Use Of Mathematical Modeling Methods Research Articles

Methods and algorithms of intellectual support in making managerial decisions in the implementation of security alarm tasks at objects of special importance

Objective. Currently, there is a problem of developing low-cost and functional SOTC controllers with support for algorithms for controlling the totality of elements of life support systems and subsystems of HMB OOV, for example, access control and management systems (ACS), as well as the possibility of integrating the proposed SOTC solutions into existing HMB facilities. This article proposes circuit engineering and software approaches to the organization of promising STS implemented on the basis of programmable microcontrollers. Method. To achieve this goal, a systematic approach has been applied, and obtaining a quantitative assessment of the probabilistic characteristics of detecting an intruder is based on the use of mathematical modeling methods. Result. A completed circuit design for a special-purpose COTS controller has been developed, capable of solving highly specialized tasks in OOV, and also characterized by an obvious balance of functional characteristics and cost indicators. Conclusion. The developed SOTS based on universal microcontrollers makes it possible to ensure ease of implementation of security complexes and, if necessary, change the composition of the modules used to transform the intended purpose of the OTS device while maintaining the parametric indicators of the quality of the information system, helps to optimize control and automation processes at OOV in conditions of minimizing costs.

FEATURES OF TEACHING BIOMECHANICS FOR STUDENTS OF THE SPECIALTY PHYSICAL EDUCATION AND SPORTS

The work is devoted to the use of mathematical modeling methods and computer technology for research and analysis of the motor actions of an athlete. Any motor action can be analyzed from the perspective of dynamic programming, that is, a method of optimi

Mathematical modeling of the dependence of the risk of vitamin D deficiency on anthropometric and laboratory parameters

Recently, data on the use of mathematical models to determine the status of vitamin D in clinical practice in patients with various diseases appear in the literature, but there is no data on the creation of a mathematical model that allows screening in the general population. The creation of a mathematical model, with the help of which it is possible to identify groups at risk of vitamin D deficiency, will contribute to the reduction of laboratory research costs and allow screening of vitamin D status on a more massive and reasonable basis.
 Goal. Study of the relationship between the risk of vitamin D deficiency and anthropometric and laboratory parameters using mathematical modeling methods.
 Materials and methods. 928 residents of the southern region of Ukraine between the ages of 19 and 82 (average age - 47.2 years) were surveyed. Based on the correlation analysis of the studied data, the most influential data were selected as the following indicators: age, body mass index, atherogenicity coefficient, high-density lipoproteins, and the ratio of waist volume to hip volume.
 Conclusions. The study emphasizes the importance of anthropometric and laboratory parameters in predicting the risk of vitamin D deficiency. The use of mathematical modeling methods makes it possible to identify the most important risk factors and quantify their contribution. The results of the study may have important implications for public health by helping to identify high-risk groups in a timely manner.

INCREASING CHARACTERISTICS OF BSNR 9С32 DURING IMPLEMENTATION IN ITS ANTENNA SYSTEM OF THE ELEMENTS ON A MODERN ELEMENT BASE

