Mathematical Analysis Method Research Articles

Landau vs Einstein: mathematics represents the universe

The modern theory of gravity is the Einstein space theory, which is described by mathematical methods of tensor analysis of Riemannian geometry. Einstein built on this basis one of the most successful and amazing theories. Complexity theories often lead to the extraction of foundations and, as is customary in theory, to obtaining meaningless results. Now the entire intellectual power of numerous researchers is directed at alternative theories, often based on erroneous ideas about Einstein's theory. An example of this is the catastrophic error in the definition of the coordinate transformation in the top manual on theoretical physics by L. D. Landau and E. M. Lifshitz.

Effect of water saturation on uniaxial constant amplitude tensile fatigue performance of ECC and its statistical analysis of fatigue life

The degree of water saturation has a significant influence on the tensile fatigue properties of Engineered Cementitious Composites (ECC). The half-saturated and saturated state ECC can be rapidly prepared by a vacuum saturation equipment. The fatigue tensile mechanical tests under five tensile stress levels and corresponding studies on the damage morphology, fatigue life, S-N relationship, fatigue strain and fatigue damage on dry, half-saturated, and saturarted state were conducted. The mathematical and statistical analysis method was also utilized to predict ECC’s fatigue life and strength with high confidence and high reliability, providing a reference for assessing structural safety. The study found that free water significantly reduces ECC fatigue strength, with fatigue life decreasing as water content increases. At 2 million cycles, fatigue strength reduction coefficients for 0%, 50%, and 100% water saturation are 0.623, 0.550, and 0.423, respectively. The three-parameter Weibull distribution best describes ECC fatigue life. Using this model, S-N and P-S-N curves were developed, incorporating confidence limits to derive γ-P-S-N relationships, ensuring high confidence and reliability.

Study on the spatial distribution characteristics of traditional villages and their response to the water network system in the lower yangtze river basin

Traditional villages hold significant historical and cultural value as the precious heritage of China’s agricultural civilization. Currently, against the backdrop of increasing urbanization and rapid expansion of urban construction land, the spatial patterns of traditional villages across various regions in China are being encroached upon and damaged, with protection pressures growing daily. As one of the important cradles of Chinese civilization, the Lower Yangtze River Basin (LYRB) has traditional villages closely linked with its water systems, forming a unique human-land relationship and spatial distribution pattern. However, influenced by the rapid urbanization process, the spatial patterns of traditional villages in this region also face a crisis, and the contradiction between protection and development is becoming increasingly prominent. How to balance this contradiction and ensure the reasonable protection and sustainable development of traditional villages has become an urgent issue to address. Therefore, this study focuses on the LYRB. Using ArcGIS tools and combined with mathematical analysis methods, the spatial distribution characteristics and essential influencing factors of traditional villages in this area were screened and analyzed. The objective was to examine the spatial structural relationship between traditional villages, four water system types, and nine sub-basin units, intending to reveal the unique interdependence between the water system and traditional villages in this area. This would provide scientific support for the formulation of scientific conservation strategies. The research results show that: (1) Traditional villages in The LYRB form two core clusters spatially and exhibit substantial spatial accumulation; (2) Water system characteristics are the main factors affecting the distribution of traditional villages; (3) In the LYRB, the spatial distribution of the nine sub-basins is closely related to the spatial distribution of traditional villages, resulting in typical regional spatial differentiation of traditional villages in this area. This study is based on a watershed perspective, and the results highlight the importance of the water system network in the development of traditional villages, revealing a unique spatial dependency relationship between traditional villages and the water network in the LYRB. In order to ensure the comprehensive protection of the traditional village system in this region, it is essential to adhere to the fundamental principles that govern its spatial configuration. A tripartite collaborative protection system based on the watershed should be formulated from the perspective of the overall distribution relationship between the water network and the traditional villages. This system would serve to protect the overall landscape, the water network pattern, and the traditional villages. Establishing an overall pattern view of integrating the water system network and the traditional villages is essential.

