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Іndustrial synthesis of gas hydrates is a promising area for storage, transportation and utilisation of natural gas. The aim of this work is to evaluate the factors that affect the efficiency of gas hydrate synthesis, in particular, the influence of gas microbubble generation. To achieve the goal, the following tasks were solved: the experimental unit was developed and assembled; the experimental research methodology was proposed; experimental data were obtained and their statistical analysis was performed; a mathematical model of hydrodynamic and heat and mass-exchange processes in the nozzle was developed; оn the basis of the mathematical model, a calculation program was created which allows analyzing the nozzle operation in different thermobaric conditions under different hydrodynamic regimes. The most important are the results of experiments, which allowed us to determine the factors that have the greatest influence on the intensification of propane hydrate synthesis: the presence of gas microbubbles, liquid temperature, gas temperature, gas pressure in the reactor and others. The influence of individual factors and the presence of gas mixture microbubbles on the intensity of mass transfer processes of hydrate formation in the reactor was determined. The influence of nozzle design features on the efficiency of hydrate formation was analyzed. The significance of the obtained results is to expand knowledge about the influence of various factors on the intensification of gas hydrate synthesis. The research results can be used for designing industrial plants for gas hydrate synthesis.

Background. The using of mirror asymmetric chemical compounds for doping quartz makes it possible to metamaterial creation that has the chirality property. In such a compositional structure, unusual effects may arise when interacting with an optical wave. Aim. We calculate the transmission and reflection of a linearly polarized optical wave through a multilayer structure consisting of two doped quartz glasses separated by two air gaps. Methods. Based on a homogeneous mathematical model of a chiral metamaterial, taking into account the dispersion of the dielectric constant and the chirality parameter based on the matrix method, a system of linear algebraic equations is obtained for the complex reflection and transmission coefficients of an electromagnetic wave of linear polarization. Results. An analysis of the frequency and angular characteristics of the modules of the reflection and transmission coefficients was carried out at various values of the quartz doping level. It is theoretically predicted that at some wavelengths, most of the incident optical energy can be concentrated in the air gaps of the multilayer structure. Conclusion. The data obtained as a result of calculations can be used in the development of planar structures for frequency-selective concentration of energy in the visible and infrared spectrum based on quartz glasses doped with chiral chemical compounds.

A distinctive feature of Roots type vacuum pumps is the selective of pumping, which is due to the dependence of reverse flows on the type of gas. To study this phenomenon, a mathematical model of the work process is used, based on solving differential equations of a system with variable mass. Comparisons of the experimental and calculated values of pumping speed and pressure increase for helium, argon and air show a discrepancy of no more than 10 %. Calculations have shown that under viscous flow conditions, switching from pumping argon to helium reduces pumping speed by more than 10 % and pressure increase by 50 %.

Objective. The purpose of the study is to develop a mathematical model for constructing a matrix of thermal conductivity coefficients under low-temperature exposure to the multilayer epidermis of biological tissue. Method. The research is based on methods of thermo dynamic analysis, full-scale and computational modeling of processes under low-temperature influence. Result. A mathematical model of the matrix of thermal conductivity coefficients under low-temperature effects on biological tissue has been developed. Heat transfer in a multilayer medium under low-temperature influence on biological tissue is presented as a process with a discrete step in time and coordinate. Thermal properties are evenly distributed throughout the volume of layers of biological tissue. For exposure to cold, layers of the epidermis of biological tissue were used, divided into uniform identical cells, where the cell area of the biological tissue was taken to be equal to one. Conclusion. The results obtained in this work can be useful to specialists who deal with modeling problems with free boundaries.

Practical usefulness of factor-vector autoregression has been considered, which makes it possible to study macroeconomic processes impact on the monetary policy state, to conduct full-scale monitoring and to identify economic growth impact on monetary policy. Publications devoted to the issues of unstable economic development and mathematical models describing the process of economic dynamics under conditions of high inflation and unstable development have been analyzed. The basic scenario in economy has been given. Monetary policy impact on macroeconomic variables using vector autoregressive (VAR) models has been studied. The FAVAR model with international reserves as the monetary policy variable and MIACR where the responses of one-year government bond rate and consumer index were positive have been estimated as the main instruments. The impulse responses shown indicate that the Russian authorities had a lack of monetary policy independence due to the country’s high dependence on the oil and natural gas sectors, which does not reveal evidence of monetary policy impact on lower consumer prices.

At the moment, the use of digital models in the development of oil and gas fields is an effective tool for making informed tactical and strategic decisions to maximize the extraction of hydrocarbon reserves in a field. At the same time, the permanent increase in the share of hard-to-recover reserves leads to an accelerated increase in the role of simulation of reservoir hydrocarbon systems in the development of oil and gas fields. Many gas-condensate fields in Eastern Siberia can be characterized as reservoirs with low permeability and porosity and difficult thermobaric conditions, and, as a result, the issue of improving the efficiency of the development of such reservoirs to increase the cumulative production of gas and condensate is relevant. If the initial reservoir pressure of a gas-condensate field corresponds to the dewpoint pressure, dropout of a significant amount of retrograde condensate is observed when the pressure in the reservoir decreases. Condensate dropout in the pore space of a reservoir leads to a decrease in both the condensate recovery factor (CRF) and the gas recovery factor (GRF). The predictive calculations of the development of a gas-condensate reservoir by vertical and horizontal wells were carried out with the use of the hydrodynamic simulator T-Navigator of a domestic manufacturer Rock Flow Dynamics. The calculations were performed under various process conditions on the example of a gas-condensate field, which is characterized by complicated thermobaric conditions (the initial reservoir pressure corresponds to the dewpoint pressure), while the target process parameter was the amount of condensate dropout in the reservoir. Based on the results of the study, the main conclusion can be drawn. The development of the reservoir by horizontal wells can significantly reduce the reservoir drawdown pressure compared to vertical wells, while the condensate dropout in the reservoir occurs in a larger volume; the condensate becomes immobile and prevents further gas production, reducing the total production of condensate. An increase in reservoir condensate recovery in the course of the development of a gas-condensate reservoir by vertical wells compared to horizontal wells is observed under certain reservoir conditions corresponding to the simulation performed in this study, namely, at low reservoir permeability and porosity and the presence of a saturated gas-condensate system.

The purpose of this study — construction and research of a new mathematical model of a bilingual community, which takes into account: the effect of mutual assistance within a group of speakers of the same language, the effect of language acquisition by children of bilingual parents at an early age, different prestige of languages for adults. Methods. A new model is being built that takes into account new effects. The model is studied using classical methods with an unlimited increase in dynamics time. The effect of mutual assistance is compared with the effect of language volatility introduced by Abrams and Strogatti. Based on the observed statistical data, using the regression method, the parameters of some languages of England and Canada are determined: Welsh, Scottish, English, French. A forecast is being made for the further development of dynamics. Results. The effects taken into account in the model are confirmed by the correspondence of the development of language dynamics to the characteristics of the language: large values of the parameters of mutual assistance correspond to such a development of language dynamics in which one language displaces the second; at low values of mutual assistance, languages coexist. To model language dynamics using the new model, real statistical data on language pairs is used: Welsh-English, Scots-English, French-English. A forecast is being made for the further development of dynamics by language. Conclusion. General concepts in language dynamics have been supplemented with new ones — the power of mutual assistance within a group of speakers of the same language. The similarity between the effect of language volatility and the effect of mutual assistance is noted.

