Methods Of Mathematical Modeling Research Articles

From Chaos to Fractals: A Review of Mathematical Modeling of Population Dynamics

The dynamic changes in population size are a core issue in ecological research and are crucial for understanding ecosystem stability and biodiversity. Chaos theory and fractal theory offer new perspectives for exploring population dynamics. Through mathematical modeling and computational methods, the complexity and intrinsic patterns of population changes can be revealed. This paper reviews the application of chaos theory and fractal theory in the study of population dynamics. The research covers the role of chaos theory in revealing the nonlinear characteristics of population dynamics and sensitivity to initial conditions, as well as the ability of fractal theory to describe population spatial distribution patterns and scale effects. Special attention is given to the application of the fractal model (_p_ model) proposed by Su et al. in analyzing species abundance distributions (SAD) within communities, and the potential value of chaos and fractal theories in practical ecological conservation and management. This paper finds that chaos theory and fractal theory provide powerful analytical tools for studying population dynamics, helping to understand the complexity and unpredictability of population size changes. The application of these theories not only enhances the understanding of population spatial structure and distribution patterns but also provides a scientific basis for biodiversity conservation and ecosystem management. Future research may further deepen the application of these theories, develop new mathematical models and computational methods to better predict and manage population dynamics. Through interdisciplinary collaboration, these theories are expected to play a greater role in ecological conservation and resource management

Algorithm performance study pulse suppression of auto-oscillation phenomena in the electromechanical system of the electric traction drive in braking mode electric traction drive system in braking mode by methods of simulation modeling

Research relevance. Modes accompanied by increased sliding of a wheel with negative viscous friction, characterized by reduction of friction force at growth of sliding speed, can arise at the movement of the vehicle. In these cases, a loss of stability may occur, resulting in the excitation of auto-oscillation phenomena in the electromechanical system (road-wheel-mechanical drive-electric motor). The emergence of this process sharply increases the dynamic load of the system, which can lead to its failure or breakdown. As a consequence, the development of suppression methods of auto-oscillation phenomena is considered to be an urgent task.Purpose of the research. Verification of operability and efficiency of the suppression method of auto oscillations in the electromechanical system of wheel drive during braking of the vehicle.Materials and Methods. With the help of Lyapunov’ function analysis for the electromechanical system of wheel drive the suppression method of auto oscillation phenomena is substantiated. The study of the algorithm performance has been carried out with the use of MATLAB Simulink program complex.Research results. The operability and efficiency of the algorithm is proved by methods of simulation mathematical modeling, which allows its further use in the development of traffic control systems. In case of braking of the vehicle equipped with antilock braking system with the function of suppression of auto oscillations on a slippery support base the reduction of amplitudes oscillation of angular velocities of wheels by 80% and braking moments by 96% is observed. When this vehicle is braked on a high adhesion base, the amplitudes are reduced by 98% in angular velocities and 81% in torques. In simulation modeling of vehicle braking dynamics on a support base with low adhesion properties it has also been shown that in these cases the evasive maneuver can be performed, which indicates on the increase in controllability and active safety of the vehicle.Conclusion. The practical value of the study lies in the possibility of using the developed algorithm for suppressing auto oscillations in practical application as part of vehicle control systems. The developed algorithm can be used on vehicles of different classes equipped with individual traction electric drive of driving wheels.

Modeling of the qualitative state of oilseeds from soybean seeds by multifactorial analysis of factor areas

