Methods Of Mathematical Modeling Research Articles

A Formal Model of the Exploitation Process for Railway Signalling Devices

Railway signalling devices are used to ensure the safety of trains running on the railroad network. With the passage of time, the technical state of railway signalling devices deteriorates. During the exploitation of these devices, processes dependent on changes in technical states and changes in exploitation states occur. Achieving the maximum efficiency in the operation of a railway signalling system requires a shift from traditional corrective servicing to preventive service based on ongoing diagnosis of the technical state of the devices involved in train movements. An even greater opportunity is provided by the introduction of mathematical modelling methods into the exploitation testing of railway signalling devices and the prediction of their basic reliability indices well in advance. The proposed method allows the exploitation strategies for the signalling systems to be changed from a service-life-based strategy to a current-technical-state-based strategy while ensuring the required safety level.

Sharp Cone-Broad Cone-Disk: Analytical Solutions in the Tunnel Mathematics Space to the Steady Navier-Stokes Equations in the Area of Boundary Layer for Incompressible Symmetric Flows Entrained by these Rotating Bodies

More than 150 years of history of efforts to solve the Navier-Stokes equation have clearly shown that, applying standard mathematical tools, it is possible to do this in only a small number of simple cases. Therefore, to solve such equations, we can try non-standard methods of mathematical modeling. In this case, the emphasis should be placed not on the mathematical accuracy of the proposed solutions, but on their correspondence to experimental data or solutions to the Navier-Stokes equations obtained by numerical methods. We believe that tunnel mathematics is such a method of mathematical modeling. Main theorem of tunnel mathematics allows us to reduce a system of the steady Navier-Stokes equations to simple ordinary differential equations that give solutions in planes parallel to the basic xy plane. Collecting such solutions, we finally obtain full 3D solution of a system of the steady Navier-Stokes equations. Approximate solutions for a system Sharp cone—Broad cone—Disk in the area of boundary layer can be obtained without use of specific software (including case of turbulent motion of fluid). We get solution for a rotating disk as a limit transition for a broad cone. If such solution will be similar with famous Karman`s solution for a rotating disk (we mean laminar flows), then we could conclude that our theory is successive.

On some algorithms for comparing models of femtosecond laser radiation propagation in a medium with gold nanorods

The study of the features of the nonlinear optical interaction of laser radiation with various media is currently widely studied, including by mathematical modeling methods. In particular, the interaction of the laser pulse with the medium doped with nanorods leads to the melting of these nanorods and distortion of the laser pulse. In addition, the passage of a laser pulse through a medium with nanoparticles can lead to a change in the shape of the pulse and a significant distortion of its spectrum, as a result of which a number of undesirable effects may occur. The corresponding process can be described by the nonlinear Schrödinger equation. Analytical studies of the corresponding variants of the equation and numerical calculations have shown that the propagation of the resulting soliton subimpulses is characterized by the formation of a so-called nonlinear frequency chirp in the region of subimpulses. When considering the graphs of such a process, the following assumption arose: it is possible to measure the degree of nonlinearity by calculating the correlation coefficient between the frequency distribution in a linear and nonlinear medium. In the course of calculations using correlation analysis, we obtained statistical characteristics similar to those that were assumed in advance. At the same time, the most adequate variant of the pair correlation coefficient is obtained in the case of applying the algorithm proposed by us for its calculation.

Porous aggregate developed with the use of coal-containing clays of the Angren field