The military conflicts of the last decade are characterized by the wide use of air assets including small - sized and (or) unmanned ones by the warring parties. In modern conditions one of the effective measures to combat them is to increase the accuracy of coordinate information provided to combat (or fire) means. Increasing the accuracy of coordinate information determines: the possibility of non-searching detection and (or) capture of aerial targets by fire means, increasing the survivability of air defense systems due to the reduction of working time (including the time for "radiation") and rapid change of their positions after completing the assigned task.
 The modern development of science and technology makes it possible to create effective means of air defense to combat existing and promising means of air attack but their development and commissioning requires large costs. In this regard, the issue of improving the characteristics of existing complexes without significant capital investments is gaining relevance.
 One of the important characteristics of the detection means and tracking of a multi-channel air assets anti- aircraft missile complex is the resolution and accuracy of measuring the angular coordinates of objects. This is due to the fact that modern air defence anti-aircraft missile complex uses information about the angular velocities of the missile-target line and the missile velocity vector when aiming anti-aircraft guided missiles using the proportional approximation method. Therefore, the accuracy of their measurement depends on the features of the missile’s flight trajectory when firing at the target and as a result the probability of its damage. The resolution and accuracy of angular coordinate measurement depends significantly on the characteristics of the antenna system.
 It is proposed to use their analogues on a modern element base instead of standard multi-channel missile guidance station 9C32 antenna elements in the work . Estimates of the characteristics of the phased antenna array when introducing promising pass-through ferrite phase shifters (in particular the increase in the accuracy of measuring angular coordinates and the range of aerial targets detection) were obtained using mathematical modeling and calculation methods. Obtained ratios allow for an appropriate assessment.
 The obtained results can be used in the development of proposals for the introduction of modern antenna elements (ferrite phase shifters) into the antenna systems of multi-channel radio equipment of anti-aircraft missile systems.The last decade is characterized by a number of military conflicts, in most episodes of which the achievement of the goal (reconnaissance and (or) defeat of certain targets) by the warring parties is mostly achieved through the use of aircraft, including small and (or) unmanned. The main difference is to obtain the desired results without a direct collision with the enemy ground component of troops (forces).
 Most of the recommended measures to combat aircraft in modern conditions can be reduced to: the rational construction of battle order (using the air defense separation), the widespread use of covert communications, radio reconnaissance and electronic warfare, the creation of erroneous and camouflage combat (reserve) air defence means positions, automation of transmission and processing of information about the air situation with the use of modern technologies and increase the accuracy of coordinate information provided to combat (or fire) means.
 Improving the accuracy of coordinate information causes: the possibility of searchless detection and (or) capture of air targets by fire, increasing the survivability of air defense systems by reducing working hours (including time for “radiation”) and rapid change of their positions after the task. Modern algorithms for processing coordinate information provided by air defense systems take into account the errors of primary coordinates measurement by radio engineering, the delay time of information in communication channels and its possible distortion. At the same time, they do not explicitly take into account the influence of topographic errors and orientation errors of radio equipment.
 In the work with the use of mathematical modelling methods, an assessment of the characteristics of the phased antenna array was carried out with the introduction of a promising pass-through ferrite phase shifter (in particular, an increase in the accuracy of measuring angular coordinates and the range of detection of aerial targets). The obtained ratios allow to make an appropriate assessment.
 The obtained results can be used when introducing modern ferrite phase shifters to the antenna system of the multi-channel missile guidance station 9С32.

Methodical approach to quantitative assessment of the risks of the implementation of threats unauthorized access to an information resource automated systems of internal affairs bodies

Objective. A characteristic feature of the current stage of development of the sphere of informatization of internal affairs bodies (OVD) is a significant increase in the volume and variety of types of service information of limited distribution, stored, processed and transmitted in automated systems (AS). This gives rise to the emergence of a large number and expansion of the range of threats to information security, primarily threats associated with unauthorized access (UAS) to the information resource of the ATS AS, and necessitates the improvement of existing methods to combat this type of crime in order to ensure the information security of objects of informatization of ATS. To obtain information that allows assessing the degree of threats, it is necessary to conduct a quantitative risk assessment.Method. The method for assessing the risks of implementing threats of unauthorized access to the information resource of the ATS AS and obtaining data in a quantitative representation is based on the use of mathematical modeling methods. The advantage of a quantitative assessment compared to a qualitative assessment is the ability to compare risks with the final result, which can be represented in monetary terms, and further use in assessing the likelihood of information threats and calculating the damage caused.Result. A methodical approach to the quantitative assessment of the risks of the implementation of UA threats to the information resource of the ATS AS is proposed, which makes it possible to assess the level of security of service information.Conclusion. The proposed methodological approach to quantitative assessment of the risks of the implementation of UA threats to the information resource of the ATS AS provides a visual representation in monetary terms of the objects of assessment (damage, costs). These calculations can be used to justify the requirements for the level of security of ATS ASs during their development and operation.