ASSESSING THE DYNAMICS OF CHANGES IN ROAD SAFETY INDICATORS IN UKRAINE

Purpose. A study of road traffic in Ukraine shows that despite several legislative and regulatory documents aimed at improving road safety, the total number of road traffic accidents (RTAs) is increasing from 2015 to 2021. According to statistical data, each road traffic accident involves more than one injured person on average. A significant reduction in the accident rate can be achieved by developing a national action programme to improve road safety, which should be based on a systematic analysis of the nature and causes of road accidents. Therefore, the purpose of this paper is to conduct a comprehensive study of the level of road safety in Ukraine based on a systematic approach to assessing road accident data. Methodology. In the course of the research, the methods of regression analysis were used to study the absolute, specific and relative accident rates and the causes of accidents. All calculations were performed using Excel software. Results. This paper studies the international regulatory framework and national legislative documents aimed at improving traffic safety. An analysis of changes in absolute, specific and relative accident rates in 22 regions of the country is carried out. The general trends in accident rates in Ukraine from 2015 to 2021 are identified. The total number of road accidents in Ukraine, with some fluctuations in some years, has been increasing from 2015 to 2021. However, the percentage of road accidents with victims in the total number of accidents is decreasing. The social risk indicator in 2021 decreased by 15.86% compared to 2015. However, this figure remains almost twice as high as in top countries, where even those who died within 30 days of being injured in a road accident are taken into account. The scientific novelty. Based on the methods of mathematical statistics and regression analysis, the methods of estimating absolute, specific and relative accident rates, which take into account the number of victims, injured and killed in road accidents in the study of different regions of Ukraine, have been further developed. The practical significance. The obtained regression dependencies of accident rates can be used to formulate the provisions of an effective national road safety system aimed at significantly reducing the number of people killed and injured in road accidents, as well as reducing the economic losses caused by them.

Assessment of the functional capabilities of the heart and the severity of the stress response in women 30-49 years old who are starting to engage in fitness

In this article, based on the results of scientific publications, the current state of the fitness industry development in Kazakhstan in terms of the volume of fitness services and the number of people involved is studied. The results of our own research are presented using modern technologies: in particular, using the method of cardioscanning of cardiovascular system indicators, assessing the fitness level and cardiostress index, as well as based on bioimpedance analysis, the body mass index of untrained women (30-49 years old) of the Royal Club Bukhar Zhyrau fitness club in Almaty in a state of relative rest was determined. The bicycle ergometry method was used to assess the response of hemodynamic indicators of the surveyed contingent to standard physical activity of subthreshold intensity. The obtained data were processed using the methods of mathematical statistics and correlation analysis, analyzed, summarized and formulated in the research results.

Quantifying Agricultural Residues Biomass Resources and the Energy Potentials with Characterization of Their Nature and Ethiopian Case Consumption Inference

As the Ethiopian energy demand urges for fuel options, it is essential to identify biomass fuels and estimate their energy potential. This study quantified the agricultural residues’ biomass resources and their energy potential. Further analyzed and characterized the potential nature through quantitative and qualitative methodologies with descriptive, comparative, explanatory, and exploratory studies. Five-year crop yield data of 27 crops were collected from the Central Statistical Agency of Ethiopia. Conversion factors into energy were surveyed from the literature. Subsequently, the residues available and their energy potentials were estimated. Mathematical and statistical analysis methods were considered in an Excel sheet. A new measure of natural potential capacity for energy was defined in two views (resource and application). Accordingly, their potential capacities were rated and prioritized comparatively. The gross energy potential of all the residues was estimated to be 494.7 PJ. With 30% collecting efficiency, it corresponds to the imported petroleum fuel in 2018. Five major crops contributed to 80% of this gross potential. Maize and sorghum presented the highest potential due to their superior yields and good natural potential capacities. They are also well distributed in all the regions. Cotton and maize’s natural potential capacities are the best in both views. Generally, commercial crops presented better capacities than the major cereal crops. However, major crops’ energy potentials dominated due to their yields. These resources need mobilization into modern and commercially accessible fuel forms that await intervention. Densified and carbonized forms of consumption in nearby industries and households are most viable for the Ethiopian case.