Introduction. The relevance of the study is related to the problem of increasing soil fertility. The value of soil as the main means of agricultural production in a specific economic infrastructure is determined by its fertility that is its ability to satisfy the needs of specific plants for nutrients, water, and to provide the root system of plants with air and heat. The effectiveness of increasing soil fertility depends on objective soil assessments and forecasting. Therefore, mathematical modeling for the fertility level of soils for the agricultural production is an urgent task for agroengineering studies. Aim of the Study. The study is aimed at developing a mathematical model for an integrated assessment of soil fertility levels. Materials and Methods. When conducting the study, analytical methods were used and the results obtained by various authors on this problem were summarized. The object of the study was the published results of scientific researches by the authors from other scientific institutions obtained on the problem under consideration. Results. Based on an analysis of the literature references, there was made a scientifically-based list of the most significant indicators for assessing soil fertility, which includes the content of organic matter (humus), acidity, humidity, soil porosity, presence of microorganisms and clay particles, content of mobile forms of nitrogen, phosphorus and exchangeable potassium. A mathematical model has been developed based on the criterion of maximum soil fertility, which makes it possible to assess the level of soil fertility using the proposed indicators. Discussion and Conclusion. The examples of calculations based on average and basic values of indicators with the use of the proposed mathematical model are presented. They give an idea of the most typical procedures for generating indicators and assessing the process under consideration. The value of the fertility probabilistic coefficient 1 indicates soil depletion (degradation), which will not ensure an economically sound harvest. In this case, measures must be taken to increase soil fertility. When 1, the soil is fertile and is able to supply plants with nutrients, water and air for their growth and development. The soil fertility level is an important criterion for assessing the impact of agricultural technologies on environmental safety and the environment state.

The article presents the results of the research aimed at developing and verifying a mathematical model for managing the ecosystem risks of marine areas. The main purpose of the research is to create an effective tool for assessing and managing the risks arising from anthropogenic influence, climate change and other natural factors. The proposed model is based on the existing theory of sea ecosystem risks management and takes into account the relationship between natural and anthropogenic factors, condition of marine ecosystems, their vulnerability and ecosystem services. The model uses mathematical methods, in particular, differential equations, statistical analyses, simulation modeling and network analysis, allowing creation of detailed models that reflect marine ecosystems' dynamics and their response to external influence. Numerous experiments were conducted in order to verify the model. They demonstrate its ability to predict changes in the condition of marine ecosystems under influence of various factors. The results of the research show that the proposed model can be an effective tool for optimizing management strategies, minimizing ecosystem risks and improving sustainability of marine ecosystems. Practical recommendations developed on the basis of the results of the research include strategies for preventing, minimizing and adapting to potential threats, taking into consideration each region's and ecosystem's specifics. The proposed model helps to optimize management decisions, reducing risks and improving the condition of marine ecosystems affected by anthropogenic impact and climate change. It is a reliable tool for ensuring sustainability and preservation of marine ecosystems. This approach allows for evidence-based risk management that increases sustainability of marine ecosystems and their preservation for future generations. The model also considers key factors influencing marine ecosystems, including biological diversity, water quality, industrial fisheries, tourism and recreation, and allows evaluation of effectiveness of various management decisions in the context of such factors. The application of this model in ecosystem management practices allows making more informed decisions regarding protection and preservation of marine resources. It contributes to their sustainable development and provision of ecosystem services having critical importance for society.

A mathematical description of the process of ethylene oligomerization on a NiO/B2O3-Al2O3 catalyst in a liquid heptane solvent is given. Problems of optimal process control are formulated. The temperature and time of the process are taken as control parameters. An algorithm is proposed for solving the problem of optimal control of the industrially significant catalytic process of ethylene oligomerization. The search for solutions to the formulated problems is carried out using a genetic algorithm with real coding. For each of the problems under consideration, a method is proposed for representing a mathematical analogue of a population on the basis of which a solution is searched. A step-by-step algorithm for determining the optimal parameters for the ethylene oligomerization process is presented. A special feature of the algorithm is the simultaneous search for the values of a continuous control parameter (temperature) and a discrete control parameter (process time). A program (application) has been developed to determine the optimal values of process parameters. The application allows the user to select an optimal control problem, set the values of the genetic algorithm parameters to find a solution, and visualize the results obtained. A computational experiment was carried out for the process of ethylene oligomerization. The optimal duration of the process under isothermal conditions was calculated, at which the highest concentration of C4 hydrocarbons is achieved. The optimal temperature conditions and duration of the ethylene oligomerization process were determined to ensure the maximum concentration of C6 hydrocarbons. The conducted numerical experiments demonstrated lower resource consumption compared to the methods of uniform search and variations in the control space. The proposed algorithm can be used to study the patterns of catalytic processes without resorting to laboratory experiments associated with additional material and time costs.

An important section of spinal biomechanics is the analysis of various types of movements in spinal segments, which are difficult to observe, and setting up experiments is quite complex. There are few articles devoted to this topic, and the methodological approaches outlined in these studies are so heterogeneous that they do not allow for a comparative analysis. In this situation, the abstract language of mathematics allows us to objectively answer the questions that arise. Aim of the study was to develop a mathematical model of a spinal segment to calculate the combination of rotation angles and lateral inclination of the vertebra, as well as to identify factors influencing these parameters. Material and methods. The developed mathematical model of the motion segment of the spine was used as the main tool for the study. The initial data for this model were the coordinates of the reference points of the vertebrae, which makes it possible to determine a number of parameters describing their complex structure. Using this model, the parameters of the combination of vertebral movement in the frontal and horizontal planes were calculated. Results and discussion. The developed model of the combination of movements in the spinal segment is adequate to the ideas about the nature of movements in the spinal segments. The coefficient of combination of lateral tilt and rotation of the vertebra for the cervical vertebrae is from 0.5 to 0.7, for the thoracic vertebrae from 0.3 to 0.5, and for the lumbar vertebrae from 0.0 to 0.1. Fluctuations in the value of this coefficient depend on the angle of inclination of the upper articular surfaces of the underlying vertebra. Reducing the size of the articular surfaces leads to a decrease in the magnitude of the angular movements of the vertebra, and their convergence leads to an increase in mobility in the spinal segments. A negative angle of inclination of the articular surfaces causes opposite rotation of the vertebra.

В работе предложена математическая модель нелинейного осциллятора Ван дер Поля-Эйри с учетом наследственности. Нелинейность осциллятора обусловлена наличием зависимости коэффициента трения от квадрата функции смещения, что характерно для осциллятора Ван дер Поля. Также собственная частота колебаний представляет собой функцию от времени, которая линейно возрастает при его возрастании. Последнее характерно для осциллятора Эйри. Эффекты наследственности вводятся в модельное уравнение посредством дробных производных в смысле Герасимова-Капуто. Они указывают на то, что колебательная система может обладать эффектами памяти, которые проявляются в зависимости текущего ее состояния от предыдущих. Для предложенной математической модели был разработан численный алгоритм, основанный на явной конечно-разностной схемы первого порядка. Численный алгоритм был реализован в компьютерной программе на языке Maple, с помощью которой была произведена визуализация результатов моделирования. Были построены осциллограммы и фазовые траектории при различных значениях параметров модели. Показано, что дробная математическая модель может обладать различными колебательными режимами: от автоколебательных, затухающих и хаотических. Дается интерпретация результатов моделирования.

