II error rates will be. This work focuses on algorithms that extract unique features from static characteristics of signature, as most signature peculiarities are identified from the dependencies of writing individual segments of the signature image.

Keywords: static algorithms, metrics, signature length, scaling, signature angle

Currently, to access information contained in autonomous and external information systems, user must pass an authorization process using modern methods of identity verification, such as: password protection, protection based on one-time codes, electronic signature-based protection, etc. These methods as always have worked well and still continue to provide secure access, however, biometric authentication methods are more reliable when access to confidential information should be limited to a single user. Today, there are two types of biometric authentication methods: static and dynamic. Static methods based on a person's biological characteristics that remain with them throughout their life, while dynamic methods based on a person's behavioral characteristics. Static methods are considered some of the most accurate, because most biometric parameters do not change over a lifetime. However, this method should only be used if chance of data compromise is very low, because in the event of leak, user will not be able to continue using these types of methods anywhere else. Dynamic methods, due to their behavioral characteristics, do not have sufficiently satisfactory type I and II error rates, as they directly depend on user's psychological and physical state. However, unlike static methods, user can control the information that will serve as a secret key for authorization in the future, so in case of a leak, user can always change the contents of the key for current and future services. This work examines one of these dynamic methods of biometric authentication: verification by handwritten signature. This method is considered more attractive among its counterparts, as in case of successful type I and II error rates, it can be applied in most existing services as a tool for authentication and confirmation of user intentions when signing various types of documents. The article discusses the main algorithms for verifying handwritten signatures by identifying unique dynamic features, dependent on the temporal and coordinate values of the analyzed samples of handwritten signatures.

Keywords: dynamic algorithms, feature extraction, signature writing time, proximity of point coordinate functions, Fourier transform

The article is devoted to the development of a mathematical model and a software package designed to automate scientific research in the field of financial industry news analysis. The authors propose an approach based on the use of graph theory methods to identify the most significant scientific hypotheses, the methods used, as well as the obtained qualitative and quantitative results of the scientific community in this field. The proposed model and software package make it possible to automate the process of scientific research, which contributes to a more effective analysis of it. The research results can be useful both for professional participants in financial markets and for the academic community, since the identification of the most cited and fundamental works serves as the starting point of any scientific work.

Keywords: software package, modeling, graph theory, news streams, Russian stock market, stocks, citation graph

The article presents the state of technology of websites for designing robots with artificial intelligence. The image of a modern technical site-book as a place for the development of artificial intelligence applications is considered, the possibility of executing algorithms from the page to ensure the connection of robots with real and virtual objects is shown.

Keywords: mathematical network, technical website-book, artificial intelligence, algorithms executed on the website-book, network development of robots

The paper presents a brief overview of publications describing the experience of using mathematical modeling methods to solve various problems. A multivariate piecewise linear regression model of a steel company was built using the continuous form of the maximum consistency method. To assess the adequacy of the model, the following criteria were used: average relative error of approximation, continuous criterion of consistency of behavior, sum of modules of approximation errors. It is concluded that the resulting model has sufficient accuracy and can be used for forecasting.

Keywords: mathematical modeling, piecewise linear regression, least modulus method, continuous form of maximum consistency method, steel company

The features of the (m,m) implementation scheme of visual cryptography are considered, which differs from the existing ones by the formation of shadow images (shares) of an image containing a secret. The proposed approach is based not on the decomposition of the secret image into shares, but on their step-by-step transformation by multiplication by orthogonal Hadamard matrices. The images obtained during each transformation of the stock are noise-resistant in the data transmission channel.

Keywords: image with a secret, image decomposition, image transformation, orthogonal Hadamard matrices, two-way matrix multiplication, noise-resistant image encoding

The article deals with the issues of major repairs of rooms for radiation diagnostics in medical institutions, which is becoming more and more relevant in modern conditions. Functional diagnostics plays a key role in early detection of diseases, correct diagnosis and effective treatment of patients. With the development of technology and the advent of high-tech diagnostic equipment, there is a need to upgrade medical institutions to integrate such equipment. The study, conducted on the basis of an analysis of regulatory and technical documentation and scientific papers, highlighted the main stages of major repairs of radiation diagnostics facilities, identified the main participants in these stages. Organizational charts have also been developed for each stage, which emphasize the importance of coordination between all project participants, including builders, engineers, architects and medical specialists. The implementation of such schemes helps to minimize time and financial costs, ensures the implementation of all necessary requirements and standards, and guarantees the high quality of the work performed. As a result, we receive an organized repair process that allows medical institutions to effectively use new diagnostic equipment to improve the quality of medical services and improve the diagnosis and treatment of patients.