Modal analysis of Lamb waves of steel pipeline with calcium deposits

The relevance of the work lies in the study of the effect of calcium deposits of various thicknesses on the inner walls of the pipeline on the parameters of its own vibrations.OBJECTIVE: To construct a mathematical model of a steel pipeline without deposits and with calcium deposits of various thicknesses on its inner walls. To perform a modal analysis of the natural vibrations of the steel pipeline. Theoretically confirm the dependence of the change in the oscillation frequency of the pipeline when exposed to sediments.METHODS. The paper highlights a method for analyzing the natural frequencies of the pipeline using the acoustic method of non-destructive testing, since it can be implemented with one-way access and does not violate the integrity of the object of control. In solving this problem, the method of mathematical analysis in the software package of finite element analysis was used. results. The article describes the relevance of the topic, discusses the main methods of non-destructive testing, and defines Lamb waves. A mathematical model of a steel pipeline section with out internal deposits and with calcium deposits of 5 different thicknesses has been constructed.CONCLUSION. Calculations have shown that the natural vibration frequencies of the pipeline without deposits and with calcium deposits change in the direction of increasing values, the frequency increase occurs in waves. The highest frequency values are obtained when modeling calcium deposits with a thickness of 10 mm on the walls of the pipeline.

Testing the operation of protection devices against parallel arc breakdown and spark gaps in the event of a ground fault

Testing the operation of protection devices against parallel arc breakdown and spark gaps in the event of a ground faultTHE PURPOSE. Develop a laboratory rig for testing parallel arc fault and spark gap protection devices for tripping in the event of a ground fault. Conduct laboratory rig tests with subsequent development of requirements for the use of parallel arc fault and spark gap protection devices for tripping in the event of a ground fault.METHODS. Mathematical and statistical methods of analysis were used to achieve the stated objective. Laboratory tests of parallel arc fault and spark gap protection devices for different network parameters for correct tripping in the event of a ground fault.RESULTS. Laboratory tests of parallel arc fault and spark gap protection devices for correct tripping in the event of a ground fault were conducted with different network parameters. The oscilloscope recorded the shape of the voltage and current curve in the event of a ground fault and the tripping time of the devices. The tested devices demonstrated the ability to recognize and disconnect a ground fault. The tripping time of the devices varies, however, does not exceed the established requirements.CONCLUSION. A laboratory stand has been developed for testing parallel arc breakdown and spark gap protection devices for operation during a ground fault. This stand makes it possible to test devices for adequate operation during a ground fault with subsequent certification. The tests conducted demonstrate the need to develop mandatory requirements for the device to standardize their operating algorithm. Therefore, the use of this protection device can contribute to safer operation of low-voltage electrical networks by preventing emergency situations and reducing the risk of fires. This is an important technical aspect for improving the reliability and safety of power supply.

Implementasi Pendekatan Jurimetri dalam Penyelesaian Sengketa Hak-Hak Perempuan dalam Putusan Cerai Talak

The divorce gives rise to rights and obligations, especially women's economic rights after divorce, namely iddah, mut'ah and madhiyah livelihood. Judges in determining the amount of alimony still vary and there are no standard rules and methods so that judges can guide them in determining the value of alimony for wives as a result of divorce which reflects propriety and justice. The author will put forward the idea of ​​the jurimetric method as a mathematical analysis method related to determining the amount of iddah, mut'ah and madhiyah maintenance for wives after divorce. The aim of the research is to analyze the application of the jurimetric approach in resolving disputes over women's rights in divorce decisions for talak at the Gedong Tataan Religious Court and the Sukadana Religious Court and to analyze the perspective of maslahah al mursalah and the theory of justice towards the implementation of the jurimetric approach as a method for determining the amount of women's rights in decisions divorce. This research is normative legal or normative juridical research which is descriptive analytical in nature. The application of jurimetry in determining the amount of women's rights in divorce and divorce decisions regarding 'iddah, mut'ah and madhiyah income, is carried out by collecting empirical data which is then expressed in variables. Jurimetry is a tool to interpret norms for the sake of realizing justice. By applying a jurimetric approach in determining the amount of 'iddah, mut'ah and madhiyah income, it has fulfilled procedural justice and distributive justice and fulfilled maslahah al-mursalah.

