Nowadays, numerical methods are widely used to realise complex calculations.Verification of the correctness of the numerical calculation results is a relevant task. The validity of the results can be confirmed by determining the stress-strain state by various methods. This paper presents the results of the calculation of thin isotropic ring spherical shells of constant thickness with half-shell angle in the range of (90-170) degrees by two numerical methods. The results of solving the system of differential equations of the general moment theory of shells with the use of the computer mathematics system (Maple 2017) and the finite element method (FEM) are discussed. The given examples show that the calculation results with the use of the selected finite element KE-44 coincide with an accuracy of 10-15 % for shells with a half-shell angle of 120 degrees. When the angle is increased to 170 degrees, the difference in function values becomes significant. The paper gives some examples of calculation of ring spherical shells under the action of one and three annular loads. The variation of axial and radial displacements, of meridional bending moment for shells with the ratio of radius of the curvature to shell thickness 25, 50, 100, 200 is shown. Plots of meridional bending moment and moment isopole are given.

Keywords: elastic, spherical shell, numerical method, computer mathematics system, finite element method.

The article discusses the use of simplex methods of experiment planning to determine the optimal composition of composite building materials. Composite building materials are multicomponent systems, so their properties depend on a large number of factors that are diverse in nature and influence. The use of orthogonal plans is not able to adequately describe experimental data with a wide range of varying factors. Therefore, the article proposes to use simplex-lattice Scheffe's plans. A complete third-order model was developed to determine the optimal composition of the filled cement composite, and a regression equation was written. The adequacy of the equation was confirmed at the control points of the plan using the Student's criterion. The proposed planning method can be used to optimize the composition of multicomponent systems.

Keywords: multicomponent system, optimization methods, composite building material, experiment planning, simplex plans, Scheffe's polynomial, regression equation

A Simulink model of a lightweight aircraft is being studied as part of the Aerospace Blockset package, including a system model of the aircraft, an environmental model, a model of pilot influences, and a visualization block. The structure of the flight model is considered and models of the effects of the environment and wind are disclosed in detail, consisting of blocks of physical terrain features, wind models and an atmospheric model, a gravity model, each of which is set to an altitude. The Wind Shear Model block calculates the amount of wind shear as a function of altitude and measured speed wind. The Discrete Wind Gust Model block determines the resulting wind speed as a function of the distance traveled, the amplitude and length of the gust. The turbulence equations comply with the MIL-F-8785C specification, which describes turbulence as a random process determined by velocity spectra. Simulation results are presented that reflect changes in the trajectory of movement under various wind influences specified in the wind speed gradient block.

Keywords: modeling, airplane flight, Simulink, Aerospace Blockset, crosswind, turbulence, turbulence equations, gravity model, motion trajectory

The paper presents an algorithm for modeling production and economic characteristics for obtaining crop products, with the help of which planning problems are solved using multi-level parametric programming methods under average and unfavorable operating conditions for commodity producers. Since time series of characteristics associated with the production of products can be described by trends to assess adverse events, an algorithm for their identification was used based on the construction of multi-level trends according to the idea of ​​​​the hierarchical structure of the time series. When using this algorithm, a sequence of local minima is formed from the original series, a trend is built, and levels located below this trend, called unfavorable events, are identified. The assessment of the probabilities of these events is determined by the distribution law, which describes a number of differences in actual data and trend values ​​of a sequence of local minima. In the absence of trends and considering series of characteristics in the form of random variables, statistical and physical criteria are applicable to identify unfavorable events. As such, it is proposed to use the average value of local minima. Of the adverse events received, the smallest of them are distinguished, which represent rare events. Based on the identified events and other characteristics, the problem of optimizing the production of agricultural products is formed, the solution of which allows us to obtain optimal production volumes in accordance with maximum incomes corresponding to the calculated probability of events. A comparative analysis of planning results under average conditions and taking into account unfavorable events shows the likely losses of commodity producers at the enterprise and municipal district level.

Keywords: parametric programming, trend, adverse event, production and economic characteristics, crop production, losses, risks

motion of the body are obtained, which can only be solved numerically. The equilibrium equations are solved and the basic stationary modes of body motion are obtained. The main result is the most gentle body planning mode. In the matlab computer mathematics system, a set of programs is written that searches for a numerical solution and outputs trajectories. The movement of the modes under consideration is modeled and the stability of the main modes is looked at using numerical calculations.