КРИПТОВАЛЮТА ЯК ОБ’ЄКТ ІНВЕСТУВАННЯ

Introduction. In the last decade, the cryptocurrency market has shown significant development. The active growth of this market has created significant investment opportunities for entrepreneurs. In order to form highly profitable investments, one should pay attention to the price behavior of cryptocurrency coins and their niche in the cryptocurrency market. Scientific research analysis. Despite the impact of investments in cryptocurrencies on the economic development of many countries, scientific research in the field of cryptocurrencies is still inconsistent. Investment activities on the primary and secondary cryptocurrency markets were analyzed in the scientific publications by M. Duchenko, T. Pavlenko, Z. Dvulit, H. Peredal, M. Rebryk, I. Gonak and other scientists. However, scientific research on cryptocurrency investing is at an initial stage since a significant number of aspects of their implementation have not yet been worked out and require systematic development due to the rapid transformation of both the cryptocurrency market and the legislative provision of their functioning in the conditions of dynamic geo-economic changes. The purpose and tasks of the research. The purpose of studying cryptocurrencies as an investment field is to find out the advantages of investing in cryptocurrencies in comparison with other investment objects, as well as to evaluate the effectiveness of such investment through the use of mathematical modeling methods. Research methodology and methods. The following special research methods were used: direct observation; applied information processing methods for the development of tables of linear dependence; to determine the closeness of the relationship between the dynamics of the value of the main cryptocoins, the method of conducting analytical work on the calculation of the correlation coefficient was used. Research results. Cryptocurrencies have taken an important place in the development of investment activities. As an investment object in the primary cryptocurrency market, it is advisable to mine the Ethereum cryptocurrency, and in the secondary market, it is advisable to buy Ethereum and Bitcoin for investments, which occupy two thirds of the cryptocurrency market and between which there is a significant correlation. Investing in cryptocurrencies is advisable due to the significant potential of mining, the growth of the value and limits of the cryptocurrencies use. Investing in cryptocurrency coins is advisable both in the short term and in the long term. There is an average (not high) correlation between the primary and secondary markets of cryptocurrency, so an investor is recommended to focus on one of the forms of investment in order to obtain a high profit, and to reduce risks, you can diversify your business by investing in the primary and secondary markets. Scientific novelty of the research results. The possibilities of cryptocurrency investment in short-term and long-term periods were considered, and a slight correlation between the primary and secondary markets of cryptocurrencies was revealed. Cryptocurrency is a relatively new object of savings and investment, therefore, with dynamic changes in the legal regulation of the cryptocurrency market, the transformed conditions for the attractiveness of cryptocoins will be formed, and this will require reflection in further scientific publications. Practical significance of the obtained research results. According to the authors, investing in cryptocurrencies is appropriate both in the primary and secondary markets of cryptocurrencies (although the correlation between them is not high) in both the short-term and long-term perspectives. The obtained research results will be useful for use in the practical activities of conducting cryptocurrency business. The article contains: formulas: 6, fig. 2, table 5, bibl. 24).

Possibilities of personalized finite element segmental analysis of the cervical spine for predicting the course of dorsopathy

Introduction. The use of mathematical modeling methods in clinical practice will make it possible to identify the pathogenetic forms of dorsopathies and thus reasonably use the concept of targeted treatment in the management of patients of this category.Aim. To evaluate the possibilities of finite element segmental analysis of the cervical spine for personalized treatment and prediction of the course of dorsopathies.Material and methods. Based on the combined data of computed and magnetic resonance imaging of the patient (female, born in 1951), a model of the C5 – C7 segment was generated, including: vertebrae C5, C6, C7, IVD, anterior and posterior longitudinal ligaments, two pairs of facet joints, spinal cord, nuchal ligament. Computer modeling and finite element method were used to analyze the stress-strain state of the cervical spine of a patient with degenerative-dystrophic changes in the C2 – C7 segments. In the Abaqus/CAE 6.14 software, finite element analysis of the C5 – C7 stress-strain state was carried out in the state of flexion, rotation and compression. The data obtained during compression were compared with previous experiments in silico and in vitro for the norm.Results. For each state, stress and displacement diagrams, load-displacement curves, stress profiles in the MPD were obtained. The axial mobility of the segment under compressive load is two times lower compared to the norm under the same boundary conditions and material models. The degree of involvement of the spinal cord in conflicts with the surrounding anatomical structures was studied. When the model was rotated to the right, conflicts were observed between the spinal cord roots and the bone structures of the vertebrae in the foraminal zones, as well as at the level of the C5 – C6 and C6 – C7 discs with the left posterolateral surfaces of the fibrous rings. When the model was turned to the left, conflicts of the spinal cord were observed in all foraminal zones, as well as at the level of the C6 – C7 disc with the left posterolateral surface of the fibrous rings. Based on the data on stresses in the studied segment, further development of dorsopathies and degenerative changes in the cervical spine was predicted.Conclusions. The use of finite element segmental analysis of the cervical spine creates objective prerequisites for the formation of a combined personalized treatment and prediction of the course of dorsopathies.