Relevance. One of the ways to solve the issues of resource and energy conservation is the production and use of porous aggregates. Porous aggregates allow obtaining effective lightweight concrete for thermal insulation, wall panels, monolithic walls and other load-bearing structures, contribute to the increase of energy efficiency, improvement of thermal insulation, reliability, increase of fire resistance, frost resistance and seismic resistance of buildings, reduction of their weight. Therefore, in the production of porous aggregates, the primary task is the use of industrial waste and products of their processing. Solving these problems leads not only to saving valuable natural resources, but also to solution of environmental problems. Aim. Development of compositions and study of properties of porous aggregate based on bentonite clay of Navbakhar deposit and coal-containing clay of Angren brown coal deposit. Object. Coal-containing clay of Angren brown coal deposit, bentonite clay of Navbakhar deposit and artificial porous aggregate based on them. Methods. Chemical, energy-dispersive X-ray, X-ray phase and infrared spectroscopic analysis, scanning electron microscopy, mathematical modeling, etc. Results. The authors have determined chemical and mineralogical compositions of the clays used. Using the mathematical modeling method they developed the regression equations describing the effects of the amount of bentonite clay in the batch, firing temperature and isothermal holding time on the bulk density and water absorption of the porous aggregates. The resulting porous aggregates with a bulk density of 395 to 690 kg/m3 have a compressive strength in a cylinder of 2.74 to 6.46 MPa, respectively. It was found that the aggregates obtained meet the requirements of regulatory documents.

Development of a machine for cultivation and sowing of grain crops

BACKGROUND: When designing sowing machines, requirements are imposed to ensure soil preparation and sowing of grain crops as part of the implementation of energy-saving technology, since their productivity largely depends on these types of work. Thus, increasing the efficiency of sowing machines is an urgent task. AIM: – the development of a seeder design that allows, with maximum simplification of the design compared with analogues, reducing metal consumption and increasing the manufacturability of the product, both in production and in operation, to ensure the best conditions for the growth of crops and a significant increase in yield. In one pass, the seeder sows the main crop, small-seeded crop (binary component) and introduces mineral fertilizers, and can also be used when putting waste and fallow lands into circulation. METHODS: Methods of system analysis, mathematical modeling, and experiment planning were used in the development of the drill design. Experimental studies were conducted in the field and laboratory conditions in accordance with existing methods, using modern electronic and mechanical devices. Experimental data processing was carried out in the environment of the MathCAD system, Microsoft Office Excel. RESULTS: In contrast to known analogues, the proposed technical solution of the seeder simplifies the design, reduces the weight and improves the manufacturability of the product - on a simple frame welded in one plane from pipes, but free enough for the passage of crop residues and soil particles, on one side are installed stands with tines for mounting discs, and on the other - for mounting the hopper. The plane of attachment of tines for disc mounting is as close as possible to the soil surface, which reduced the load on the frame and reduced its material intensity. The seed drill-cultivator developed by the authors allows to realise all operations related to soil cultivation and sowing of grain crops Translated with DeepL.com (free version). CONCLUSIONS: The design solutions for the cultivator planter obtained by the authors simplified the design of the planter compared to its analogues, reduced its metal consumption, and therefore its weight, which makes it possible to use tractors of a smaller class with lower fuel consumption. The adjustment of the angle of attack of the discs has also been simplified, and the additional installation of baking powder has reduced the clogging of the seeder with crop residues and soil lumps.

МАТЕМАТИЧНА КОМПЕТЕНТНІСТЬ МАЙБУТНЬОГО ВЧИТЕЛЯ МАТЕМАТИКИ: ТЕОРЕТИЧНИЙ АНАЛІЗ

In the context of modernization of contemporary education on the basis of a competence approach, the problem of professional training of future mathematics teachers, who are able to be actively implemented in the information society, have professional competences that would meet the needs of today, becomes especially relevant. It is emphasized that an important task of training future mathematics teachers is the formation of their mathematical competence. The hierarchy of competences is characterized (according to N. Bibik): key super subjective (basic) competences, which are based on cognitive processes and displayed in different contexts; general subject competences, which belong to a certain set of subjects or branches of knowledge; subject competences - partial to the above, which are acquired in the process of studying a particular subject. The article describes the various definitions of mathematical competence proposed in the State Standard of Basic and Complete General Education (2011), the Concept of the New Ukrainian School (2018), the European Reference Framework of Key Competences for Lifelong Learning (2018), and the PISA International Education Quality Assessment (2022). Based on the analysis, it is determined that mathematical competence is defined by modern scientists as an integrated characteristic of the qualities of a mathematics teacher’s personality, which is expressed in the ability and willingness to apply mathematical knowledge and skills in order to solve professional problems using mathematical methods, applying modern methods of design, mathematical and computer modelling if necessary. Mathematical competence as a result of mathematical training of a graduate of a pedagogical education institution implies a high level of knowledge and experience of independent activity based on this knowledge for the effective professional activity of a future mathematics teacher. The structural components of mathematical competence are allocated: motivational, cognitive, value, activity, and reflexive.