The effect of rehabilitation measures on the severity of endotoxicosis and its relationship with changes in hemorheology in acute poisoning

Introduction. The use of multidimensional statistical analysis methods (factorial and cluster methods) to study the pathogenesis and sanogenesis of acute poisoning (AP) with psychopharmacological agents (pPPhA), neurotoxicants (pNT) and corrosive substances (pCS) did not allow us to judge the presence of a direct connection between the hemorhealogy system (HR). We received a positive answer to this question earlier with the help of pair correlation analysis (PCA). New data on the sanogenetic effect of the applied methods of rehabilitation treatment in terms of changes in the indicators of HR and endotoxicosis (ET) and the relationship between them are also interesting. The purpose of the work is to assess the initial state of the indicators of HR and ET and the effect on them of a combination of medicinal and non–medicinal products used as part of rehabilitation measures for AP. Material and methods. Paired correlation analysis of the block structure of the obtained correlation matrices was applied to 52 patients with severe pPPhA, pNT and pCS. This analysis established the relationship between two indicators – both before the start of rehabilitation measures (the use of ethylmethylhydroxypyridine succinate, laser hemotherapy, hyperbaric oxygenation and mesodiencephalic modulation in accordance with the type of AP), and after their completion, before the discharge of patients from the hospital. Results. Statistically significant correlations were established between the indicators of HR and ET both before the start of treatment (0.44–0.94, without sign) and after its completion (0.49–0.99, without sign), which allowed us to confirm at a higher level a direct link between the development of HR and ET disorders, as well as to draw a conclusion about the sanogenetic effect of rehabilitation treatment. Limitations. The study has no limitations for further use of this methodological approach. Conclusion. The obtained data can serve as a justification for the introduction into practice of the proposed methods of mathematical analysis of the results of treatment measures.

The effect of independent activities in healthy fitness on the psycho-emotional state of female students of vocational schools in the conditions of marital state

The full-scale war on the territory of our country affected all Ukrainians without exception, including student youth. Therefore, the relevance of studying the problems of the psycho-emotional state of the individual in today's conditions is extremely important. The purpose of the study was to analyze the influence of self-remedial fitness classes on the psycho-emotional state of female students of higher education institutions under martial law. Research methods: theoretical analysis, testing, pedagogical experiment, methods of mathematical analysis and statistics. The article presents the developed methodology of self-improvement fitness classes, which is conventionally divided into three stages. The test results obtained at the end of the study indicate that the psycho-emotional state of female students improved after the implementation of the method of self-remedial fitness classes, in relation to each indicator, namely: the increase in the indicator of low level of anxiety improved by 4.1%, medium and high level of anxiety, respectively, by 2% each . For low and high levels of frustration, in percentage terms, the scores improved by 2% each, and the average scores improved by 5%, respectively. The indicators of low and high levels of aggressiveness respectively improved by a percentage of 2% each, and indicators of medium level of aggressiveness respectively improved by 5%. Regarding the average level of rigidity, the indicators in percentage ratio improved by 1%, respectively, low and high level of rigidity in percentage ratio by 3% each, which ensured the achievement of the set goal. Further scientific research can take place in the area of determining the impact of independent health fitness classes on the level of physical fitness of female students of higher education institutions under martial law.

Characteristics of health-preserving competence of future physical education teachers in the structure of professional training

This article presents the results of a sociological study aimed at assessing health-preserving competence and its role in the professional training of future physical education teachers. The goal of the research is to characterize the health-preserving competence of future physical education teachers within the structure of professional training during wartime and postwar conditions. Research methods include theoretical analysis of scientific and methodological literature, sociological research, pedagogical research methods (observation), and mathematical analysis methods. The study involved 53 students from the first to fourth years of the specialty 014.11 Secondary Education. Physical Culture at Yuriy Fedkovych Chernivtsi National University. Students' self-assessment of their level of health- preserving competence was divided into four levels: high, sufficient, average, and low. Only 7.4% of respondents rated their level as high, while the majority rated it as sufficient or average. The research identified the main reasons leading to low or average self- assessment of professional culture: insufficient number of practical classes (27.8%), lack of independent work (20.4%), insufficient theoretical knowledge (14.8%), and low level of motivation and interest (14.8%). Key aspects of health-preserving competence for future physical education teachers were determined. Despite the significant attention of higher education institutions to the formation of health-preserving competence, only 51.9% of students regularly implement components of a healthy lifestyle. The most effective means of forming health-preserving competence were identified as the integration of relevant aspects into the curriculum, conducting master classes, practical exercises, and organizing sports events. The study emphasizes the need to improve educational programs to enhance the level of health-preserving competence, which includes increasing the number of practical classes, stimulating students' independent work, and strengthening their motivation to actively apply the acquired knowledge in everyday life and professional activities.