Математичне моделювання оптимального тренувального навантаження в парусному спорті

Introduction. Sailing is a sport that places high demands on the physical fitness of an athlete. Despite the fact that this sport has been practiced for a very long time, experts have not paid due attention to assessing the impact of the athlete’s load during training on his physical fatigue. The use of mathematical modeling methods at the stage of training athletes to select the optimal load will make training more effective. In order to determine the modeling method, which will allow quite simply and easily to find the dependence of the optimal physical load on the physiological indicators of athletes, a review of the most popular modeling methods in sports was carried out. The purpose of this article is to study the problem of modeling the optimal training load in sailing in order to find an effective method for building models of the dependence of the athlete’s fatigue indicators on the indicators characterizing the athlete’s condition. Results. A number of indicators characterizing the choice of optimal physical activity in sailing are given. An approach to the construction of a mathematical model for choosing the optimal physical load for yachtsmen during training is proposed. Conclusions. The article explores approaches to modeling the processes that occur during the selection of a training load in sports. Based on a review of existing methods, an inductive approach was chosen to build models for choosing the optimal load in sailing. It is planned that with the help of this approach, models of the dependence of indicators characterizing physical activity on indicators characterizing the state of athletes will be obtained, which will be given in subsequent works.

The Use of Mathematical Modelling Methods in the Creation of Composite Materials Based on Carbon Fibre Materials

The report provides data on the electrochemical modification of carbon-graphite fibers as the basis for the creation of composite materials. The results of studies of the electrodeposition of metals on pre-electrochemically modified carbon fiber materials (CFM) in order to obtain composite materials based on them are presented. The use of CFM for the creation of composite materials is associated with the possibility of deposition of metals, alloys or their compounds on the surface of their constituent fibers. Electrochemical treatment in aqueous solutions of electrolytes is a promising method for modifying the surface properties of carbon materials, including in order to improve their adhesive properties. Preliminary electrochemical modification of carbon fiber materials in indifferent solutions of electrolytes made it possible to obtain composite and nanocomposite materials with good adhesion of the electrodeposited metal to the surface of the fibers of carbon materials.When metals are deposited on carbon fiber materials, it is necessary to solve the problem of applying a uniform metal deposit or with a certain profile in the thickness of the material. In this case, it is effective to use methods of mathematical modeling of metal deposition processes in a flowing three-dimensional electrode. Depending on the selected modes of deposition of metal sediment on the CFM, some electrochemical parameters of the process and system may be dependent on both the time of the process and the thickness coordinate of the electrode. This is especially true for the value of the resistivity of the solid phase of the system, that is, carbon-graphite fibrous material. Other electrochemical parameters, such as the specific electrode surface, the exchange current and the transfer coefficient of the electrochemical reaction, the porosity of the material, etc., can also change during the electrodeposition of the metal on the CFM. It is proposed to take into account the change in the characteristic properties of modified carbon fiber materials in the mathematical modeling of the processes of electrodeposition of metals on carbon fiber materials in order to determine the technological parameters to improve the efficiency of the properties of composite materials. In order to implement mathematical models used in the calculation of electrochemical processes in the volume and on the surface of carbon fiber materials, a set of programs based on modern computational methods and programming languages has been developed.