RESEARCH AND ANALYSIS OF THE FEATURES OF MATHEMATICAL MODELS OF MODERN SOCIAL RELATIONS

Modern approaches to the study of mathematical modeling methods make it possible to consider society as a complex system andto apply methods tested primarily in the varieties of the development of scientific fields. It should be noted that approaches that arebased on the application of exact methods and mathematical formalism, for example, simulation modeling, in fact, can give mostlyqualitative conclusions, which is due to the multi-parameter nature of socio-legal models. An analysis of the state of modeling inthe social and legal spheres shows that it is entering a stage of growth throughout the world. The understanding of the importance ofthis direction is growing both on the part of the scientific community and on the part of practical sociology, jurisprudence andeconomics. A community of people with relationships between them is modeled as a directed graph with weighted vertices andarcs. There are groups of mutual influence, leaders, outsiders, the degrees of influence of some people on others are calculated.

Forecasting the quality of fluid seals and reservoirs for the Upper Jurassic deposits in the southeastern part of the West Siberian oil and gas province

Background. Upper Jurassic natural reservoirs are the main deposits containing 65–75% of recoverable hydrocarbon reserves in the Tomsk Region. They are overlapped by the fluid seals of the Bazhenov–Georgievsk complex, the quality of which deteriorates in the easterly direction. Therefore, to predict new promising areas, it is necessary to determine the quality and thickness of the Upper Jurassic seals and natural reservoirs. Objective. The need to forecast the quality of the Upper Jurassic fluid seals and reservoirs of the “Yu group” in the southeastern part of the West Siberian oil and gas province (Tomsk Region). Materials and methods. The paper uses regional and local studies of different years, materials and methods for interpreting geophysical well studies and seismic data from 2D reflection and core studies, databases of geological and geophysical information, methods of mathematical modeling of sedimentary basins and an original methodological approach proposed by the authors. Results. The time of the beginning of the lithification of the Bazhenov–Georgievsk rocks of the Upper Jurassic–Early Cretaceous (Aptian–Albian) was determined, and a regional model of the Georgievsk horizon distribution was constructed. The porosity of the Upper Jurassic natural reservoirs and the thickness of the Bazhenov fluid seal at the selected fields were calculated. Conclusions. The assessment of the quality of fluid seals and natural reservoirs made it possible to determine more promising areas for geological exploration using the oil and gas exploration criterion determined on the basis of the analysis of the thickness of the Georgievsk horizon (Kontorovich criterion). The efficiency of the proposed method is described using the example of the Upper Jurassic oil and gas fields in the Tomsk Region (Western Siberia).

Application of mathematical models in predicting drug dosage and its efficacy

The purpose of the research is to form a comprehensive understanding of how mathematical models are used to interpret complex dynamics related to the distribution, metabolism and excretion of drugs in the human body. The use of mathematical models to predict the required dose of drug prescriptions and establish its effectiveness means a paradigm shift in the field of pharmacology.Methods. The methodology used in this study was aimed at identifying and analytically reviewing articles that correspond to the objectives of the study. The publications included in the analysis were analyzed and data extracted, focusing on key information such as the mathematical modeling methodology used, the exact predicted treatment effects, the populations studied, long-term prognostic effects, and the assessment of the use of various drug dosing regimens.Results. In total, 12 publications were analyzed, which used four different methodologies: models with the effects of several different conditions, models that take into account the occurrence of various discrete events, models based on the effects of informative signs taking into account the physiology of individuals, as well as survival models and generalized linear models.Conclusion. The conducted study of the current state of mathematical modeling in medical research for the purpose of comparative effectiveness is intended for practicing scientists and doctors in conducting further research and introducing innovations. Despite the challenges, the potential impact of these models aimed at bridging the gap between the controlled clinical environment and the real health context is undeniable. The use of mathematical modeling methods to predict the dosage of medicines will improve the quality and effectiveness of personalized medical appointments in the coming years.