Background. Cervical cancer (CC) refers to cancer of visual localization and in women of reproductive age remains one of the most common oncological diseases. The carcinogenesis of CC is caused by the persistence of highly oncogenic types of human papillomavirus (HPV), the level of carcinogenicity of which is the highest based on the criteria of the International Agency for Research on Cancer. However, cervical carcinogenesis does not occur in all cases of persistence of highly oncogenic types of HPV. This, in turn, determines the need for a thorough search, study and analysis of possible cofactors that can lead to neoplastic changes in the cervix.Aim. To develop a model for predicting the individual risk of CC in women of reproductive age, taking into account clinical, anamnestic, laboratory and histological data.Materials and methods. The material for the study was retrospective examination data from 251 patients of reproductive age who were treated at the Center for Gynecology and Reproductive Technologies of the National Medical Research Center “Medical and Rehabilitation Center”, Ministry of Health of Russia in the period 2015–2022. Results. Highly oncogenic HPV types were significantly more common in the group of patients with verified СС who took combined oral contraceptives (COC), compared with patients who did not take COC (p = 0.035). Multifactorial analysis allowed us to determine that long-term use of СОС for a total of more than 7 years is associated with a tendency to increase the risk of developing СС (hazard ratio 1.68; 95 % confidence interval 1.1–2.5; p = 0.010). According to the results of statistical calculation, the values of regression coefficients were obtained and the tendency to increase the risk of developing CC was predicted in the presence of such factors as: HPV type 16 persistence, body mass index, and the duration of COC intake in years.Conclusion. Thus, taking into account all possible risk factors for CC, the negative effect of cofactors, namely increased body mass index and prolonged intake of COC, on the course of HPV as the leading etiological factor of breast cancer, will allow us to identify groups at increased risk of developing CC, form an individual algorithm for monitoring and examination throughout the entire period of taking COC, as well as conduct individual cancer prevention by limiting the duration of taking COC.

The creation of new and improvement of existing machines and mechanisms requires the development of drive engineering and the creation of new drive systems capable of competing with currently known circuit solutions. Under these conditions, the creation of combined pneumatic-mechanical drives is an important scientific and technical task. The purpose of this work is to increase the speed at a given accuracy of auxiliary movements of the target mechanisms of technological machines by creating a pneumatic-mechanical drive with improved energy and dynamic characteristics. The technical solution of a positioning pneumatic-mechanical drive of executive movements of technological equipment is presented, mathematical and computer models are developed. In this case, the method of solving the differential equation in the SimInTech program is used. As a result, an oscillogram of transients is obtained. The developed models allow for dynamic analysis of pneumatic-mechanical systems.

The paper shows the relevance of using a laser tracker as part of an automated technological complex to improve the accuracy of movements of an industrial robot manipulator in the process of incremental shaping. The requirements for the measuring system of the technological complex are formulated. A mathematical model of the magnitude of the signal recorded using a laser tracker based on the results of measuring the movements of the robot manipulator is constructed. An algorithm for correcting robot movements in the process of incremental shaping in real time is described.

The article substantiates the need for a practical, professional focus of studying the course of higher mathematics by students of professional pre-higher education institution. The aim of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the education of students in various specialities of vocational higher education. Modern requirements for the development and reform of higher education require an increase in the professional competence of a bachelor’s graduate in each field of knowledge, the ability to creatively approach and find the solution to emerging professional tasks. Therefore, teachers of higher mathematics have the task of reorienting the teaching of the academic discipline with the use of professional problem solving. The purpose of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the training of students of professional pre-higher education in various specialties of the college. In connection with the rapid development of science and technology, the training of competent, competitive, and highly qualified specialists requires a high level of skills in applying mathematical apparatus in professional activities. Mathematics is the basis of studying physics, technology, general technical and special disciplines. At present, mathematical education has a significant impact on the formation of professional qualities of a modern specialist who is able to navigate the directions of development of modern science and methods of learning about the world around them, predict the impact of human production on society and the environment. Modern mathematics is used in the study of economic, humanitarian, biological, physical, technical and other phenomena. This is done by building a mathematical model. It takes into account all essential connections within the phenomenon. Under mathematical modelling we will understand the method of researching processes or phenomena by building their mathematical models and researching these processes. The applied direction of solving problems by students of various specialties is oriented towards future professional activity. This is an effective means of increasing learning motivation, and developing mathematical and professional competences. The results of the research are examples of practical problems of various sections of higher mathematics for students of economic and technical specialties. The applied nature of the given problems aims to combine the study of higher mathematics with special training of future bachelors and to give them the opportunity to gain experience in solving production problems, and to increase their professional competence. This is very important in times of fierce competition in the labour market. Conclusion. Practical skills and the ability to use the mathematical apparatus when solving applied, profession-oriented problems increase the motivation of students of higher and pre-higher education, and aid students to study other courses of professional disciplines, and do coursework and diploma projects, which will contribute to the maximum use of mathematical methods in the educational course of higher education mathematicians in the future professional activity. The obtained results open up prospects for further research in the following directions: development of methods of formation of skills to solve applied problems by students of various specialties, as well as strengthening integration links between fundamental and profession-oriented courses

Introduction. The question of the dependence of the intensity of the operational management of construction production on the organization of interaction between key production executors, services and management of a construction enterprise is considered.Materials and methods. The method of coordinating solutions of current production, support and management tasks based on a unified structure of algorithms of technological processes in the design elevations of the structure, the organization of production activities at the construction site and operational management is presented. The definition of the intensity of operational management as a measure of the effectiveness of the organization of interaction between production, services and management of the enterprise is proposed.Results. The form of analytical continuous, piecewise linear dependence of the intensity of the operational management of the construction process on the coordination of the values of the parameters of the organization of construction production is obtained: its provision with resources, as well as compliance with the requirements of construction control in a changing production situation. The formula for the intensity of operational management of the implementation of the assembly and laying technological process in specific design elevations of the structure within the established timeframes was obtained. The parameters of the mathematical model of the intensity of operational control, as well as the digital interface for its use, are obtained. Boundary values for the variables of the domain of determination of the permissible values of the parameters of the organization of technological processes, providing measures, material supply, as well as a relative scale for the intensity of operational management are obtained. Graphs of changes in the intensity of operational control during the execution of the technical process in the local design elevations of the structure were obtained and analyzed.Conclusions. The conclusion is made about the formation of a unified information environment for the organization of construction production during construction and operational management through compatible algorithms, data structures and AWS interfaces based on a mathematical model that coordinates the algorithms for solving production problems and communication of key performers in terms of the parameters of the organization of construction production and operational management.

Aim – to develop and provide clinical substantiation of experimental mathematical models for the chronic kidney disease (CKD) progression rate in patients with type 2 diabetes mellitus (T2DM) using the glomerular filtration rate reduction index (RI_GFR) as original diagnostic parameter. Material and methods. A cross-sectional observational study of clinical status indices was performed in a sample of patients with type 2 diabetes. The significant predictors of a high rate of CKD progression were identified by regression analysis, three variants of experimental mathematical models were developed with different combinations of arguments with an emphasis on modifiable factors. Results. The method of one-dimensional logistic regression analysis revealed the indices of clinical status having a significant impact on the rate of CKD progression on the scale of changes in RI_GFR by 1 ml/min/1.73 m2 and on the binary classification of outcomes in the groups of "slow" and "fast" decrease in kidneys filtration function with a threshold value of RI_GFR of 4.21 ml/min/1.73 m2 per year. These indices were age, body mass index (BMI), glycemia and duration of diabetes at the time of visit, history of insulin therapy, acute myocardial infarction in the anamnesis, pulse on the popliteal artery, concomitant retinopathy, hypertension risk group, treatment with sulfonylureas and calcium antagonists. Using multidimensional logistic regression, three types of experimental mathematical models were developed, including various combinations of predictors that demonstrated high values of diagnostic significance. Conclusion. The mathematical modeling of CKD progression in patients with T2DM with the RI_GFR diagnostic index allows for better understanding of the pathology's development patterns. An experimental mathematical model using modifiable drug factors that a doctor can manage during the treatment (administration of sulfonylureas and calcium channel blockers) demonstrated 55.6% sensitivity, 85.3% specificity, AUC 0.76 (0.65; 0.86), which ensured high quality prediction with an accuracy of 77.5%.