The production of oil products in Ukraine is a leader not only in the European but also in the world market of food and processing industry products, therefore, the priority areas of scientific research in this field are the effective assessment of the quality of the oil obtained. Existing methods for assessing this product by organoleptic characteristics are subjective and do not allow the use of parameters that require more complex measurement technologies; which in general makes it impossible to conduct a comprehensive analysis of the quality of the studied product. The purpose of this study was to develop and implement a mathematical modeling method for numerical analysis of the quality of soybean oil product varieties. Qualitative assessment of the studied oil varieties was carried out using such indicators as the mass fraction of fat, peroxide, and acid number; content of free fatty acids, phosphatides, moisture, and impurities; it allowed to perform a numerical analysis using dimensionless complexes regarding the condition of the studied oil product varieties and compliance with regulatory indicators. When processing experimental data and calculating the developed quality criteria, programming methods, Excel, and COMPASS mathematical environments were used, which allowed the construction of geometric quality models and the necessary assessment criteria. According to the results of the research, it turned out that the characteristics of the studied varieties "OAS Avatar", "ES Mentor", "Sigalia", "ES Mentor" and "Gallek" do not meet the requirements for compliance with the quality thresholds by 160 - 220%, however, their current characteristics, which were selected for assessment, are within the average normative indicators. The proposed mathematical models can be implemented for practical application in assessing the condition of any complex object of research using an unlimited number of characteristics. At the same time, the main requirements for these parameters are their breadth of coverage of the physical, mechanical, and chemical-biological properties of the product and the ability to provide an objective and thorough assessment of its condition.

Performance Analysis of NOMA Systems over Rayleigh Fading Channels in 5G Communication

This paper aims to analyse the performance of Non-vertical Multiple Access (NOMA) systems operating in radio communication systems, especially under Rayleigh fading channels. While NOMA technology improves spectrum efficiency by allowing users to share the same time and frequency resource, Rayleigh fading channels represent multipath propagation effects commonly encountered in real radio environments. In this research, the effects of different user power levels and channel conditions on performance metrics such as system capacity, error rate (BER) and energy efficiency are investigated. Using mathematical modelling and simulation methods, the performance advantages and limitations of NOMA under Rayleigh fading conditions are evaluated. The findings show that NOMA systems offer significant advantages in terms of spectrum efficiency and user fair sharing in Rayleigh fading channels, but require careful design for error rate and energy consumption optimisation. This study provides an important reference for more effective implementation of NOMA technology in radio communication systems.

Mineralogical indicators of Holocene climate in sediments of the high-mountain Lake Sagan-Nur (East Sayan Mountains)

We present the first results of study of bottom sediments taken from the high-mountain freshwater Lake Sagan-Nur of glacial origin which is located on the Oka plateau (East Sayan Mountains). Comprehensive investigations of the mineral composition of Lake Sagan-Nur sediments accumulated during the last ~8600 cal. years were carried out. The research methods include X-ray diffractometry (XRD), infrared spectroscopy, laser grain size analysis, SiO2bio determination, AMS and 210Pb dating. The mineral composition of the bottom sediments is dominated by layered silicates, quartz and plagioclase; and also, the X-ray amorphous component consisting of biogenic silica and organic matter is constantly present. The method of mathematical modeling of XRD profiles was used for correct identification of the layered silicates. It was found that the clay mineral assemblage was stable comprising muscovite, chlorite, illite, mixed-layer illite-smectite and chlorite-smectite, kaolinite. At the same time, the quantitative ratios of these minerals and their structural characteristics were modified significantly in response to paleoenvironmental changes in the region. This feature reveals the potential of a number of phyllosilicates (illite, mixed-layer minerals) as indicators of paleoclimate in sedimentary sections of freshwater basins. The study of sediment composition and, especially, the precision mineralogical-crystallochemical analysis of layered silicates allowed us to reconstruct the paleolandscapes and climatic conditions of sediment accumulation for different Holocene sub-stages.