Assessment of the Ecological Safety of Honey with the Help of “Factor Area” Models

The man-made load on the environment and the decrease in biodiversity cause a direct negative environmental impact on the existence of honey bees and beekeeping products. The priority directions of the food industry are the use of high-quality environmentally friendly raw materials and the prevention of the ingress and formation of harmful substances in food products, including honey. This implies the need to develop methods for assessing the environmental safety of the studied raw materials and products. The purpose of this study was to implement a mathematical modeling method for studying the environmental safety of honey. Five types of honey were studied: Robinia, rapeseed, linden, buckwheat, and sunflower. Mathematical models were built according to the following parameters: total activity of β-emitting radionuclides; residues of levomycetin (chloramphenicol), nitrofuran (according to AOZ and AMOZ), metronidazole, and pesticides (according to hexachloran); and the content of water-insoluble substances (mechanical impurities) and heavy metals. On the basis of the obtained data and established quality criteria, calculation graphic models were built. Using algebraic methods, they derived new formulas for calculating quality coefficients. Multivariate analysis and programming methods were used to evaluate honey using mathematical modeling. The most and least ecologically dangerous contaminants and their share of influence for different types of honey were determined based on the complex of research on negative factors. The proposed mathematical models can be implemented for practical use in specialized laboratories as a tool for determining the environmental safety of honey of various botanical origins.

Study the Dynamics of the Transformation Processes for Nitrogen and Phosphorus Compounds in the Ecosystem of the Vistula Lagoon of the Baltic Sea using the Methods of Mathematical Modeling

By using mathematical modeling methods, a systematic study of the interaction of hydrobiological, hydrochemical, hydrological and hydrophysical processes that occur in the ecosystem of the Vistula Lagoon (VL) of the Baltic Sea was carried out, taking into account the processes in the active layer of bottom sediments (BS). The features of the dynamics of nitrogen and phosphorus compounds, the turnover time and the components of the balance of compounds of biogenic elements in the VL ecosystem, as well as the degree of their temporal variability have been analyzed. It is shown that the variability of nitrogen and phosphorus compounds in the aquatic environment increases in spring and autumn periods. This is due to an increase in river flow into the lagoon and an increase in the level of external biogenic load on the water area of the VL. Model calculations of matter fluxes allow us to state that the inputs of dissolved organic and suspended matter into the lagoon from external sources and the removal to the Baltic Sea are important processes that significantly affect their content in the VL ecosystem. It has been established that under strong winds the process of sedimentation of suspensions can be largely blocked, and the intensity of BS resuspension can increase significantly. An analysis of the main qualitative and quantitative features of the nature of the temporal dynamics of the DON and DOP turnover times, as well as the mineral compounds of nitrogen and phosphorus, indicates a close conjugation of the processes of transformation of dissolved organic and inorganic substances in the water of the VL. A quantitative assessment of the processes of consumption and excretion of compounds of biogenic elements by different groups of aquatic organisms has been performed, and the important role of heterotrophic bacterioplankton and protozoa in the processes of transformation of compounds of nutrients in the VL ecosystem has been shown. The model can be used to perform scenario modeling and analysis of possible changes in the VL ecosystem under changing climatic and anthropogenic conditions.