Introduction. The technological operation of soil tillage is an energy-intensive preparatory operation. The traction resistance of tillage units has a direct impact on this indicator. Aim of the Study. The study is aimed at searching optimal operating parameters for the field cultivator tool through determining the traction resistance created by this tool. Materials and Methods. The study was carried out in the field on an experimental facility using a full factorial experiment technique with a working model based on a three-level design. Results. Through the regression analysis of experimental data, there was obtained a mathematical model that allows determining the optimal operating parameters for the field cultivator tool when performing a technological operation of soil tillage. Discussion and Conclusion. While calculating, it was found that the lowest traction resistance PТ = 0,72 kN created by the tool is for the following values: tillage depth h = 4 cm, crumbling angle of the left-hand and right-hand flat-cutting wings f = 0° and the speed of the tillage unit v = 2,61 m/s. As the optimal operating parameters for a field cultivator tool, determined using the obtained mathematical model, it is recommended to use the crumbling angle of the left-hand and right-hand flat-cutting wings of the working body f = 0°, and the speed of the tillage unit v = 2,91 m/s. Taking into account the recommended optimal operating parameters of the tool, it is possible to calculate the value of the traction resistance index at different tillage depths. The traction resistance will change within the range of 0.79–1.81 kN, when the soil tillage depth changes from 4 to 12 cm. The resulting mathematical model of the traction resistance created by the tool will allow a more accurate approach to the issue of designing agricultural machines.

The aim of this research is to design algorithms and develop software for the automated assessment of stability criteria in the dynamic behavior of unmanned aerial vehicles (UAVs), modeled through systems of ordinary differential equations (ODEs). By employing advanced symbolic computation techniques, an application has been created that facilitates the automatic linearization of nonlinear equation systems and the derivation of the characteristic polynomial for the resulting linearized ODE systems. The introduced methodologies and models provide substantial practical significance in the evaluation of stability across a broad range of both economic and technical systems. [ABSTRACT FROM AUTHOR]

Background. In radio engineering systems for various purposes, microwave antennas with a radiation pattern of a sector type are used to solve problems at maximum ranges in a wide range of angles. To form such a directional pattern in an antenna, it is necessary to create a variable-phase distribution of excitation sources (currents or fields). A model study of the influence of the shape of individual areas by the variable-phase field distribution in the aperture of a microwave antenna on the parameters of its quasi-sector radiation pattern can be carried out by representing this distribution by a combination of mathematical functions using predicate logic. Materials and methods. An approach to solving this problem is proposed based on the use of the additivity property of a definite integral, which allows replacing it with the sum of definite integrals taken over partial intervals and independently controlling the distribution of the field over these intervals. At the same time, it becomes possible to additionally control the shape of individual areas of the variable-phase field distribution in the aperture of the microwave antenna by changing the degree of functions describing these areas. The possibility of software implementation of the proposed mathematical model in the MATLAB system using predicate logic is shown. Results and conclusions. The results of a model study of the influence of the shape of individual sections of the variable-phase field distribution in the aperture of a microwave antenna on the main parameters of its radiation pattern are presented. The results obtained indicate the prospects of a model representation of the variable-phase field distribution in the aperture of a microwave antenna with a quasisector radiation pattern by combination of trigonometric functions of arbitrary degree using predicate logic to study the influence of the shape of its individual areas on the radiation pattern of this antenna and improve its parameters.

Background. The aim of the work is to implement numerical methods and algorithms in the form of a software package that allows for a parametric study of the "flow tube – liquid" system of a Coriolis flow meter, and to analyze the influence of the shape of the flow tube on the sensitivity of measurements of liquid mass flow parameters. The relevance is due to the need to identify the geometric design of the flow tube with the most acceptable characteristics when pumping highly paraffinic oils. Materials and methods. For the mathematical model, the finite element method and an iterative approach to solving systems of equations based on rigidly coupled coupling were used. A computational algorithm based on linear interpolation and an algorithm that automates the processing of data arrays and the calculation of average time and phase delays have been implemented. The structural and logical diagram of the software complex is presented and described. Results. In the course of computational experiments carried out to study the influence of the flow tube shape on the sensitivity of measurements of the parameters of liquid mass flow as a function of the average time delay using the developed hardware and software complex, it was revealed that the model of a Coriolis flow meter with a radius of curvature of the flow tube of 30° is recommended for use in oil and gas industry as a tube geometry that is less susceptible to waxing and at the same time has sufficient sensitivity for measurement. Conclusions. A software package has been developed and tested. A relationship has been identified between the geometric shape of the flow tube of a Coriolis flow meter and the measurement sensitivity of the device, which is characterized by the fact that at high values of the radius of curvature of the tube, the sensitivity increases compared to straight-tube designs.

Introduction. The model and results of calculating the smoothness of a light three-axle off-road vehicle for the Arctic zone of Russia are considered. The model on standard approaches and uses a system of assumptions that limits the number of degrees of freedom for the vehicle body to three, as well as one degree of freedom for the unsprung masses is based. The mathematical model is a system of ordinary differential equations and is supplemented with the necessary algebraic equations, as well as initial conditions. The system is integrated using the 4th order RungeKutta method, for which a program was written in C++. The calculations presented in the article demonstrate the possibility of conducting research on the smoothness of a vehicle under conditions of arbitrary terrain, typical for off-road conditions in the winter conditions of the Arctic zone. The dimensions and other parameters of the vehicle were taken from a full-scale model that was used in real expeditions in 2003-2019. Based on the model, suspension characteristics will be developed for a new all-terrain vehicle.Theory. When operating a wheeled vehicle in a wide range of conditions, even in northern regions, transverseangular vibrations are very often insignificant, so only vertical linear and longitudinal-angular vibrations of the frame can be considered. This problem enables to construct a system of equations of vehicle motion using selected degrees of freedom. From a mathematical point of view, these equations are classified as second-order ordinary differential equations with a variable structure of the right-hand sides, which reflects the non-linear nature of the behavior of the suspension in terms of its geometric constraints.Methods. The work uses numerical methods to solve the equations of the constructed model, which enables to gradually weaken the accepted assumptions and build more general calculation algorithms. The main integration method for ensuring the stability of solutions is the multi-step Adams method, which, with the correct choice of step, ensures the necessary stability of the solution over sufficiently long model times. However, in this work, the 4th order Runge-Kutta method was adopted, which turned out to be quite sufficient.Results and conclusions. The paper presents the results of a numerical study of the oscillatory processes of an off-road vehicle during uniform translational motion of the vehicle on a horizontal surface with a given profile of irregularities. The graphs show a transition process of oscillations, which ends with reaching a steady state. The shape of oscillations in a steady state can be irregular and significantly depends on the given speed of the all-terrain vehicle. Analysis of the dependencies presented in the figures shows that the shape of the oscillations of the allterrain vehicle’s frame, as well as the amplitude and frequency, significantly depend on the speed of the vehicle (at a constant road profile). Changing the road profile leads to corresponding changes in the forms and characteristics of forced vibrations of a vehicle on a suspension, which makes it possible to build the necessary amplitude-frequency characteristics, optimize the elastic and dissipative parameters of suspensions, optimize their number and location, and also monitor the movements of arbitrary points at which various units are located.