ЭЛЕКТРОИНДУКЦИОННЫЙ МЕТОД РАЗМОРОЗКИ НАДЗЕМНЫХ ВОДОВОДОВ С ВНУТРЕННИМ ОБЛЕДЕНЕНИЕМ

The purpose of the work is to determine the thermal fields in the wall of a pipe of different diameters from surface heating and to find the capacities invested and changing over time. Subject: thermophysical processes in a steel unlimited plate study of the distribution of temperature fields in the wall of a pipe of different diameters, using Fourier equations. Materials and methods: the methods of mathematical modeling of thermophysical processes are based on. The method consists in using an upgraded mathematical model of the Fourier thermal conductivity equation, while, during the calculation and to simplify it, the steel pipe is mentally cut and represented as an unlimited plate. When plotting the temperature distribution over the thickness of the pipe, the Lira CAD PC 2022 software was used. Results: the method allows you to quickly determine the capacity invested and changing over time. Conclusions: the method of determining heat distribution based on the modernized Fourier method of thermal sources allows you to flexibly model and quickly solve practical problems of estimating the distribution of thermal fields in the wall of a large-diameter pipe under transverse strip sections of surface heating and cooling with specified embedded positive specific capacities.

Algorithm for Detecting Reference Points on a Digital Electrocardiogram in Real Time

Relevance. The use of digital electrocardiographs and cardiac monitors with built-in algorithms for automatic processing, analysis and interpretation of electrocardiograms allows the doctor to effectively diagnose cardiac arrhythmias. It is known that in order to provide emergency care to a patient, the duration of arrhythmia diagnostics should not exceed several tens of seconds, which requires the emergence of new algorithms for detecting informative features indicating arrhythmia, operating in real time. The need to introduce new and effective technologies for diagnosing cardiovascular diseases is also reflected in public health development programmes.Research goal. Development and quality indicators analysis of the algorithm for reference points detection on a digital electrocardiogram, bearing informative signs for the procedure of arteries diagnosis.The methods used. The study is based on an analysis of existing approaches to the problem of reference points detection on digital electrocardiogram, as well as conducting a test of the proposed algorithms by mathematical modelling methods. The quality indicators of the algorithms defined in accordance with the principles of signal detection theory and diagnostic testing, at the junction of which the task of electrocardiogram reference point detection is located. The proposed algorithm was tested on materials of MIT-BIH Arrhythmia Database, which is widely used for verification and validation of real-time digital electrocardiogram signal processing algorithms.The results. The study proposes an algorithm for detecting reference points on a digital electrocardiogram that carry informative features for the arrhythmia diagnostic procedure. The proposed algorithm is based on digital signal filtering using a decision rule based on a three-step two-threshold principle of pre-processed electrocardiogram signal values comparison on a sliding window. An experiment on the materials of the open verified MIT-BIH Arrhythmia DB showed that the quality of the proposed algorithm for detecting reference points is higher than that of the algorithms used in modern digital electrocardiographs and cardiac monitors. The proposed algorithm based on digital signal filtering and the three-step two-threshold decision rule have elements of scientific novelty.The significance. The results of this work can be used in the development of digital heart rate monitors, cardiac devices and for automatic processing, analysis and real-time computer-assisted digital electrocardiogram signal interpretation.

Promising areas of scientific and technological transformation of the world's largest economies

Subject. The article addresses indicators characterizing the level of scientific and technological development of the world's major economies as of 2023. Objectives. The purpose is to examine trends and promising areas of scientific and technological transformation of the world's largest economies within the framework of global relevant concepts. Methods. The study employs methods of descriptive statistics, correlation and regression analysis, with the construction of a dendrogram of distribution of countries into clusters by the Ward's method. The statistical databases of the World Bank for 2022–2023 served as an information base. Results. The paper presents an overview of popular areas of domestic and foreign research within the topic under consideration, determines the circle of the largest economies in the world by the largest volume of GDP at purchasing power parity, assesses the level of scientific and technological development of the world's largest economies, defines the key parameters of scientific and technological transformation, and classifies countries by level of development based on methods of economic and mathematical modeling, provides a developed conceptual model of global scientific and technological transformation. Conclusions. The findings are of interest to government-specific governance structures and can be integrated into programs for scientific and technological transformation of industry within the framework of global concepts, taking into account potential spillover effects expressed in the form of expanding opportunities for diversification and commercialization of domestic research and development.