The sanctions’ resistance analysis of economic sectors: Priorities of sovereign development and technological modernization

The purpose of the study is to develop analytical tools and methodological support for assessing the stability and vulnerability of sectors of the national economy to the effects of external sanctions. The study of the problem was based on the general scientific methods of generalization, analysis and classification. Methods of logical, economic, content, statistical, investment and expert analysis were used, as well as methods of econometric and mathematical modeling to achieve the research goal. A system of indicators for assessing the operational (technological and commercial) and investment dependence of the economic sector on imports is proposed. Methodological methods for assessing the sanctions dependence of the industry in the formation of production and investment development programs are substantiated. Examples of calculations of dependence indicators by levels and aspects of the industry description in the operating and investment areas are given. Recommendations are given on the use of the proposed indicators in the process of strategic and programming development in the conditions of ensuring technological independence and structural adaptation of the Russian economy.

FORECASTING FIRE RISK VALUES USING MACHINE LEARNING AND TIME SERIES ANALYSIS

The probability of occurrence of emergencies and their consequences can be minimized by predicting events that contribute to the emergence of such a situation. An optimal and useful tool for such prediction and forecasting can be modeling, which can be carried out on the basis of information technology using computer programs.The methods of modeling and forecasting emergencies related to fires are the same as for other emergencies, but there are some specifics. The forecast of emergencies related to fires is aimed at three main stages: 1. forecasting the probability of occurrence with the determination of the place of the highest probability of fire occurrence, time and factors contributing to it; 2. forecasting the development of the situation and the spread of the fire (direction, speed) when it occurs, the process itself; 3. forecasting the consequences of a fire at a specific facility.The forecast is made based on the analysis of all possible unfavorable factors, their fields of action, features of the facility, its fire hazard and other data.The use of machine learning methods and time series analysis for forecasting fire risk values is substantiated. The possibility of using statistical methods of mathematical modeling of fire occurrence as the basis of the machine learning model is noted. This approach enables the machine learning model to process and analyze a large amount of statistical information for specific time periods and issue forecasts.

Metaphorical meaning dynamics: Identifying patterns in the metaphorical evolution of English words using mathematical modeling techniques

Abstract Conceptual metaphor theory has been criticized due to its emphasis on concepts instead of words and its top-down direction of analysis. In response to these criticisms, this paper employs a new strategy, utilizing established mathematical modeling methods to allow a systematic, quantitative analysis of the entire dataset produced by the Mapping Metaphor project at the University of Glasgow. This dataset consists of 9609 words performing 18916 metaphorical mappings between 414 domains. The data is represented as a network consisting of 414 nodes, the domains, connected by shared words. Words are represented by groups of directed mappings between all domains in which they occur. This is made possible by the use of a directed hypergraph representation, a tool commonly used in discrete mathematics and various areas of computer science but not previously applied to the metaphorical meanings of words. Examining the dataset as a whole, rather than focusing on individual words or metaphors, allows global patterns of behavior to emerge from the data without pre-filtering or selection by the authors. Outcomes of the analysis relating to the distributions of source and target domains within the network, the growth mechanisms at work in the spread of metaphorical meanings and how these relate to existing concepts in CMT are discussed.

Enhancing the quality of wholemeal bread with chia, sesame, and rosehip: mathematical modelling and organoleptic analysis

In this paper, the research was conducted using mathematical modelling methods to improve the quality of the product. This study aimed to determine the optimum composite mixture for producing whole wheat flour by adding sesame seeds, chia seeds, and crushed rosehip. Following the mathematical matrix, 20 different samples have been baked. The basic criteria were porosity and specific volume. The results were entered into Exel to draw up a graph. According to the graphic analysis, the most optimal mixture in terms of the dry matter mass in the dough was as follows in %: rosehip - 1.1%, chia seeds - 1.5%, and sesame - 2.2%. The organoleptic and physicochemical properties of the resulting samples were later analysed according to the recipes based on the selected composition of seeds. By swelling the protein shells of chia and sesame in a humid environment, amino acids in the flour combine into a chain to form a skeleton. At the same time, the ascorbic acid in the rosehip binds with the carbon atoms in the chain, strengthening the framework. As a result, large amounts of gases formed in whole grain flours are trapped in these frames, increasing the porosity of bread by 21.8%, increasing the volume of production by 29.5%, absorbing proteolytic enzymes under the influence of globulins in chia grain, slowing down amino acid degradation, reducing moisture content by 3%.