A mathematical model was developed, during which the voltage equations of the three-phase winding of a brushless DC motor with permanent magnets, the electromagnetic torque of a brushless DC motor, electromagnetic power, the induced emf of each winding, and the differential torque equation of the servo system were obtained. Based on the constructed mathematical model of the BLDC for a specific motor with given parameters, simulation modeling was carried out and the dependences of electromechanical quantities were obtained: angular velocity of the rotor, electromagnetic torque, stator phase current and rotor rotation angle on time. The simulation results confirmed the theoretical justification of the mathematical model. The resulting mathematical description of the BLDC can be used to build the architecture of a control unit based on a neural network controller.

Objective. The goal of the study is to optimize a computer model of a Vivaldi antenna with conductive plates on the same side as the resonator.Method. The study is based on electrodynamic modeling methods.Result.The paper presents a computer model of a Vivaldi antenna with conductive plates on one side with a resonator. A comparative analysis of two types of Vivaldi antennas was carried out of the dependence of the beam width and the voltage standing wave ratio on the radius of the current-conducting plate curve in the form of lobes and the values of the opening in two planes θ = 900 (the plane of the antenna's opening) and φ = 00 (the plane perpendicular to the antenna's opening plane) in the frequency range from 3 to 24 GHz. The influence of the shape, size and position of the resonator on the SWR value and the width of the antenna radiation pattern was determined. VSWR values are given for different shapes and sizes of the resonator. The main parameters of the resonator have been identified, which affect the characteristics of the antenna.Conclusion. Electrodynamic modeling allows us to obtain a Vivaldi antenna with the required radiation pattern width with an improved standing wave ratio.

Ensuring high and stable biogas output during digester operation is ensured by regulating and monitoring values of control parameters. The purpose of article is to develop model of process of functioning of digester during methane mono-fermentation of cow manure with establishment of values of control parameters. A solution to model was found to obtain dynamics of biogas yield, while experimental and simulated dynamics of biogas yield were as close as possible. The developed model is system of differential equations that describe changes in concentrations of substrate nutrients , methanogen biomass and dynamics of biogas output in digester . The system of differential equations was solved in Simulink package , obtaining dependencies and . The dependence was compared with results of studies conducted on laboratory biogas plant with digester with useful volume of 30 liters at temperature of 37°C with periodic substrate loading system. By selecting parameters of model, resulting function was compared with similar one obtained experimentally. It has been established that in model of digester functioning process during methane mono-fermentation of cow manure, following coefficients have following meaning: bacterial growth rate m3/(kg day); substrate assimilation ; bacterial growth rate m3/(kg day); rate of conversion of nutrients into biogas m6/kg. The obtained values of coefficients make it possible to carry out modeling of process of methane mono-digestion of cow manure and predict biogas yield at different initial values of concentration of methanogen biomass, concentration of substrate nutrients, digester volume, which is used in industrial biogas plants.

A generalized kinematic scheme of the installation of quadcopter motors is presented and its main advantages are described. In accordance with the scheme, a mathematical model of the kinematics of the quadcopter was developed. The model was implemented in the MatLab software environment. The presented mathematical expressions are used to calculate kinematic characteristics, such as the values of the thrust of the motors and the reverse effect of the motors on the body of the quadcopter. The comparison of the obtained data with the experimental characteristics showed a 5% deviation of the magnitude of the dependence of the thrust on the average value of the voltage on the motors and a 30% deviation of the magnitude of the dependence of the motor action on the thrust magnitude.

The purpose of the process safety management system is to identify hazard factors and develop a set of methods to prevent injuries at an airline, occupational illness, material costs in case of damage to property and the environment. The analysis of the structure of occupational pathology depending on the factors of the production environment and the working process for the period 2013–2022 shows that the percentage of diseases associated with the impact of production physical factors for this period remains at the same level. This fact, in turn, confirms the relevance of the chosen study. Analysis and identification of the current production situation is necessary to assess the impact of adverse production factors. In this study, a new approach to the mathematical model for a process safety management system is implemented. Mathematical modeling allows a deeper understanding of the nature of certain phenomena and to obtain information about the real situation, which in turn stimulates the development of new scientific problems and methods of solving them, and is also the basis for choosing specific solutions for the implementation of certain projects. The successful implementation of strategies in order to create a process safety system for a flexible monitoring and management structure depends on how effective its functional structure is; this provision is explained by the fundamental nature of the tasks that are solved at the management stage. The article discusses the theoretical statements concerning mathematical modeling. When creating the model, the apparatus of abstract algebra-set theory – was used. The model developed in the course of the study makes it possible to introduce a model of the process safety management system into the activities of aviation enterprises.

Background. The need to create antenna-waveguide paths for multi-band reflector antennas of satellite communication systems requires the use of various methods for selecting the structure, determining and optimizing the parameters of antenna-waveguide paths. Aim. Development of a mathematical model of antenna-waveguide paths of multi-band reflector antennas, built on the basis of the «polarization separation – frequency separation» method with the implementation of the auto-tracking function. Methods. A mathematical model of antenna-waveguide paths of multi-band reflector antennas, built on the basis of the «polarization separation – frequency separation» method, allows us to determine the main characteristics of antenna-waveguide paths and incoming devices with an auto-tracking function. Results. The main elements of the mathematical model of multi-band antenna-waveguide paths built on the basis of the «polarization separation – frequency separation» method are determined. Conclusion. A mathematical model has been proposed that makes it possible to reduce the requirements for the computing tools used when developing antenna-waveguide paths in terms of RAM capacity and performance. The ability to analyze and determine the characteristics of antenna-waveguide paths using a mathematical model has been implemented. The stages of determining the parameters of antenna-waveguide paths are presented, based on the developed mathematical model of the corresponding design option, as well as theoretical and experimental data confirming the correctness of the model of antenna-waveguide paths.

Within the framework of the put forward hypothesis that energy costs of working movements of the links of racking stacker cranes are inextricably linked to the shape of the working area of the warehouse in which the crane operates, to reduce energy costs, it was pro-posed to use a rotating boom in the design of the stacker crane. With the help of program implementations of mathematical models of stacker cranes of traditional bicycle design and the proposed design with a rotating boom, it became possible to determine the average energy costs for all possible movements of loads of the same mass within the corresponding working areas of these designs. For this purpose, systems of differential equations in Cauchy form were developed, where dissipation of energy was taken into account. The total value of work of crane drives during acceleration and braking was determined. The latter were carried out with constant accelerations, and the movement after acceleration — with constant speeds. The developed simulation mathematical models of cranes of traditional design and the proposed design with a rotating boom allow to determine the energy costs in the drives when moving the crane links along the given trajectories. According to the criterion of average total energy costs, adopted for all possible combinations of movements within areas of the same capacity of one hundred square meters, the stacker crane of the proposed design has an advantage over the crane of traditional design. This makes it possible to significantly reduce energy costs when using such cranes in warehouses and hangars. It is reasonable to recommend the use of a stacker crane of the developed design in warehouses of round shape — it will allow to reduce significantly the energy costs when using such cranes in warehouses and hangars.

This paper is devoted to solving the inverse problem (determining the parameters of a system of ordinary differential equations based on additional information determined at discrete points in time) and analyzing its solution for a mathematical model describing the dynamics of changes in the population and capital of two regions of the world. The inverse problem is reduced to the problem of minimizing the target functional and is solved by the method of differential evolution. A numerical method for solving direct and inverse problems is implemented. The developed method was tested on model and real data for countries such as Russia, China, India and the USA.