АНАЛИЗ ПОДХОДОВ К МОДЕЛИРОВАНИЮ ВОЗНИКНОВЕНИЯ, РАЗВИТИЯ И ЛИКВИДАЦИИ ЧРЕЗВЫЧАЙНЫХ СИТУАЦИЙ НА ГИДРОТЕХНИЧЕСКИХ ОБЪЕКТАХ

Currently, an important problem, both for society and for the economy of the country as a whole, remains the problem of the safety of water bodies, especially dams and other hydraulic structures. To date, there are more than 29 thousand hydraulic structures in the Russian Federation. The destruction of such facilities is of both defense, economic and social significance for the country, as well as a potential danger to the health and life of the population, as well as the entire natural environment. About 100 million people live in the zone of possible impact of damaging factors. Based on this, we can conclude that there is a need to minimize the probability of such events. Recently, the use of new innovative methods of monitoring hydraulic structures, including mathematical methods, has been intensively developing. In this paper, an analysis of approaches to modeling the occurrence, development and elimination of emergencies at hydraulic engineering facilities is carried out. Methods of mathematical modeling and forecasting of the situation in case of emergency situations at hydraulic engineering facilities are considered. The technology of situational modeling of natural and man-made emergencies is considered. The features of using various calculation methods to assess the consequences and dynamics of hazardous situations at hydraulic structures are shown

ANALYSIS OF SYMMETRICAL ELECTROMAGNETIC APPARATUS FOR THREE-PHASE ZERO-WIRE NETWORKS

The most common problems of electricity quality in 0.4 kV power transmission lines are voltage deviations and voltage asymmetry, which are clearly manifested at the end sections of long lines with uneven distribution of consumers by phases. The technical means of solving these problems include devices for the uniform distribution of 1-phase consumers across the phases of a 3-phase network based on electromechanical relays, static semiconductor devices and electromagnetic devices. The purpose of the article is to analyze the operation of a symmetrical electromagnetic apparatus consisting of one three-phase winding located on a common magnetic conductor. The scientific novelty consists in determining the operating conditions of a symmetrical electromagnetic apparatus, obtaining qualitative and quantitative characteristics of its operation. The materials and methods. The object of the research is a static electromagnetic apparatus that exhibits properties of voltage and current symmetry when connected to a three-phase unbalanced electric network. The methods of theoretical electrical engineering are used, in particular, the method of symmetric components, including generally accepted methods of analyzing electromagnetic processes in electric machines, methods of mathematical and computer modeling, analysis and generalization. The accepted assumptions are: sinusoidal voltages and currents; the linearity of the magnetization curve of the magnetic core material and the absence of electrical and magnetic losses in the electromagnetic apparatus. The results of the study. It is established that the effect of equalizing currents in the line and voltage symmetry when connecting an electromagnetic device containing one three-phase winding on a common magnetic circuit occurs in the case of simultaneous fulfillment of the conditions: a) the use of a three-phase magnetic circuit in which the zero-sequence magnetic flux cannot be closed in the magnetic circuit; b) connections of transformer windings according to a scheme that allows the flow of zero-sequence currents in linear conductors. The models of the 0.4 kV line with concentrated and distributed load are considered. It is shown that with an asymmetric load, the SEA currents acquire a component of zero sequence, and the linear currents are aligned compared to the load currents. The coefficient of voltage asymmetry of the zero sequence decreases practically to zero, the reverse sequence practically does not change. The effect of voltage symmetry when connecting the SEA occurs both before and after the place of its installation. A decrease in the total losses of electrical energy in the line due to the equalization of currents is demonstrated. Conclusions. An electromagnetic device containing one three-phase winding on a common magnetic circuit has the effect of balancing the voltages and currents of a three-phase power line with a zero wire, if the design of the magnetic wire does not allow the possibility of closing the magnetic flux of zero sequence within its limits, and the winding connection circuit contains a neutral outlet connected to the zero wire of the network, through which zero-sequence currents can flow. The action of the considered electromagnetic apparatus manifests itself in equalizing the line currents in magnitude and, as a result, in reducing the total losses in it. The electromagnetic device symmetrizes the voltages before and after the place of its installation, the greatest effect is manifested when placing the proposed electromagnetic device at the end of the line or at the connection point of the most powerful consumer.