Reliability and sensitivity analyses of monopile supported offshore wind turbines based on probability density evolution method with pre-screening of controlling parameters

To reasonably investigate the influence of pile-soil interaction on the dynamic reliability of monopile supported offshore wind turbines (OWTs), a framework with high efficiency and good accuracy is proposed for reliability and sensitivity analyses of monopile supported OWTs. This proposed framework combines the grey relational analysis (GRA), the probability density evolution method (PDEM), and the interval mathematical analysis method (IM). Firstly, the GRA is applied to identify the main controlling parameters influencing the stochastic dynamic response of a monopile supported OWT, considering various factors such as pile elasticity modulus, soil internal friction angle and soil unit weight. Secondly, combining the probability density evolution theory, a complete sample probability set is established to obtain the dynamic reliability of the monopile supported OWT under wind and wave loads. Finally, the effect of each controlling parameter on the dynamic reliability of the monopile supported OWT is systematically analyzed by combining the IM and the change of probability measure. The proposed GRA-PDEM-IM-based framework for reliability analyses of monopile supported OWTs can effectively reduce the number of samples for probability density evolution calculations and provide reasonable and accurate reliability analyses results which can serve as a reference for design and construction of monopile supported OWTs.

METHODS OF MATHEMATICAL ANALYSIS AND PROCESSING OF EEG SIGNALS: OVERVIEW OF THE CURRENT STATE AND LATEST TRENDS

Aim. With the help of retrospective analysis, establish the current level of achievements in the field of applying methods of mathematical analysis and processing of biomedical signals, in particular EEG, and characterize the main trends. Materials and methods. The research was conducted using theoretical methods, by studying and analyzing freely available literature, publications, materials of working groups of domestic and foreign scientists over the past few years. Results. The analysis of scientific works devoted to the development and development of EEG showed that over the past five years there has been a deepening of the tendency to separate the methods of improving the hardware and software parts of electroencephalographic complexes. The last of them, in turn, can be divided into several main directions. The first direction is the improvement of real-time EEG analysis methods, including automatic processing included in the software of EEG complexes. The second direction combines mathematical methods of signal analysis to detect existing pathologies and predict the onset of pathological conditions, such as statistical, spectral-correlation analysis, building mathematical models. The next direction brings together the application of mathematical methods for EEG signal processing and further use in deep learning, the use of convolutional neural networks to detect epileptic seizures, sleep disorders, differentiation of neuropsychiatric disorders, etc. The direction of using EEG in prosthetics deserves special attention. Methods of mathematical processing of the EEG signal are widely implemented in the development of bionic prostheses. The main achievements in these directions are considered in detail in the work. Conclusions. While the improvement of the material and technical part of the EEG is focused on the issues of improving the methods of recording biological signals, finding optimal methods of suppressing noise without losing the useful signal and does not currently have breakthrough results, the methods of analysis and processing of the already received signal have developed rapidly. The use of EEG to detect pathological conditions, the study of the neurophysiological basis of cognitive processes, etc., has always attracted the interest of scientists, but the use of neural networks for EEG processing and analysis and their implementation in robotics developments has given this direction a new impetus.

A Deep Learning Approach for Intrusion Detection Systems –A Review

Throughout the past decade, the researchers have developed many a number of intrusion detection systems. Some of these were developed to work on host based and some were network-based intrusion detection systems. The presented systems are combination of HIDS/NIDS and signature/anomaly based, or hybrid systems. The intrusion detection system is an intelligence system known as computational intelligence. The main goal of computational intelligence is to provide solutions to complex real-world problems. An effective IDS must use more than standard mathematical techniques and conventional analysis methods combined with soft computing techniques to synergistically create a more robust IDS. In this paper, we review three important areas of research that have significant implication for proposed framework. First, we review existing shallow learning intrusion detection systems both in machine and deep learning. In the second section, we review existing hybrid intrusion detection systems. Finally, we provide some findings and analysis of the literature studies.