The Efficiency Assessment of the Blockchain Networks Adaptive Algorithm as Part of a Multi-Consensus System on Communication Networks

The relevance of the approaches and solutions proposed in the work is due to the desire for distributed computing and decentralization of system modules using blockchain technology in order to increase the autonomy, security and independence of system components. The implementation of blockchain technology for decentralization is hampered by the lack of flexibility in terms of the algorithm for making a single decision in the asynchronous system ‒ consensus, which affects the amount of generated network traffic and the requirements for the hardware component. Due to the changing nature of the transmitted traffic, the load on the communication channel, the time of day of traffic transmission, the equipment, and the network protocols used, the development of a single universal consensus algorithm is not possible, since it depends on a very wide range of variable and specific parameters characteristic of different tasks. The introduction of adaptation mechanisms to current network conditions and a change in the consensus algorithm without losing information and with a satisfactory level of delays would provide sufficient flexibility for further implementation in existing telecommunication systems. The purpose of this paper is to evaluate the effectiveness of the proposed adaptive algorithm for choosing a consensus for blockchain networks.The essence of the presented algorithm is to change the consensus algorithm on a section of the blockchain network upon reaching certain network conditions, which allows regulating the amount of generated load on the communication network to reduce the loss of transaction blocks and the subsequent delay in their processing. The proposed efficiency assessment model is based on mathematical modeling methods, differential equation analysis, queueing theory and network graphs. The analysis of the results showed the efficiency of the proposed model when comparing the results of the analytical calculation and the experiment. The scientific novelty of the proposed approach is to developing an adaptive consensus selection algorithm, as opposed to developing a universal consensus algorithm, and the efficiency assessment model of the proposed algorithm on the communication network, taking into account a number of parameters characterizing the devices and the section of the communication network.The theoretical significance is in the universality of the proposed efficiency assessment model for calculating the synchronization speed of all nodes of the blockchain network with specified network parameters.The practical significance of the proposed algorithm and efficiency assessment method lies in the formation of new approaches and opportunities for integrating blockchain technology into modern communication networks, abstracting from the problem of consensus selection in changing conditions of the communication network section.

Investigation of attitude control actuators for large flexible space structures using inverse simulation

This paper proposes a modular mathematical model and Inverse Simulation methods to investigate a variety of attitude control actuators for Large Space Structures. The modular model is developed to allow for different actuator types to be easily implemented and combined, facilitating investigations into a variety of actuator configurations. The generic Inverse Simulation method allows for the inverse dynamic solution to be found for any configuration of actuators without any modifications to the solution process, facilitating rapid experimentation. Reaction wheels, magnetorquers, and solar pressure torque actuators are all considered with mass scaling laws ensuring that each actuator type is compared realistically. The investigations consider the limitations of each actuator type and the deformations experienced by the structure during a large slew manoeuvre. It is found that the distribution of smaller torques across the Large Space Structure reduces deformation and combinations of different actuator types, instead of a single type of actuator, allow for a good compromise between mass, power and structural deformation.

SIMULATION OF THE INFLUENCE OF THE INVESTMENT ENVIRONMENT ON THE FORMATION OF AN ATTRACTIVE MACRO SPACE OF THE ECONOMY OF UKRAINE

The economic situation in most countries demonstrates an ever-increasing demand for investment resources while their supply is significantly limited. A system of factors characterized by multidirectional action forms the so-called investment environment in the country. Its structure and level of efficiency are crucial determinants for ensuring the sustainable economic development of a country. The purpose of the study is to substantiate scientific and practical recommendations for the formation of a highly efficient macro-space of the economy of Ukraine based on the implementation of rational investment policy measures. In the course of this research, an analysis of foreign investment volumes in Ukraine was conducted, and a list of factors ensuring the positive investment image of the country in the international arena was identified. The result of the study is constructed trend lines of GDP dependence on direct foreign investors in Ukraine and abroad, as well as trend lines of GDP dependence on the level of the tax burden and the integral indicator of the level of the shadow economy; the delineation of the main directions for forming an investment environment in the context of attracting foreign capital investments. The priority vectors of optimizing the investment environment in Ukraine are substantiated and the main problems of Ukraine's investment attractiveness as a motivational factor for investment activity are determined. The strategic directions for the development of investment attractiveness of the national economy under modern business conditions have been justified. The methodological basis of the research consists of a systematic, comprehensive, and evolutionary approach. The main scientific results of the study were obtained through the use of methods such as structural-logical analysis, theoretical generalization, comparative analysis, structural-functional analysis, and a comprehensive approach based on identifying cause-and-effect relationships, as well as logical, economic and mathematical modelling, analytical, and graphical methods.