METHOD OF INTEGRATING AN UTILITY MODULE WITH SIEM

The current tool for information security is the use of SIEM-type systems, which allow collecting and processing a large amount of data on the protected infrastructure by defining dependencies between emerging security events. The ways in which such systems used more effectively are therefore equally valuable. This process linked to the development of new algorithms for infrastructure monitoring and the need for its (infrastructure) modernization. Classical analysis methods were used to identify important aspects and stages of the SIEM process, mathematical modelling methods for analytical calculations were used to increase the efficiency of the SIEM interaction – protected infrastructure, methods of comparative analysis in determining the advantages and disadvantages of using current software development architecture, synthesis methods for determining the applicability of intelligent application methods as a means of expansion of the obtained for the calculation of correlation events without-danger information. The objectives of the study are to increase the level of automation of SIEM decision-making and the efficiency of critical information security parameters: the speed of analysis of incoming events and decision-making, the load on information security resources in the protected infrastructure, the quality of the protection system when separating SIEM functionality into small local network «representative offices». Materials and methods. Subject of study, the process of functioning SIEM, whose efficiency does not reach optimal for solution given to systems of this type value. Classical analysis methods were used to determine important aspects and stages of the SIEM process, mathematical modeling methods for analytical calculations increase efficiency of interaction construction «SIEM – protected infrastructure», methods of comparative analysis in the determination of pre-advantages and disadvantages of using today’s current architecture for software development, synthesis methods for determining the applicability of mining methods as a means of extending the information security events correlation obtained. Results. Based on the results of the research, a new architecture of protected infrastructure for implementing SIEM interaction proposed – an infrastructure based on decentralization of information collection and preprocessing processes through delegation of SIEM software functionalities platform. The structural features of the implementation of the program platform as well as its basic functionality defined. In addition, based on the results of a comparative analysis of monolithic, service-oriented and micro-service approach, the most preferred way to implement the proposed software platform was determined, and a list of advanced functionalities, taking into account the need to use information-mining techniques to improve SIEM performance. Conclusions. The use of the proposed solution increases the performance of SIEM systems when implementing such stages as information collection and pre-processing, expands the capabilities of information security specialists by obtaining new correlated data through the use of intelligent analysis methods, and also allows you to move from a centralized implementation of the protection process to a decentralized one. The implementation of the software platform based on a service-oriented approach makes it possible to increase the level of system integration and its fault tolerance. In addition, the use of the proposed platform in conjunction with second-generation SIEM systems allows you to get an alternative assessment of the state of the infrastructure, which indicates the possibility of improving the accuracy of decision-making.

Modeling the motion of a ship with suspended cargo

The stability of a vessel determines its ability to safely navigate in any sea state. In the process of studying the dynamics of a vessel in rough seas, the method of mathematical modeling based on the linear theory of waves and rolling has been used. The models allow obtaining calculation formulas and methods used to analyze the rolling of vessels with shifting cargo on board (liquid, bulk, suspended). The effect of suspended cargo on the seaworthiness of a vessel is currently considered only when solving problems of static stability. When solving problems of dynamics, mathematical models of the roll of a vessel with suspended cargo in calm water and regular waves have been proposed, and linear differential equations of the roll of a vessel with suspended cargo have been obtained. The presence of suspended cargo on a vessel significantly changes the parameters of the roll due to the occurrence of heeling and variable moments of inertia of the vessel. The proposed mathematical methods allow simulating the roll in any regular waves, taking into account arbitrary values of the transverse metacentric height, cargo weight and suspension length.