Keywords: body, planning mode, stability, geometric dimensions

Numerical methods for calculating shells provide a wide range of solutions when varying various parameters. The object of this study is a mathematical model of thin isotropic elastic shells of revolution of constant thickness. The problem is solved from the position of moment theory.To determine the stress-strain-state of the shell, the solving system is obtained by transforming the basic systems of equations of rotational shells by moment theory and the variables separation. All SSS and load components are decomposed into Fourier series along the circumferentail coordinate. A programme in the Python programming language was written to verify the numerical solution by a computer mathematics system (CMS-Maple 17). Matplotlib library was used for plotting graphs. Examples of numerical calculation of ring spherical shells for the action of ring loads are given. The variants of action of one and two ring loads on shells with different conditions of support along the contours and different half shell angles are presented. The difference between the calculation results of the two methods for bending moment functions and displacement functions is tabulated. The highest value of the difference is 0.0015%. Plots of the variation of meridional bending moment under the action of two ring loads are presented. The variants of rigid pinching along the contours and hinged support are considered. Exsmples are given for shells with the ratio of radius of curvature to shell thickness equal o R/h = 25, 50, 150, 200. Considered of the half shell angles equal to 90, 100, 130 degrees.

Keywords: rotation shell, spherical, isotropic, elastic, computer mathematics system, Python programming language

Automatic classification of electrocardiogram signals will allow providing timely medical care to patients when providing first aid. Neural network models of electrocardiogram signal classification, including the stage of preliminary signal processing, allow increasing the accuracy of classifying electrocardiograms into a particular category of arrhythmia. The paper presents a computational method for preliminary processing of electrocardiogram signals, including noise reduction using discrete wavelet transform and extraction of morphological features using frequency analysis methods. The results of modeling the classification of 12-channel electrocardiogram signals using the stage of their preliminary processing showed an increase in classification accuracy by 23.2% compared to classification without preliminary signal processing.

Keywords: electrocardiogram signal classification, long-term short-term memory neural network, metadata, signal preprocessing wavelet transform, spectral analysis, PhysioNet Computing in Cardiology Challenge 2021

The article discusses standard models of titanium dioxide-based memristors. A memristor is similar to a memory resistor and demonstrates a nonlinear resistance characteristic in which the charge parameter is a state variable. They can be used to create new types of electronic devices with high energy efficiency and performance, as well as to create machines that can learn and adapt to changing environmental conditions and in many practical applications: data storage memory (binary and multilevel), switches in logical electronic circuits, plastic components in neuromorphic artificial systems intelligence based on nanoelectronic components. It has been shown that when voltage is applied to charged ions, they begin to drift, and the boundary between the two regions shifts. When a sinusoidal alternating voltage of a given frequency is applied to the memristor, the shape of the volt-ampere characteristic (VAC) resembles a Lissajous diagram centered at the origin.

Keywords: memristor, model, voltage characteristic, nonlinearity

The article addresses the issue of determining the ultimate eccentric compressive longitudinal force from an external load acting on a compressed reinforced concrete element. The calculation assumptions are adopted in accordance with the current code of practice SP 63.13330.2018. The transformation of the initial formulas given in this code allowed the explicit solution of the cubic equation with respect to the compressive longitudinal force without the need for iterative calculation methods. The solution thus obtained can be employed in the design process to determine the optimal section dimensions.

Keywords: reinforced concrete, excentric compression,ultimate forces

This article presents the results of simulation of the stress-strain state of the base under dies with a stepped shape of the bottom of the support. Numerical modeling was performed using Plaxis 2D. The results of modeling stamps with different angles of descent of steps with an equal surface area of ​ contact with the soil showed the dependence of stresses and displacements on this parameter.

Keywords: effective foundation, shallow foundation, columnar foundation, die with convex support surface, stepped sole, soil mechanics, settlement of foundations

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

The article studies the possibility of using the continuous form of the maximum consistency method when constructing regression models to calculate the forecast values of the air transport passenger turnover indicator in the Russian Federation. The method under study is compared with classical methods of regression analysis - least squares and moduli. To assess the predictive properties of the methods, the average relative forecast error and the continuous form of the criterion for the consistency of behavior between the calculated and actual values of the dependent variable are used. As a result of the analysis, a conclusion was made about the possibility of using the method under study to solve forecast problems.

Keywords: least squares method, continuous form of the maximum consistency method, modeling, passenger turnover, air transport, adequacy criteria

The article examines the application of the method of mathematical planning of an optimal experiment in determining the strength characteristics of reinforced soils. For the analysis, a multicomponent soil system was studied, consisting of unsalted and saline soils reinforced with bitumen with cement additives and surfactants. During the planning of the experiment, factors affecting the strength characteristics and their levels, as well as the intervals of variation of factors, were determined. As a result of solving the problem, mathematical models of adhesion and angle of internal friction of reinforced soils were obtained. Based on the obtained regression equations, the main conclusions were drawn.