Analysis of the third class mechanism using the modeling method in the Mathcad software environment

Purpose. To carry out a kinematic analysis of a flat twelve-link hinged mechanism with three leading links, the basis of which is a structural group of links of the third class of the fourth order with rotational kinematic pairs, which is used in technological equipment. Methodology. The kinematic study of a flat complex mechanism of the third class with three leading links was performed using the mathematical modeling method in the Mathcad software environment. Findings. Using the method of mathematical modeling, the mechanism was presented in the form of free vectors built on its links, for which, taking into account the presence of three leading links, three vector contours were selected, which made it possible to draw up a system of vector equations of their closedness with further solving by a numerical method in the Mathcad software environment. The functions of the rotation angles of the mechanism links, their angular velocities and accelerations were obtained in analytical and graphical form depending on the rotation angle of the first driving crank of the mechanism, the calculation of the angular velocities and accelerations of all the driven links of the mechanism was performed. Originality. A sequence was developed and a kinematic study of a complex planar mechanism of the third class with three leading links was done, the basis of which is a structural group of links of the third class of the fourth order. Schematic modeling of the mechanism with three leading links was performed, a visualization schedule of its kinematic scheme was built, and a valid version of its assembly was obtained from many possible ones, for which the values of kinematic parameters of all its links were determined. Practical value. An analysis of the effect of the kinematic parameters of the three leading links of the third-class mechanism on the movement of the working body of the technological equipment was carried out. From the analysis of the obtained research results for the cycle of the mechanism the reason was found for the incomplete technological stoppage of the link, which should provide the working body of the machine for the required period of time. Recommendations of the elimination were made to identify the deficiency and proposals for the need to improve the drive of this equipment.

Assessment of the efficiency of functioning of the environmental management system of enterprises

Purpose. A multifactor model is developed to assess the efficiency level of an enterprise’s environmental management system, depending on the effectiveness of organizational environmental measures. Methodology. The authors’ method for determining a comprehensive criterion for monitoring the effectiveness of the environmental management system, which characterizes the efficiency of operation and determines the level of environmental safety of enterprises, is proposed and used. To solve the tasks, a complex research method was also used, which included the analysis and generalization of literary and patent sources, and analytical, experimental research using computer and mathematical modeling methods. Findings. According to the studies and calculations of the generalized environmental quality indicator – 0.64, 0.66 and 0.66, the largest negative impact on the environment is caused by the activities of enterprises in the Pecherskyi, Podilskyi, and Solomianskyi districts of Kyiv, respectively. The obtained data testify to the relationship between the effectiveness of the implemented environmental measures (saving and rational use of resources, application of environmental technologies, advanced training, and environmental competence of employees) and the level of efficiency of the environmental management system of enterprises. Originality. As a result of the studies conducted using actual data, a system of indicators of the generalized environmental quality indicator has been proposed for the first time, which allows determining the environmental efficiency and effectiveness of the implemented environmental measures to assess the effectiveness of the functioning of the implemented environmental management system of the enterprise. Practical value. Based on the research results, a technique is proposed to assess the effectiveness of the environmental management system of enterprises by determining a generalized environmental quality indicator in terms of reducing the negative impact of the enterprise’s activities on the environment. Such an assessment system will help the management of the enterprise to promptly introduce corrective actions to improve the efficiency of the environmental management system and increase the level of environmental safety.