Risk assessment for the population consuming soybeans grown with the use of pesticides in the chemical plant protection system

the use of pesticides in the agro-industrial sector of Ukraine is an essential condition for obtaining high yields and is the most common means of protecting agricultural crops. The issue of the impact of pesticide combinations when they are used in chemical plant protection systems remains relevant. The work aimed to assess the risk to the population consuming soybeans grown with the application of pesticides in the chemical plant protection system, predict the danger of their impact, and reduce the pesticide load on the population. We use methods of in-field hygienic observation, mathematical modelling, chromatography, calculation, and statistical analysis in the work. The obtained results of mathematical modelling showed that in the soil and climatic conditions of Ukraine, sedaxan, fludioxonil, metalaxyl-M, promethrin, and diquat are degraded with half-lives (τ50) <5 days and pertain to low-stable compounds, lambda-cyhalothrin was degraded in soya plants with τ50 in the range of 15-30 days, which indicates the persistency of the compound; abamectin, chlorantraniliprole, azoxystrobin, difenoconazole, and pydiflumetofen were degraded in soya plants with τ50 in the range of 5-14 days, which indicates moderate persistency according to State Sanitary Norms and Rules 8.8.1.002-98. Findings showed that the majority of the studied active substances, according to the integral indicator of hazard when consuming foodstuffs (IIHCF), pertain to class 4 (low risk), except for abamectin, lambda-cyhalothrin and difenoconazole, which pertain to moderately hazardous compounds (class 3). The calculated total cumulative risk of exposure to residual quantities of active substances when using the Vibrance mixed pesticide is 1.13% of fludioxonil ADI, Ampligo – 0.38% of lambda-cyhalothrin ADI, Amistar Gold – 1.32% of difenoconazole ADI and Miravis Duo – 1.09% of difenoconazole ADI. Calculating the combined effect of all components in the chemical protection system of soya plants showed that the total hazard of exposure to active substance residual quantities (sedaxan, fludioxonil, metalaxyl-M, promethrin, abamectin, chlorantraniliprole, lambda-cyhalothrin, azoxystrobin, difenoconazole, pydiflumetofen, and diquat) when using Vibrance, Gezagard, Vertimek, Ampligo, Amistar Gold, Miravis Duo, and Reglon Forte pesticides is 15.1% of abamectin ADI. Findings showed that the combined effect of pesticides (as components of the soya chemical protection system) on humans is within acceptable limits. The medical and sanitary standards for safe application (preharvest intervals for soybeans) are substantiated: for the Vibrance and Gezagard preparations – not required, Reglon Forte – 6 days, Amistar Gold, Ampligo, Miravis Duo, and Vertimek – 30 days.

Поиск оптимального начального состава реакционной смеси процесса полимеризации с помощью искусственных иммунных систем

To establish regularities of polymerization processes, it is advisable to use methods of mathematical modeling. On the basis of mathematical description of the process it is possible to determine the optimal conditions of its course, providing an increase in its efficiency, as well as the quality of produced polymers. One of the problems of optimization of polymerization processes is the problem of determining the initial composition of the reaction mixture, which ensures the achievement of given quantitative or qualitative indicators of the process. The aim of the work is to develop an algorithm for determining the initial concentrations of polymer synthesis reaction. The statement of the problem of searching for optimal concentrations of components of the polymer synthesis process and a numerical algorithm for its solution are given. Since the kinetic model of the polymerization process is an infinite system of ordinary nonlinear differential equations, its solution using classical optimization methods encounters computational difficulties. Therefore, it is proposed to apply the method of artificial immune systems to calculate the optimal initial composition of the reaction mixture of the polymerization process. This method allows to overcome local extrema in multidimensional search spaces and it is easy to implement for a particular process when the number of optimized parameters is changed. The developed algorithm based on the method of artificial immune systems includes a procedure for converting an infinite system of differential equations describing the kinetics of the polymerization process to a finite form using the method of moments. The algorithm has been tested on an industrially significant polymerization process of butadiene on a neodymium-containing catalytic system. The optimum concentrations of reagents that provide the polymer with the desired properties have been calculated.