Keywords: stabilized soils, complex soil strengthening, experiment planning, complete factor experiment, mathematical model, regression equation

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 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 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 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 validity of analytical models of the process of one-parameter selective assembly of two elements was evaluated by comparison with the results of simulation modelling. A series of machine experiments including one-factor and two-factor experiments were carried out. At the accepted levels of variation of factors, the confidence interval of the probability of yield of good products from the initial population of elements that did not pass sorting was determined using Student's criterion at the given level of significance and number of degrees of freedom. Comparison of the simulation results revealed the facts of reaching the specified process indicator, determined by the analytical model, for all experiments within the confidence intervals and the presence of relatively small deviations from their centres.

Keywords: selective assembly, analytical model, simulation model, measurement error, simulation results

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

The article is devoted to the study of the flow rate depending on the pressure in the gas supply system of the plasma head. The problem was solved by conducting a computer experiment with subsequent verification of the results by a full-scale experiment. The laboratory plasma installation MAK-10 assembled on the basis of the IMET UB RAS, used in the processes of coating, powder production and surface modification of parts, was simulated. The computer experiment was carried out using the SolidWorks Flow Simulation software package. As a result of the work performed, the distribution of the flow rate along its axis was demonstrated during the operation of the plasma installation with a pressure in the gas supply system of 0.1; 0.2 and 0.3 MPa. Recommendations for conducting coating, powder production and surface modification processes have been developed, which have practical benefits for consumers of process equipment.

Keywords: mathematical model, flow, velocity, pressure, plasma method, powder production, coating, surface modification

The general characteristics of the innovative RAID-60 data storage system, which combines the best aspects of RAID-6 and RAID-0E technologies, as well as the reliability model of this data storage sys-tem, are presented. The main purpose of this connection is to provide outstanding performance with maximum data redundancy. The arti-cle discusses in detail the structural analysis, advantages and various scenarios for the use of the specified RAID-60 data storage system and the proposed model of its reliability. An important aspect is also the comparison of the RAID-60 system with other widespread vari-ants of data storage systems, such as RAID-0, RAID-1 and RAID-5, as well as with the reliability models of these systems. Particular at-tention is paid to the formula that allows you to calculate the average operating time to failure of a disk array. Also, for completeness of the analysis, attention is paid to plotting the probability of a RAID-60 failure (P(t)) over time (t). This graph is an important tool for visu-alizing the dynamics of reliability of data storage systems.

Keywords: RAID-60, reliability, disk array, data redundancy, manufacturer, parity blocks, data storage

The study of the influence of the number of layers of glass composite pipe on dynamic loading, including operation in seismically active areas, is conditioned by compliance with the requirements of the latest documents in the field of construction standard control. Mechanical characteristics of glass composite pipe depend on elastic and strength properties of glass fibre, silica sand and binder, their ratio and bonding strength between layers. The key parameter of glass composite pipe compliance with the given requirements is ring stiffness. The strength of the composite material is determined using the rule of mixtures. The properties of the glass composite pipe using the rule of mixtures are determined. The influence of the number of layers of glass composite pipe on its elastic-strength properties is considered. The experiment with uniaxial compression of the pipe link is simulated in Midas GTS NX software package. The maximum load at which the sample reaches 5% deformation was determined. According to the results of the study, it was obtained that the best elastic-strength and operational properties have three-layer composite structure.

Keywords: glass composite pipe, layer scheme, earthquake resistance, continuous winding method, elastic-strength properties

Algorithms and structures of spatial partitioning kd-tree, BVH are considered and studied in relation to the problem of modeling the flow of air around a body of complex shape. The use of these algorithms makes it possible to significantly reduce the computation time when searching for collisions of air particles with each other and with a streamlined body.

Keywords: collision detection, computational geometry, data structures and algorithms, kd-tree, BVH

The paper offers one of the variants of construction and use of fuzzy query mechanism for modeling of telecommunication network state estimation. The modular architecture of the application is considered in detail, the logic of calculating the degrees of belongingness to each term of the selected linguistic variables is described, the stages of the algorithm of work with the mechanism of fuzzy queries are given.

Keywords: fuzzy query, search, membership function parameters, state estimation modeling, database, knowledge, fuzzy classification

The article is based on the results of a scientific study on modelling the operation of the system ‘foundation - ground mass’ of a special type of deep foundation - gantry piles in conditions of ground mass during the construction of the overpass of the M-12 ‘Vostok’ highway. Gantry inclined piles are designed to transfer more load to the foundation than traditional vertical piles. The purpose of this study is to select the angle of inclination of gantry piles for overpass support on the basis of mathematical modelling. The scientific novelty consists in the selection of the gantry pile foundation design for the support of a motorway overpass by mathematical modelling.

Keywords: gantry piles, deep foundation, overpass, modelling, finite element method, soil massif, stresses, deformations, stanchion, foundation-soil massif system