METHODOLOGICAL PROBLEMS OF TEACHING HIGHER AND APPLIED MATHEMATICS OF STUDENTS OF ELECTROMECHANICAL DIRECTION

The article considers the main problems characteristic of mathematical education in higher technical institutions. The purposes and tasks of training of higher and applied mathematics of students of technical specialties, and also separate features of training of students of an electromechanical direction to mathematical disciplines are covered.
 Achieving the current goal of modernization of mathematics education in technical universities is associated with the solution of a number of pedagogical issues. The problem is the systematic and comprehensive reform of mathematics education in accordance with current trends in both production and education. The content of mathematical education needs to be changed, in particular: curricula and study programs, the level of educational material, methods, teaching technologies, procedures for diagnosing the quality of teaching. Curricula of specialties should contain mathematical disciplines, which include special mathematical sections that allow to provide quality training of professionally oriented disciplines and allow to form mathematical competence as part of the professional competence of the future professional. The solution of the problem of formation of mathematical competence as a part of professional competence of graduates of technical universities becomes actual. This necessitates the strengthening of the professional orientation of the content of teaching mathematics, the intensification of the activity approach in learning technologies, the importance of the formation of appropriate value orientations of students. Actualization of students' activities strengthens the role of such educational technologies as multilevel learning, independent work of students, computer technology, project activities. Thus, additional mechanisms are created for the systematic acquisition of knowledge and skills by students, for the systematic control of the formation of mathematical competencies, for a differentiated approach to learning.
 To improve the quality of mathematical education of students of technical universities it is necessary to pay attention to the construction of mathematical models of real production problems and methods of their solution. The use of mathematical modeling methods leads to the need for a deeper study of the relevant sections of mathematics. This approach changes the structure of training, gives the opportunity to use more independently the independent work of students. At the same time, students' knowledge will be deeper and stronger.

Modeling the risk of territories flooding by flood waters on the Kan River

Throughout the existence of human civilization, flooding of territories as a result of the influence of flood and ground waters has threatened normal life. One of the ways to prevent negative impact of floods is the use of mathematical modeling methods using modern software. The paper presents the results of solving the problem of modeling the dynamics of flood waters within the boundaries of the settlement of Kansk and making a forecast of possible flooding for 2021. To calculate flooding zones of territories within the boundaries of Kansk by spring waters, the TUFLOW program was used in the Surface-water Modeling System modeling environment, as well as neural network forecasting using the NeuroPro software product and visualization of forecasting results in the AIMS RSChS-2030 software environment. Simulation of the passage of floods within the boundaries of Kansk was carried out under the condition that the timing of the onset of the maximum flow on the Kan River and its tributaries coincide. The simulation results made it possible to predict local flooding of the settlement during the flood of 2021 and take preventive measures to reduce the risk of flooding.

MATHEMATICAL MODEL OF THE MANAGEMENT OF DEVELOPMENT OF INTEGRATED BUSINESS STRUCTURES

BACKGROUND AND OBJECTIVES. In modern economic conditions the formation of financial and economic factors to enhance the development of integrated business structures cannot take place without the active use of mathematical modeling methods. One of the main directions of improving the financial and economic mechanism is the use of these methods as an effective modern tool for strategic management of the development of integrated business structures.METHODS.The methodology of scientific research are general scientific and special research methods: All scientific research carried out within the framework of established integrated business structures, use general scientific methods, such as the method of scientific abstraction, the method of analysis and synthesis, the method of unity of historical and logical, positive and normative methods, as well as specific research methods. To the specific methods of research can be attributed modeling, which is presented in the study as the basis for effective management of the development of integrated business structures.FINDINGS. The hypothesis of the scientific study is to model the process of development of integrated business structures as a given condition for managing the available combined potential. The aim of the study is to substantiate theoretically the use of mathematical modeling in the management of the development of integrated business structures.CONCLUSION. It was determined that in modern conditions, under the specifics of the formation and development of integrated management structures, which includes many structural units, to improve the management mechanism can be achieved by using as an effective tool of computer technology, allowing a flexible and responsive to changing economic conditions.