Модель для контроля качества магнитопроводов линейных электродвигателей на стадии изготовления

The article presents the results of implementing an integrated approach to quality control of linear electric motor inductors at the production stage. The approach is based on the use of mathematical modeling methods and computational experiment. To assess the quality of inductors, it is proposed to use two types of indicators: differential and integral. Differential indicators are determined by conducting a series of experiments with each tooth division of the inductor. Integral indicators allow us to assess the quality of the inductor magnetic circuit as a whole, for which criterion relationships are used. To test the effectiveness of the proposed approach and the reliability of the obtained indicators, a simulation mathematical model of an electric motor inductor with detailing down to one tooth division was developed. Based on this model, an algorithm and a computer program were created that implement the proposed method of quality control during technical testing. The program is written in the Maple software product’s own interpreted programming language and requires the user to enter the parameters of the inductor and power source. As a result of the program, the user receives a conclusion on the quality of the inductor magnetic circuit, as well as numerical values of the differential and integral quality indicators. The materials of the prototype inductor with a high-quality and low-quality magnetic core were used to test the quality criteria using mathematical modeling and computational experiment methods. The results of the experiment confirmed the feasibility of implementing the proposed approach and showed that it adequately reflects the technical quality of inductor magnetic cores. The software product created as a result of the study is intended for technical control of inductor magnetic cores during their production and information support for measures to improve their quality.

Modernization of Existing Level Crossings in the Areas of Construction of the European Standard Railway Track in Ukraine

Purpose. The article aims to analyze modern technological solutions to improve the level of safety at railway crossings, prevent emergencies and ensure uninterrupted traffic. Methodology. The study is based on the use of mathematical modeling and numerical methods to analyze the impact of modernization and new projects on the level of safety at railway crossings. Using computer modeling, mathematical models were built that reflect different scenarios of crossings. Based on the data obtained, the effectiveness of the proposed measures was assessed and recommendations for further optimization of the security system were developed. To evaluate the effectiveness of the proposed measures, a system of indicators has been developed to quantify the level of safety of railway crossings before and after modernization. These indicators take into account the daily intensity of train traffic through the crossing, the daily intensity of traffic on the road, the equipment of the crossing, the radius of the curve in the plan and the longitudinal slope of the road on the approaches to the crossing. Findings. An improvement of the method of the final accident rate, which is one of the most common tools for assessing traffic safety at railroad crossings, is proposed. The application of this method made it possible to quantify the level of risk of accidents and analyze the effectiveness of measures aimed at improving safety. The method is relatively easy to use and does not require complex mathematical calculations, and allows taking into account a wide range of factors affecting traffic safety at a level crossing, such as traffic volume, design features of the level crossing, availability of signaling, etc. The final coefficient was used to compare the safety level of different crossings and track the dynamics of changes in their equipment over time. This made it possible to identify crossings that require priority modernization, as well as to predict changes in the initial and calculated data and plan measures to introduce innovative technologies that improve traffic safety at crossings. Originality. An integrated model for assessing the safety of railroad crossings has been developed that takes into account not only traditional indicators (frequency of accidents, traffic intensity) but also new factors such as equipment reliability, human factor, and the impact of external conditions. The proposed model makes it possible to determine a more accurate risk forecast and choose optimal solutions for the modernization of level crossings, taking into account specific operating conditions. Practical value. The formulated recommendations can be used to develop effective programs for the modernization of railway crossings in Ukraine. The implementation of the proposed technologies will increase the level of traffic safety by 20% and reduce the average waiting time at a crossing by 15%. In addition, it will help to increase railroad capacity and reduce infrastructure maintenance costs.

Energy structure optimization and carbon emission control based on weighted mathematical modeling and CGE model