The subject of the research is the process of logical access segregation to data in information systems. The aim of the article is to improve the accuracy and reliability of modeling processes for data processing and logical access segregation considering the heterogeneity of entities in information systems. The tasks to be solved include: conducting a comparative analysis of modern data access distribution models, integrating simpler role-based models, synthesizing hierarchical role-based models, developing enforced typing models based on trust relationships, and presenting the main provisions of the security policy integration process. The methods used are: systems analysis, component design, logical and simulation modeling in the form of role-based access segregation models. The results obtained include: development of data processing models and logical access segregation in information systems that take into account the heterogeneity of entities and the multi-level structure of information systems. The models differ from known ones by considering the heterogeneity of entities and the multi-level structure of information systems. This has increased scalability by up to 35% due to a modular approach to defining security policies. Additionally, the developed model demonstrates 25% higher implementation practicality as it easily integrates with existing access control systems and adapts to various platforms and environments. The proposed models are effective for large information systems and distributed environments due to their modularity and ability to adapt to different operational conditions. This ensures reliable access control in systems with numerous subjects and objects. The implementation of multi-level RBAC models has improved the accuracy and reliability of results.

Background. The use of mathematics in the field of environmental safety has long roots. The most famous mathematical model in ecology is the Lotka – Volterra model, which describes the relationship between predator and prey in a natural ecosystem. The authors proposed an improved three-element Lotka – Volterra model that takes into account the interaction of three elements of the territorial technosphere: a person, the environment, and an object of the technosphere. The aim of the study is to test the adequacy of the improved Lotka – Volterra model to the process of interaction of elements in the territorial technosphere. Model adequacy testing is formulated as the task of testing the assumption that the value of the model response differs from the real response of the system by no more than a given value. The object of the study is the improved Lotka – Volterra model, which takes into account the interaction of man, the environment and the object of the technosphere. Materials and methods. The study was carried out using an integrated systematic approach and methods of analysis and synthesis, grouping and generalization. Results. Of all the analyzed criteria for the adequacy of the model, there is Pearson's с2 goodness-of-fit test, Smirnov – Kolmogorov's test, Fisher's (Fischer – Snedekor's) test, Fisher's test is the most preferable, since it is suitable for comparing very small samples, it can be one-sided and two-sided. Conclusions. The improved Lotka – Volterra mathematical model describing the interaction of elements in the territorial technosphere adequately reflects the state of the territorial technosphere in forecasting and in terms of the absolute values of risk factors.

Background. As of today in Russia there are no scientific-technical and experimental-technological reserves on development of systems of structural monitoring of serviceability of products and objects of rocket-space technology (RST) and ground space infrastructure (GSI) with transducers of physical quantities on the basis of macrofiber actuators on the basis of inverse piezo effect necessary for full assessment of reliability of technically complex objects by non-destructive methods. The development of the latest generation of aerospace structures requires the creation of advanced materials that would have high physical and mechanical parameters, meet reliability and durability requirements for specific tasks. Great importance is also given to active materials and structures capable of forming functional shapes and profiles depending on the external influence, i.e. to ensure the fulfillment of one of the principles of the motion control concept – adaptronics. The formation of functional shapes and profiles will provide optimal wing aerodynamic profile, better maneuverability of the aircraft, reduce fuel, energy consumption and provide better remote control in extreme space conditions. The purpose of this article is to create a scientific-technical and experimental-technological reserve for the development of advanced technologies for the production of sensor and actuator elements of structural performance monitoring systems based on piezoceramic materials and technologies for incorporation into the elements of composite structures of RST and GSI products in order to control and manage their characteristics to prevent emergencies. Materials and methods. The paper considers the structure of the system of structural monitoring of serviceability of products and objects of RST and GSI with transducers of physical quantities on the basis of macrofiber actuators based on the inverse piezo effect. Results. As a result of technology implementation, import-independent self-regulating adaptive structures of spacecraft structures and equipment will be created on the basis of controllable properties of materials with response to external influences. Implementation of the technology will make it possible to create an effective system for controlling vibrations of structural elements. The developed piezoactuators will find applications in structural monitoring systems of the aerospace industry in rocket and space technologies and mechanical engineering.

Relevance. One of the priority areas for modern energy development is the active use of renewable energy technologies, the leading position among which in terms of the volume of commissioned generating capacity and areas of practical application is occupied by photovoltaics. In recent years, solar photovoltaic plants are increasingly being used as part of autonomous power supply systems, which is largely facilitated by a significant reduction in the cost of their components due to improved technology. Autonomous power supply systems can vary significantly in power, operating conditions, requirements for uninterrupted power supply and many other factors. This determines the high importance of the task of choosing the composition of the main electrical equipment that ensures optimal technical and economic indicators of the designed energy system. To make a reasonable choice of the equipment of an autonomous photovoltaic power plant, simulation models of all its main components are required that adequately reflect their performance characteristics under real operating conditions. An important component of autonomous photovoltaic plants is the energy storage device, which includes a battery and a solar controller that manages the energy balance of the power plant. The settings of the solar controller largely determine the operating modes of the photovoltaic power plant, on which the service life of the batteries primarily depends. Taking into account the fact that the costs of energy storage constitute a significant share of the costs of the total financial investments in the designed power plant, the problem of reliably assessing the service life of batteries is very relevant. Aim. Development of a mathematical model of energy storage system for the design and optimization of the equipment of autonomous photovoltaic plants. Methods. Mathematical and numerical modeling using the MatLab/Simulink software package. Results. A mathematical model of a battery has been developed, based on the modified Shepherd model and the kinetic model of a rechargeable battery. The model is universal and can be used to simulate the static and dynamic characteristics of different types of batteries. To identify model parameters, only the technical specification data provided by the manufacturer is sufficient. The complex model includes a battery life model, which allows you to dynamically adjust the available maximum battery capacity during operation.

The object of the study is the process of monitoring the technical condition of electrical insulation of traction electric machines in order to determine the need for their maintenance or repair. Diagnostics of electric machines is an important aspect of supporting the operation of electric drives. Failure of the windings is one of the main reasons for failure of electric motors. Therefore, the task of developing operational methods for diagnosing the insulation of windings of traction electric motors is urgent. A study of the negative impact of operating conditions on the technical condition of electrical insulation of motors was carried out. The analysis of the existing methods of diagnosis of insulation systems of electric machines was carried out. Special attention was paid to the selection of predictive parameters of the insulation state. A mathematical model was developed to study the frequency characteristics of the stator insulation system of the traction electric motor model AD914. Refined dependences of the effect of changes in the insulation parameters of the motor stator winding on its frequency characteristics were obtained. It was concluded that the method of monitoring the insulation state of electric motor windings based on the assessment of electrical resistance relative to the stator core and amplitude-frequency characteristics is the most effective. The field of practical application of the obtained results is the system for monitoring the condition of electrical insulation of traction electric machines to determine the schedule of their maintenance and repair. The conducted research is a scientific justification for the choice of methods and devices for diagnosing the insulation state of electric motors of railway traction rolling stock.

This paper examines important aspects related to the problems of forming supply chains and production volumes at forest processing enterprises. The main emphasis is on assessing the optimality of decisions made. The study focuses on enterprises that do not have their own sources of raw materials and that are seeking to find the most appropriate solution based on the planning horizon based on data on transactions carried out on the commodity exchange. The purpose of the study is to create a mathematical model that allows us to establish the optimal volume of production of goods based on the formed supply chains of raw materials from the commodity exchange, considering the share of its useful volume, the time the lots are in transit and the uncertainty associated with supply and logistics. The following research methods were proposed: mathematical modeling, theory and optimization methods. Testing the model using data from the St. Petersburg Stock Exchange and enterprises of the Primorsky Territory made it possible to determine the optimal trajectories of profit, production volume and other important indicators. The work also raises issues of planning supply chains and production volumes, analyzes regions – sources of raw materials and presents the advantages and disadvantages of the presented mathematical model. The results obtained are of interest to the top management of forestry enterprises seeking to improve the efficiency of their activities and can be the basis for assessing the rationality of commodity transactions on the Russian Commodity and Raw Materials Exchange.