Modelling of operator walking with a load of industrial exoskeleton

The proposed article is based on mathematical models of study and development setting up computational experiments of a person using an exoskeleton walking with a load process. The development and study of anthropomorphic robots’ dynamics involves the systematic approach and use of mathematical modelling methods, the automatic control theory apparatus, which makes it possible to study a complex object as a whole and also consideration of the totality of human-machine system elements, united by diverse and multi-level types of connections, as an integral object. The research objectives are the development of mathematical models describing the process of operator-exoskeleton interaction, as well as the development of a three-link mathematical model of the exoskeleton - operator system. The development of a motion control strategy when walking allows obtaining time dependences of state vector parameters changes. Mathematical models describing the process of operator and the exoskeleton interaction are being developed. The research is based on the original three-link mathematical model of the exoskeleton-operator system proposed in the paper. The original method based on interpolation, experimentally obtained data and dynamic analysis of the operator-exoskeleton system behaviour is applied. In the course of numerical modelling, time diagrams of the hinge-mechanical system torques in the process of lifting loads were obtained. Basing on the results of mathematical modelling of an operator’s walking with a load in an industrial exoskeleton, the conclusions about the possibilities of an active gravitational compensator in the hip joint are obtained.

ASSESSING THE EFFECTIVNESS OF GOVERNMENT PROGRAMS

The article presents the results of the analysis of the approved by law methodology for assessing the effectiveness of the implementation of state programs of the Russian Federation. The paper ascertains that the methodology has a number of shortcomings in terms of calculating individual indicators, does not take into account the industry specifics of measures. In order to eliminate the shortcomings of the current methodological base, the authors proposed an adjusted methodology for assessing efficiency, which involves the use of mathematical modeling methods, qualitative assessment criteria, modified coefficients. At the same time, the weighting coefficients of the main criteria of the method were revised – the study proposes to use the method of Saati hierarchies. The developed proposals are aimed at improving the accuracy and reliability of the results of assessing the effectiveness of government programs.

Investigation of physico-chemical characteristics of carboxymethylcellulose colloidal carriers for medical preparations

Introduction. Physico-chemical peculiarities of processes of preparation and aging of colloidal carriers (gels) based on carboxymethylcellulose (CMC) for medical preparations which are planned to be used as a treatment for burn wounds are considered in the article. Studies were conducted in the Central Scientific Research Laboratory of theKharkivNationalMedicalUniversity in 2019.The objectives of the study. The objective was to study the applicability of CMC solutions and their modified analogues for the gel-based pharmaceutical preparations.Material and methods. Experimental studies were carried out under laboratory conditions using equipment for viscosity and pH measuring.Results. The influence of concentration, temperature, and acidity on viscosity of gels was investigated. The gels were tested on aging during storage. The stability of these solutions and syneresis process were investigated. The influence of added modifiers – glycerol and ascorbic acid on the consistency, acidity, susceptibility to contamination and term of storage of the gels was determined.Conclusions. It is shown that unmodified solutions have the highest viscosity and the greatest stability. Increasing of temperature reduces duration of dissolution of CMC and viscosity of the gels. Modification by ascorbic acid significantly reduces viscosity and pH of gels, while addition of glycerol does not affect the stability but increases susceptibility of these solutions to contamination. Storage of obtained solutions for three months under normal conditions at room temperature leads to syneresis and total loss of initial consistency. The gels modified by ascorbic acid are shown to be the least stable. Graphic dependences of these processes are obtained and functions are calculated on the basis of experimental research with the use of mathematical modeling methods. The obtained models will allow to predict physical and chemical properties of gels in order to define the necessary parameters of preparation at the stage of development.