The study employs Hebei Province as its research object and employs the weighting method for mathematical modeling to construct an energy structure optimization calculation model under carbon emission control. Secondly, a computable general equilibrium-based model is constructed for the purpose of assessing the impact of an optimal energy structure on the economic development of the province under different planning constraints. The results indicated that when the energy constraint increased from 0.8 to 1.2, the share of coal energy decreased to 61.19% and the share of petroleum energy decreased to 5.02%. The share of natural gas energy increased to 18.41% and the share of non-fossil fuel increased to 15.02%. The total cost of energy increased to 83.04 billion dollars and abatement cost decreased to 2.74 billion dollars. With the gradual completion of the planning constraints, the effect of emission reduction was gradually obvious, but the decline gradually decreased. While abatement costs could be decreased in tandem with rising energy costs, the macroeconomy and environment in the region suffered as a result of rising energy costs. The study indicates that in order to achieve sustainable regional economic development and align with the principles of ecological governance, it is essential to enhance energy management, actively advance the development of clean energy, and strive for equilibrium between economic growth, energy development, and ecological environmental protection. Concurrently, alternative energy sources must be identified through scientific and technological innovation in order to diminish reliance on fossil energy.

A Review of Mathematical Modelling Methods for Bovine Hormone Dynamics.

This paper explores various approaches to modeling the bovine estrus cycle, focusing on improving estrus detection to enhance reproductive management in dairy cattle. The review examines a range of mathematical models, including hormonal models based on ordinary differential equations (ODEs) that simulate hormone dynamics, as well as follicular competition models that track the maturation of individual follicles. In addition to these, Precision Dairy Monitoring Technologies (PDMT) are discussed, which utilize real-time physiological and behavioral data to provide predictive insights into estrus. The paper assesses the effectiveness of both traditional modeling approaches and PDMT in improving breeding efficiency, minimizing labor, and optimising herd management practices.

Numerical Modelling of Myocardial Infarction in Multivessel Coronary Lesion. II. Patterns of Formation of Large-Scale Damages and Structures

In this work, the basic mechanisms of myocardial infarction development during its inflammatory phase have been studied using mathematical modelling methods. Complex scenarios associated with multivessel lesions of the coronary bed and variability in baseline indicators of the innate immune system state have been considered. Special attention is paid to methodological issues related to the analysis of the effectiveness of the algorithm for approximate solutions of nonlinear initial-boundary value problems and setting up computational experiments under conditions close to the conditions of laboratory experiments in the field of interest. A numerical analysis was performed of several of the most common variants in laboratory practice of the formation of a large lesion in the left ventricle of the mouse heart, caused by the spatiotemporal heterogeneity of the properties of the environment, the immune reaction and ischemic myocardial damage, including recurrent infarction. The main attention is on the following aspects: – analysis of the mechanism of formation of large-scale infarct damages with an extensive core covering almost the entire infarct focus, or with a relatively small core, and assessment of the role of inflammation in these processes; – analysis of current scenarios of structure formation and the role of nonlinear dynamic structures of demarcation inflammation in the formation of a large but highly structured focus. The obtained data allow us to conclude that there is sufficient conservatism during infarction, evidenced by the basic patterns of the inflammatory phase revealed during modeling. The variability of heart attack scenarios manifests itself as a «memory»-effect about the initial data. We observe the «memory»-effect only at a biologically significant time interval, but we also note a general tendency to switch to the usual scenario of inflammation in large-focal infarction, which eliminates the peculiarities of the initial and individual conditions. The role of inflammation has been investigated in the context of a wave process in which spatial localization and the interaction of density and concentration waves can determine the main features of myocardial damage. In particular, within the framework of the adopted mathematical model, the conditions under which the formation of local zones with a relatively low or, conversely, high level of damage is possible have been described. In our work, we have established a significant interdependence between the formation of quasi-stationary structures and the intensity of the immune response. The high probability of developing severe or even terminal myocardial infarction may be due to the high level of immune system factors, in particular, monocytes-macrophages or cytokines in the reinfarction heart.

Ignition of a gasless mixture array by a combustion wave

The methods of mathematical modeling have been used to explore the initiation of combustion of a large mass of a condensed mixture in local contact with the end face of the burning layer. It is shown that the minimum width of the igniting layer is proportional to the width of the thermal front of the combustion wave. The coefficient of proportionality is determined by the initial temperature, heat and activation energy of the reaction. The calculation results can be used to estimate the effective activation energy of the reaction that controls the combustion mechanism of gasless system.