Introduction. One of the priority areas of modern government policy is to improve the quality of life of citizens. The strategic state acts: the Decree of the President of the Russian Federation “On the national development goals of the Russian Federation for the period until 2030”, and the “National Security Strategy of the Russian Federation” formulate priority directions for improving the quality of life of citizens. Since the socio-economic development of the country is impossible without increasing the efficiency of the regions, much attention is paid to the development of new methods and approaches to analyzing the quality of life of the population. Today, despite the presence of numerous studies in this area, there is no universal mathematical apparatus for analyzing and predicting quality of life indicators in the region. This circumstance contributes to a decrease in the efficiency of management activities and, as a result, weak control over the life activity of territories. Therefore, the purpose of the study was to develop a methodology for analyzing and predicting the quality of life in the region. Materials and methods. The basis of the developed methodology is a mathematical model of system dynamics. The model includes system variables, external factors, and functional dependencies that determine positive and negative relationships between the elements of the model. Indicators of socio-economic development of the region are used as model variables. The mathematical model consists of eight differential equations, the solution of which, given the initial conditions and time interval, is the predicted values of quality of life indicators. Results. The practical implementation of the developed methodology for analyzing the quality of life in the Saratov region is shown. The characteristics of the current state of the socio-economic situation of the Saratov region are given. Multivariate forecasting is implemented in the development of various scenarios for the socio-economic development of the region. Graphs of predicted values of quality of life indicators for the time interval [2023;2027] are presented. The algorithm for implementing the developed methodology at varying time intervals and different control levels is shown using an information-logical diagram. Discussions and conclusions. The presented author's methodology for analyzing indicators of the quality of life of the population in the region is aimed at timely provision of information to decision makers for making the necessary management decisions.

The article considers a three-phase-multiphase transformer converter of the number of phases with a serial connection of coils of each phase of the secondary winding, its substitution scheme and a linear mathematical model are given. As an example, the analysis of the operation of a manufactured three-phase-seven-phase transformer converter of the number of phases is performed. As a result of electromagnetic tests of the prototype, the parameters of the replacement circuit of the device are determined. Using a mathematical model, the operating characteristics are calculated and constructed. The results of theoretical calculations and experimental measurements are compared. The largest errors obtained when comparing the calculated and experimental values of efficiency and power factor are 3,5 % and 2,2 %, respectively.

Objective. The aim of the study is to implement and evaluate the optimization method based on the Markowitz portfolio theory. Method. The model is built using the Python programming language and the necessary libraries. Also, to solve the problem, the principles of financial theory were used - the calculation of the risk of the purchased asset, portfolio diversification and the principle of optimality. These principles form the basis of financial theory and help you make informed decisions related to investment, financing, and risk management. Result. A model of the program has been compiled, which accepts historical data on changes in the value of shares of different companies as input. After that, the optimal portfolio is calculated and displayed in the terminal of the user-investor. Markowitz portfolio theory helps to determine the optimal portfolio that provides the maximum return for a given level of risk or the minimum risk for a given return. The optimal portfolio is tangent to the risk-free asset curve and is the best choice for the investor, given his preferences. Conclusion. The method of forming an investment portfolio developed by Harry Markowitz, aimed at the optimal choice of assets, proceeds from the required ratio of profitability/risk. The ideas formulated by him form the basis of modern portfolio theory. Portfolio theory Markowitz defines an efficient set, which is all possible portfolios with different combinations of assets that provide the same level of risk. Investors can choose portfolios from this set depending on their personal goals and limitations. The variety of assets in a portfolio helps reduce the overall level of risk and improve the risk-reward ratio.

Objective. The purpose of the study is the functionality of designing, building and implementing protection systems taking into account the time factor. Method. The analysis of the functional interaction of the construction of three sequentially interconnected dynamic models and data transfer between them is carried out. Result. A general model of the system of protection and forecasting of possible threats in ensuring the security of information and infrastructure, taking into account the time factor, has been developed and proposed for implementation. Conclusion. The field of information security considered in the article is a necessary component of ensuring the protection of information resources and related systems from various threats. The application of the basics of dynamic modeling of data, processes and structures in terms of time, allows you to assess risks and threats, identify certain significant shortcomings and eliminate them, thereby optimizing costs, increasing the efficiency of ensuring security

Introduction. The analysis and interpretation of hydrodynamic research data are based on theoretical models and computational algorithms. Despite the demand for this topic, numerous issues related to unsteady fluid flows in oil reservoirs still require solutions. Therefore, mathematical setting of problems related to the account of unsteady fluid flow, the development of effective numerical methods and algorithms, their solution using modern web technologies are pressing. This study is aimed at developing a web application for mathematical modeling of the process of fluid filtration in single- porosity reservoirs when conducting a hydrodynamic study at a production well.Materials and Methods. To solve the problem, the methods of continuum mechanics and computational mathematics were applied. A model of oil flow in a single-porosity reservoir was presented. Python and JavaScript programming languages were used in the development of the application. The calculation results were stored in a relational database implemented using PostgreSQL tools.Results. A new web application has been developed for modeling the oil filtration process in single- porosity reservoirs. It is applicable for studying fluid dynamic processes and can be used to predict flowrates, production and calculation of optimal well operation modes.Discussion and Conclusion. The developed web application provides for building pressure and temperature fields in the reservoir near a flowing and shut-in production well and at various distances from it. This information makes it possible to urgently assess the duration of hydrodynamic studies, as well as to regulate the operation of wells. The application can be deployed in an existing network infrastructure and use all the functionality by connecting to a remote server. It is optimized for use on various platforms and has broad prospects for further development.

Development of rifle electronic simulators (i.e. for hand weapons and not using ammunition) is an important task, since the production of any type of small arms according to regulatory documents also requires the production of a simulator to instill aiming and firing skills. A family of electronic shooting simulators "STrIzh" of four levels of implementation: initial, basic, professional and special is described. Structural diagrams of different configurations are given, functional purpose and capabilities of each level of simulators are shown. The initial level allows independent assemble the simulator from publicly available elements (laptop, webcam, weapon layouts, IR LEDs), which can contribute to widespread use both in schools and at home, but is low in accuracy and manufacturabili (requires daily calibration). The basic level also allows independent assemble the simulator, and less publicly available elements (laptop, projector, mockup weapons, laser emitters, FHD camera), which allows to be used both in schools and in DOSAAF structures, and has acceptable accuracy and manufacturability (a weekly calibration is enough, but assembling a mock-up weapon with laser emitters requires adjustments). It is recommended to limit the special level to virtual reality simulators, including a helmet with a smartphone and a mockup of a weapon with its smartphone which also contributes to its public availability and widespread use. The simulator software algorithm should fully support all implementation levels with different configurations and include a multimedia shooting training system. Mathematical models of external ballistics of thrown equipment for Kalashnikov assault rifle, Makarov pistol, hand-held anti-tank grenade launcher 7 products are described in detail, taking into account changes in atmospheric factors (temperature, air pressure, wind force) and dispersion of various types of ammunition. The above review of rifle simulators and their experience revealed the main trends of improvement – use of virtual reality and training not only direct shooting skills, but also training in the eligibility of the use of weapons, safe handling of them and even tactical interaction in the group.