ГЕОПРОСТОРОВА ОЦІНКА ВПЛИВУ ВИДОБУТКУ ВУГІЛЛЯ НА ФОРМУВАННЯ ЛАНДШАФТІВ В ЗАПЛАВІ РІЧКИ САМАРА

Розробка шахтами кам’яного вугілля у Західному Донбасі призводить до утворення на поверхні заплави річки Самара просадок (до 3-7 м). Територія, що просідає, заповнюється ґрунтовими і поверхневими водами і перетворюється в заболочену водойму. При цьому погіршується родючість ґрунтів, стан заплавних луків і лісів. Польові досліди, закладені на землях, порушених гірничими розробками земель, пов'язані з обґрунтуванням вибору пом'якшувальної технології з подальшим моделюванням і прогнозом її впливу на довкілля. Застосування методів математичного моделювання для оцінки процесів техногенного впливу на навколишнє середовище повинно базуватися на використанні даних довгострокового моніторингу. Головною метою нашого дослідження була просторова оцінка антропогенного впливу на формування ландшафтів в заплаві річки Самара з подальшим моделюванням і прогнозом вертикального засолення насипного шару ґрунту. Оцінка проективного покриття земної поверхні можлива завдяки вивченню спектральних відображаючих особливостей рослинного покриву. Мультиспектральні знімки супутникової системи Landsat були використані для дистанційного зондування заплави річки Самара в 2004-му і 2020-му роках. Порівняння рівнів проективного покриття рослинністю у заплавній частині річки Самара свідчить про деградацію ґрунтового покриву за останні 17 років. Дослідження ефективності технології рекультивації шахтних відвалів були проведені в умовах Павлоградського стаціонару рекультивації порушених земель. Вихідними даними були результати визначення реакції водної витяжки (рН) і засолення рекультивованого тришарового профілю, які були отримані в 2003-му, 2008-му, 2016-му та 2020-му роках. Дані ГІС картування експериментальних ділянок дозволили визначитися з місцем відбору проб ґрунту для оцінки вертикальної міграції солей уздовж рекультивованого профілю. Згідно з отриманими даними прогнозу засолення, процес засолення рекультивованих земель без зрошення буде поступово розвиватися. Разом з тим, необхідно визнати, що інтенсивність транспірації лучної рослинності значно нижче, ніж у сільськогосподарських культур. Останній тип природокористування в Західному Донбасі пов'язаний з меншим ризиком розвитку процесів вертикального засолення ґрунтів з огляду на тенденцію переходу до стратегії природного луківництва.

ЕКОЛОГІЧНІ ПРОБЛЕМИ ПІДЗЕМНОЇ І НАЗЕМНОЇ УРБАНІСТИКИ

Purpose. The aim of the study is to predict the potential risk of urban air pollution by toxic components of exhaust gases of vehicles in terms of the underground and terrestrial urban planning, in particular, street canyons, underground pedestrian crossings, underground parking lots, etc. Methods. The following research methodology was used in the work: on the basis of space-time field observations of the intensity, density and speed of traffic flows, as well as using mathematical modeling methods it was proved that urban air pollution (of the roadside space, adjacent territories of well-type yards, underground infrastructure, etc.) by toxicants, which are components of vehicle engine emissions, remains at a high, often environmentally hazardous level, and therefore requires urgent development and implementation of the appropriate precautionary measures. Results. The analysis of problems of ecological safety of city objects of terrestrial (high-traffic roads, adjacent territories) and underground (underground pedestrian crossings, garages, parking lots) urbanistics allowed to reveal direct and indirect negative influences on air environment from emissions of motor vehicles; using mathematical modeling methods to predict the fields of concentration of major toxicants and identify areas of local emergency pollution in different weather conditions, identify the most unfavorable directions and wind speeds and assess the level of environmental hazards to human health (residents of houses located in the well-type yards, pedestrians, owners of underground garages (parking lots), tenants of parking spaces, etc.). Scientific novelty. The study revealed direct and indirect negative effects of the motor transport complex on the air environment of urban territories (objects of terrestrial and underground urbanistics), in particular, based on the use of mathematical modeling methods. The level of environmental danger to the health of urban residents has been assessed. Practical significance. The results of the study can be used in the design and construction of urban infrastructure, as well as to reduce the technogenic load on the environment and human health in existing objects of terrestrial and underground urbanistics and other city areas.