BIOMECHANICAL ASPECTS OF ENDO-EXO-PROSTHETICS OF THE LOWER LIMBS

The prospects of creating new opportunities in the rehabilitation of patients with limb amputations are generally associated with the method of osseointegration and endo-exo-prosthetics (EEP). The results of the practical application of the method indicate attention to the analytical consideration of all its components, all stages. Objective. To substantiate the expediency and directions of research and development of the theoretical and practical principles of EEP from the standpoint of the full cycle, including both the problems of osseointegration and functional qualities, constructive and technological principles regarding the prostheses themselves, the methodology of the process of mastering and using them. Results. Considered biomechanical and other arguments, which substantiate the objects of research and development of medicaltechnical and medical-technological means, including the constructions of endo-exo-prostheses, methods of learning to use them, evaluation of the quality of locomotion, increasing the reliability of the «implant-bone» c ontact. The d esign principle of a hip prosthesis with a removable unloading module is proposed, which is installed at the stage of mastering the prosthesis, and in necessary cases, during constant use. The possibilities of the method of recognizing biomechanical patterns of movements for teaching patients to walk on prostheses, for adjusting functional nodes and assessing the quality of prosthetics are shown. Conclusions. The problemof endo-exo-prosthetics is considered for the first time from the standpoint of the requirements for the functions and qualities of the prostheses themselves. Reasoned directions of application and significance of clinical, experimental and mathematical biomechanics methods for analysis and development of the functional structure of endo-exo prostheses, to reduce risks when using them.

Experimental Investigation on Chemical Mechanical Polishing of ZA27 Alloy Considering Galvanic Corrosion at Zn/Al Interface

To improve the surface integrity of ZA27 alloy, a method of chemical mechanical polishing (CMP) considering the galvanic corrosion at the Zn/Al interface is proposed to treat the surface of ZA27 alloy. Firstly, the electrochemical experiment is carried out to study the influence of the pH, H2O2 concentration, and glycine concentration on corrosion potential between zinc and aluminum. Then the Taguchi method integrated with grey relation analysis and fuzzy inference are used to optimize the CMP parameters of ZA27 alloy. Finally, the prediction model of the MRR and surface roughness Ra is established using the mathematical regression analysis method. The experimental results showed that the minimum zinc-aluminum corrosion potential difference is 14 mV when the pH is 10, H2O2 concentration is 1 wt%, and glycine concentration is 0.4 wt%. The optimum CMP parameter is the polishing pressure of 34 kPa, the polishing plate’s rotational speed of 70 rpm, and the abrasive particle concentration of 15 wt%. After polishing with the optimum CMP parameter, the MRR is 242 nm min−1, and the surface roughness Ra is 13.91 nm. This study demonstrates that the CMP considering the galvanic corrosion at the Zn/Al interface is an effective method for treating ZA27 alloy surface.

Особенности сжигания композиционных водоугольных топлив

Russia has large coal reserves, on the average up to 173 billion tons. Although, the share of coal generation in Russia is relatively small (about 20–22 %), it reaches 65 % in the Siberian Federal District. Russia cannot deny coal, but it is necessary to update and improve energy efficiency of Thermal Power Plants (TPP) and boiler houses that burn coal. Currently, technologies have been developed to produce and use composite coal-water fuel (CWF) with various additives, primarily of organic origin to improve its target characteristics. A study of the characteristics of such coal-water suspensions has proved the promising outlook of their use as fuel in large and small Thermal Power Plants, both from an economic and environmental safety points of view. However, the lack of experimental data on the issues of combustion of composite coal-water fuel in bench-scale and semi-industrial conditions hinders the further development of CWF technology. Thus, it is relevant to study the features of combustion of composite coal-water fuels from coals of varying degrees of metamorphism. To prepare experimental batches of composite CWF, raw coals and coal slurries of various stages of metamorphism (grades D, SS, T) have been used. They were burned in a bench-scale semi-industrial plant. The research results have been processed using the methods of mathematical statistics and regression analysis. The influence of mechanical activation of CWF on the viscosity and temperature of its ignition and combustion has been established. The features of combustion of composite coal-water fuel using pneumomechanical injectors of two types are determined. The composition of harmful emissions during the combustion of CWF has been determined. The possibility to use composite coal-water fuel to ignite high-power boilers has been established. It has been proved that the combustion of CWF is environmentally safer compared to the combustion of coal and other types of fuel.