The article is aimed at considering the issue of the discursive text typology and developing a parametric model of the elementary school texts for the ontological domain by employing a corpus-based approach and methods of linguistic statistics. The research corpus of over 90,000 tokens comprises texts of 13 textbooks acknowledged in the 2nd grade of Russian schools. The applied multifactor discriminant analysis enabled identification and validation of typological characteristics of the texts under study, offering the formula for referring educational texts to a subject domain on Philology, Mathematics, and Natural Sciences. The discriminant analysis results confirmed the hypothesis that each type of text corresponds to a parametric model, which includes six constants: the average number of words in a sentence, the average number of nouns, the average number of verbs and the average number of adjectives per sentence, local noun overlap, global argument overlap. The assessment of linguistic parameters was performed by an automatic Russian text analyzer RuLingva. The classification accuracy of the parametric model was identified as 80%, which ensures its high reliability and allows for the data obtained to be employed in linguistic expertise, as well as for in automated linguistic profiling of texts. The prospect of the research implies installation of the model in RuLingva and development of similar models for texts of other subject domains.

The development of unmanned aerial vehicles can be regarded as a promising direction of modern aviation. They have significantly reduced dimensional characteristics, if compared with traditional aircraft. It is also possible to form unmanned aerial vehicles, which are aimed at performing corresponding tasks. It takes less time to train a specialist to fly an unmanned aerial vehicle compared to conventional pilots. The work is related to the creation of mathematical models that allow an integral way to evaluate the effectiveness and conduct cluster structuring of a swarm of wireless aircraft. At the same time, there are opportunities to take into account the limited resources, to carry out redistribution of resources. Resources are distributed among clusters, and the principle of inverse priorities has to be applied. After that, the distribution over the drones of the network structure that has been optimized is implemented. Monitoring information is used. The main stages of solving the problem, which are based on optimization procedures, are shown.

To increase the traction force of tractors while simultaneously reducing the specific pressure on the soil, one of the effective ways is the use of a tracked propulsion unit. The article considers a variant of a tracked propulsion unit, installed separately on each drive axle of the tractor instead of wheels. The basis of the developed design of the tracked propulsion unit is the trackbed, which reduces the pressure on the ground and increases adhesion to the soil. The results of simulation modeling of the rectilinear movement of a tractor with a tracked propulsion unit along grain stubble are presented. Realizations of oscillations of the front, sprung and rear, unsprung axles and the tractor frame were obtained. Oscillations in the ordinates of the reference surface were modeled as a random process with specified values corresponding to the reference surface of the grain stubble. The simulation results showed acceptable oscillation values of the tractor frame with the proposed propulsion design. The proposed propulsion unit can be easily installed on a tractor instead of wheels and, if necessary, can also be easily dismantled. Purpose. Investigation of oscillations of the center of mass of a tractor with a tracked propulsion unit using simulation modeling in the MATLAB Simulink environment. Methodology. Methods of mathematical modeling and analysis were used in the article. Results. The parameters showing the effectiveness of using a tracked propulsion unit instead of wheels on a tractor of traction class 6 are obtained. Practical implications. The results obtained can be applied in the design of tractors to determine the acceptable parameters of the tracked propulsion unit.

Microarc oxidation is a promising technology for producing wear-resistant anticorrosive coatings for goods made of valve metals and alloys and is used in many industries. One of the main problems of this technology is low controllability caused by the complexity and interconnectedness of physical and chemical phenomena occurring during the coating process. To solve such problems, digital twins are currently actively used. The paper covers the development of mathematical models that are advisable to use as structural elements of the digital twin of the microarc oxidation process. An equivalent electrical circuit of a galvanic cell of microarc oxidation is given, which takes into account the electrolyte resistance, the part coating resistance in the form of a parallel connection of nonlinear active resistance and capacitive reactance. The authors propose a mathematical model describing the behavior of the equivalent electrical circuit of a galvanic cell of microarc oxidation. A technique for determining the parameters of this model was developed, including the construction of a waveform of changes in the resistance of the cell and its approximation, estimation of the values of resistances and capacitance of the galvanic cell equivalent circuit. The authors proposed a calculation method and developed a Simulink model of the microarc oxidation process, which allows simulating the current and voltage waveforms of a galvanic cell. The analysis of the model showed that the model is stable, controllable and observable, but poorly conditioned, which leads to modelling errors, the maximum value of which is 7 % for voltage and 10 % for current. By the parametric identification method using experimental current and voltage waveforms, the dependences of the parameters of the galvanic cell equivalent circuit on the oxidation time are obtained. It is found that the change in the period average of the galvanic cell active resistance correlates with the coating thickness.

Issues related to possible problems in the implementation of digitalization programs for large enterprises for the processing of natural hydrocarbon and mineral raw materials, due to the discrepancy between the technical level of the existing fleet of compressor equipment of these enterprises, both with the requirements of modern production and modern achievements in the field of compressor engineering, are considered. It is noted that the discrepancy between virtual and physical technological objects leads to an overestimation of the costs of creating and maintaining IT products, as well as to a decrease in their efficiency. The ways of improving the element base of compressor equipment are proposed. A theoretical analysis of the functioning of an alternative design of a rotary vane compressor with water supply to its flow part is performed. Its example shows that there are obvious prerequisites for replacing the fleet of existing reciprocating process compressors with more advanced designs, the production of which can be completely based on domestic technologies and localized in the Russian Federation in the interests of the core industries of the processing industry.

Background and Objectives: The goal of this work is to study the impact of the shape of the 24-hour light profile on the behavior of the «sleep-wake» switching model using physiological markers: the time of minimum core body temperature, the time of melatonin peak of plasma, and sleep and wake times. Based on them, you can conclude about the synchronism between circadian, homeostatic and daily rhythms, which is an important criterion for normal human life. Mathematical model: We used the trigger population model of arousal state dynamics, which demonstrates the most realistic process of “sleep-wake” and is based on numeric experimental data. By the means of a mathematical model, we calculated the values of physiological markers and studied the influence of the daily intensity profile on them. Results: As a result of our study, we have found that the light profile, represented by a harmonic function, differs in its impact from non-differentiated forms of profiles and has a stronger influence on the moments of switching between sleep-wake states than on the duration of these states. Also, in the process of our work, we have shown that the shape of the cycle a light-dark is important in the synchronous regime, while at low values of light intensity (synchronism is absent), it has a negligible effect on the behavior of the system and it is required to proceed to the assessment of their dynamics over time. Conclusion: Features of the shape of the light profile must be taken into account when developing experimental protocols.

The article describes the theoretical basis for taking into account the complexity in solving problems of transport demand, the analysis of the concept of “self-organized criticality” is carried out. The problems of describing complex conduct in transport systems are solved, the prerequisites or causes of complex behavior are indicated, the traditional definitions of a “complex transport system” are formalized. Examples of some models demonstrating complex behavior in transport systems are given. Objective: formulation of research directions in the theory of transport systems, which should be developed with the help of conceptual and mathematical devices of individual sciences, such as complexity theory, nonlinear dynamics, to solve problems of transport demand, accompanied by flows of various events and elements in transport macrosystems, to take into account the complexity of problems in the theory of transport systems in modeling the dynamics of transport demand. Approaches used: development of mathematical models of nonlinear transport systems demonstrating complex behavior, including models with power-law distribution of system characteristics within the framework of self-organized criticality, as well as models demonstrating bifurcations. Methods and (or) methodological apparatus of research: methods of the theory of self-organized criticality and synergetics, allowing to take into account the properties of a complex system. The scientific novelty lies in the use of methods and approaches of the theory of self-organized criticality and complexity theory for a wide class of models of transport systems used in problems of transport demand and based on traffic flow models. Directions for further research, recommendations: it is required to analyze real statistics of the behavior of transport systems that correspond to various states of the transport system, including complex behavior, as well as the formulation and solution of problems of the theory of transport macrosystems.