Моделирование APT-атак, эксплуатирующих уязвимость Zerologon

Purpose: the need to assess the effectiveness of the security systems for significant objects of critical information infrastructure determines the need to develop simple and adequate mathematical models of computer attacks. The use of mathematical modeling methods in the design of security system of significant object allows without significant cost and impact on the functioning of the object to justify the requirements to the system as a whole or its individual parts. The purpose of the present paper is to develop a model of the process of multistage targeted computer attack that exploits the Zerologon vulnerability, based on the representation of the attack by a Markov random process with discrete states and continuous time. Methods: methods of Markov process theory, probability theory, computational mathematics and graph theory are used in the model to formalize the attack. Novelty: application of methods of computational mathematics for functional analysis of the results of Kolmogorov’s system of equations allows to solve the problem of maximizing the time of stable operation of critical information infrastructure during computer attacks against it, using the known methods of analysis of continuous functions. Result: formulated a general statement of the problem of modeling the process of a multistage targeted computer attack using a system of Kolmogorov equations, describing the probabilities of being in conflict states of the security system with the intruder. By the Adams method implemented in Mathcad environment, numerical solutions depending on time were obtained. We introduce a security system performance index as a ratio of probability of triggering the security system and blocking intruder’s actions during the attack to the probability of successful completion of the attack. We give an example of research of computer attack realization in a typical information infrastructure, including a corporate network with domain architecture and an automated control system of some technological process. 1 For the considered example defined the optimal values of time parameters of security system. When implementing protective measures with reasonable probabilistic-time characteristics proved an increase in time of stable operation of critical information infrastructure from 11 to 189 hours.

The Paradoxes of Aviation Security and Some Approaches to their Formal Description

Civil aviation, in the process of implementing its target function for organizing air transport, faces, among other things, the problem of ensuring the safety of these transportations. Security is a multi – valued concept that characterizes the security and low level of risk for a person, society, or any other subjects, objects, or their systems. In civil aviation, there are many areas of applicability of this concept that differ in their physical meaning and subject content. One of these areas is aviation security, which protects civil aviation from illegal interference in its activities. Currently, aviation security as a scientific field includes a set of scientific and methodological tools for solving problems that can be classified as poorly formalized. This is determined by a number of paradoxes that arise within the aviation security system. The formal description of these paradoxes is a rather complex and multidimensional problem that requires the use of complex, often heuristic, methods to solve it. The paper attempts to obtain a formal description of some of the paradoxes, which will allow the use of mathematical modeling methods for the study of aviation security systems.

Fuzzy Stochastic Automation Model for Decision Support in the Process Inter-Budgetary Regulation

The purpose of this article is to study the theoretical foundations of the concept of fiscal decentralization, as the main path of self-development of the national economy of any country, and to develop mathematical tools that support decision-making in the aspect of “hard” budget constraints. The study of the problems of fiscal policy formation in foreign countries presented in modern scientific literature has revealed that the degree of application of the concepts of “soft” and “hard” budget restrictions is an actual topic in the theory of fiscal federalism. It has been substantiated that decision-making within the framework of “soft” budget constraints (financial assistance) leads to low tax autonomy of territories and limited liability of regional and municipal authorities for the results of their financial policy. As a research hypothesis, we put forward the thesis that it is necessary to create conditions for encouraging subnational authorities to support the territorial economy by granting them the possibility to use part of the taxes collected in the respective territories. The implementation of this thesis has given rise to the problem of quantifying decisions made regarding the establishment of standards for the distribution of tax revenues between budgets of different levels of the hierarchy of the country’s budget system. In terms of solving this problem, the author has constructed mathematical models based on the use of synthesis of mathematical apparatus of the theory of stochastic automata, fuzzy algebra, and simulation. In terms of solving this problem, the author proposed the use of mathematical modeling methods. The article presents the results of constructing economic and mathematical models to support decision-making in the vertical distribution of tax revenues between budgets. The models include stochastic automata, as mathematical abstractions, describing the expedient behavior of an economic agent when choosing management alternatives for territories of different levels of economic development. The transition functions of automaton models are formally described on the basis of the synthesis of mathematical apparatus of the theories of stochastic automata operating in random environments and fuzzy sets. The expediency property of the behavior of automaton models is justified by proving the corresponding theorems. The random environment in which stochastic automata are immersed is formed by a simulation model. The article demonstrates the results of experiments carried out on models, as well as a conceptual scheme of interaction between the automaton and simulation models.