Keywords: major repairs, healthcare facilities, radiation diagnostics facilities, medical organization, project documentation

Fifth-generation networks are of great interest for various studies. One of the most important and relevant technologies for efficient use of resources in fifth-generation networks is Network Slicing technology. The main purpose of the work is to simulate the probabilistic characteristics of blocking requests for access to wireless network radio resources. The main task is to analyze one of the options for implementing a two–service model of a wireless network radio access scheme with two slices and BG traffic. In the course of the work, the dependence of the probability of blocking a request depending on the intensity of receipt of applications of various types was considered. It turned out that the probability of blocking a type i application has the form of an exponential function. According to the results of the analysis, request blocking occurs predictably, taking into account the nature of incoming traffic. Previously, there are no significant drawbacks in the considered model. The developed model is of great interest for future, deeper and long-term research, for example, using simulation modeling, with the choice of optimal network parameters.

Keywords: queuing system, 5G, two - service queuing system, resource allocation, Network Slicing, elastic traffic, minimum guaranteed bitrate

The paper deals with the problem of choosing the most rational form of spatial metallic cross-barrel coating. Mathematical models of flat structural coating, elliptical paraboloid and hyperbolic paraboloid coatings in SCAD software package based on finite element method are analyzed. Nodal connections of rod elements of coatings are taken according to the system “Kislovodsk”. The obtained parameters of stress-strain state of three different structural coverings allow us to speak about practically identical operation of the structures.

Keywords: structural covering, spatial covering, cross-bar covering, stress-strain state, “Kislovodsk” system, SCAD program complex, finite element method, hyperbolic paraboloid, elliptic paraboloid

The subject of this article is the development of a behavior pattern with AI elements for an opponent bot in the single-player game Steal Tower. The essence of which is to collect resources to build a tower faster than opponents. To create the illusion that the same people are playing against the player, an imitation stochastic model based on the Monte Carlo method for Markov chains has been developed. Based on the results of its tests, balanced system parameters were determined, which are embedded in the behavioral pattern of the bot, which is implemented using the Enum AIStates enumeration consisting of five states: Idle (inactivity), GoTo (movement) and GoToWarehouse (return to the warehouse), Win (victory), Loose (scoring). Each of them has developed functions for the optimal behavior of the bot given in the article. So for the GoTo state, functions have been created that analyze the benefits of different types of behavior: steal or collect, or walk to the warehouse or to the tower.

Keywords: game intelligence, behavioral pattern, live world emulation, bot behavior scenario, state structure, Markov chains, Monte Carlo method, simulation model, Unity environment, C# language

The problem of increasing consumption of heat and energy resources in the high-rise residential sector in the conditions of dense urban development becomes more relevant every year both for its population and for management companies. In order to reduce operating costs, to reduce the dependence of engineering systems of high-rise residential building on urban infrastructure, it is proposed to introduce some energy-efficient organisational and technological solutions in the designed apartment building. In the course of the study, on the example of a high-rise 25-storey residential building in the city of Rostov-on-Don, a comparison of operating costs of thermal energy for heating with the use of energy-saving materials and structures, and costs in typical conditions of construction. The results of this work will allow, from a practical point of view, to analyse the feasibility of using such energy-efficient building envelopes and materials as foil PIR-insulation, low-emission four-chamber glazing, "green" roofing in high-rise housing construction.

Keywords: energy efficient building envelopes, heat consumption, heating costs, high-rise apartment block, economic analysis, sustainable construction

When studying the problems of water filtration to a single horizontal imperfect drain of finite length, in a system of interacting horizontal imperfect drains, it is necessary to consider spatial (three-dimensional) filtration problems. Unlike flat (two-dimensional) problems, spatial filtering has been studied in less detail, since it is difficult to obtain rigorous solutions to their problems.

Keywords: water supply facilities, filtration, equipotentials, drainage, borehole, pressure reservoir, drain, pressure, inflow, reservoir, watercourse

A new numerical method for calculating weather conditions has been developed for airborne radar systems for Arctic purposes. Based on the numerical method obtained in the study, software was developed that takes into account various models of electromagnetic wave propagation in various weather conditions. The results of calculations for estimating the detection range of dangerous weather conditions are presented. This assessment indicates that the threshold for detecting adverse weather conditions can be reduced. The basis for lowering the threshold without deteriorating the resulting probabilities of correct detection and false alarm is the fact that the occurrence of cases of false detection is possible only when a certain total extent of difficult weather conditions is reached, which can already be considered dangerous for the flight. The features of the formation of reflected signals from Arctic rain clouds, turbulence over a snowy desert and wind shear are considered. It is shown that all of them are characterized by lower radar reflectivity, therefore the resulting detection ranges are less than those that can be obtained at more southern latitudes, but at the same time they are sufficient for the navigation of UAVs or small aircraft.

Keywords: airborne radar, numerical methods for assessing weather conditions, weather navigation in polar latitudes, UAV navigation, hazardous weather formation