A COMPREHENSIVE APPROACH TO ENHANCING THE RESILIENCE OF INFORMATION SYSTEMS: FROM MATHEMATICAL MODELING TO RISK MANAGEMENT STRATEGIES

This article examines the issue of enhancing the reliability of information systems. As a solution to this problem, an approach to assessing resilience to failures in data exchange systems is presented, based on the use of mathematical analysis methods for systems capable of operating at three levels. The developed mathematical model is represented in the form of a graph of states and failure probabilities, as well as a complex of differential equations for its description. The solution of the proposed model allows determining the probabilities of failures at different stages of the information systems' operation. This, in turn, contributes to the effective identification and elimination of malfunctions and equipment failures.

Характеристика сучасного стану іхтіофауни озера Котлован як малої штучної водойми м. Дніпро

Purpose. To investigate the current state of nearshore and pelagic communities of ichthyofauna of an artificial water body: Lake Kotlovan in the city of Dnipro. To develop a set of recommendations and bioreclamation measures to improve and maintain a balanced ecological state of the water body, to increase its recreational value. Methodology.The study of ichthyofauna was carried out in the lake Kotlovan (total area 13.4 hectares), which was artificially created in the late 1960s and 1970s, located in the Industrial District of Dnipro in the area of industrial development. The study was carried out in September 2021 - October 2022 in three main nearshore biotopes of the water body. Ichthyological samples were collected in the nearshore shallow water zone with a small-mesh (fry) seine of 15 meters long with a mesh size of 7 mm in the wings and 3 mm in the codend. Fish selected for further analysis were preserved in a 4.5% formalin solution. Processing and analysis of the collected samples were carried out at the research center “Aquatic Bioresources and Aquaculture” of the Dnipro State Agrarian and Economic University (DSAEU). Generally accepted methods of mathematical analysis were used to process the results. The study was carried out in accordance with the Program for conducting scientific fisheries research of the Scientific Research Center “Aquatic Bioresources and Aquaculture” of the DSAEU for 2022–2026. Findings. The peculiarities of the species composition and distribution of the spontaneously formed ichthyofauna of an artificial water body under the impact of negative factors - discharges of enterprises, communal and household effluents and active recreation - have been established. Ichthyofauna of the lake Kotlovan is impoverished and represented by only 10 species (4 families). The composition of the ichthyofauna lacks bottom-dwelling fish and some littoral species (representatives of the familiesCobitidae, Siluridae, Syngnathidae, Gasterosteidae, Gobiidae), a certain deformation of the taxonomic structure was observed. The absence of individual families of ichthyofauna is an atypical situation for most water bodies in this region. This is due to the artificial development of ichthyofauna and the complex negative effect of the anthropogenic factor and internal trophic relationships. Recommendations on bioreclamation measures for the development of a stable ichthyocenosis with the improvement of the trophic structure and ecological condition of the artificial water body have been developed. Originality. The species composition of the ichthyofauna of an artificially created completely isolated water body in the city of Dnipro, which has existed for about 50 years, was determined for the first time. The current structure of fish groups according to species composition, conservation status, relative abundance, type of feeding and origin were investigated. A high level of the infestation of bleak Alburnus alburnus and silver bream Blicca bjoerkna with ligulosis and perch Perca fluviatilis with eustrongylidosis was observed. Measures and recommendations for improving the state of the ichthyofauna of Lake Kotlovan and increasing the recreational value of the water body were proposed. Practical value. Based on the conducted study, it is possible to evaluate and forecast the future state of the ichthyofauna of small, artificially created and isolated water bodies under anthropogenic pressure. The proposed bioreclamation measures will allow increasing the stability of ichthyocenosis and improving water quality as well as the conditions for recreation of residents, recreational fishing within the boundaries of a large city (a complex of ecosystem services). Keywords: city of Dnipro, artificial water body, ichthyofauna, bioreclamation, biotope, recreation, ecosystem services.