Mathematical Statistics Research Articles

Method for determining the effect of destabilizing factors of digital filters on the multicriteria synthesis of radio communications of aviation robotic devices

The purpose of the research is development of a method for determining the influence of destabilizing factors, such as the unevenness of the amplitude-frequency response (AFC) and the nonlinearity of the phase-frequency response (FFC), in non-recursive digital frequency selection filters on the target function of multicriteria structural-parametric synthesis of radio communications from the payload of aviation robotic devices.Methods. In conducting scientific research, probability theory, mathematical statistics, statistical radio engineering and computational mathematics were used. The study obtained mathematical expressions of the dependence of the probability of error per bit (BER) on the average signal-to-noise ratio when signals pass through symmetrical non-recursive digital filters with quadrature amplitude modulation with a positivity of no more than 4096, signal constellation irregularities of no more than 5, which are the basis for the energy balance of radio lines with aviation robotic devices. The expressions obtained are one of the "foundations" for the implementation of a multi-criteria synthesis of radio systems adaptive to a cognitively formed flight task. In this paper, all the results of the probability of reliability of the received data by means of communication are reflected for the case of rigid decision-making (Gray coding).Results. In the course of the conducted research: 1) a mathematical model of the structural-parametric synthesis of radio communications with aviation robotic devices is demonstrated, which is based on the criteria for minimizing: electronic computing resources with a given noise immunity; radiation outside the operating frequency band; peak factor signals; the effects of narrowband, broadband and structural interference in the radio channel at a given bandwidth; the use of structural and functional nodes specific to the existing information and communication environment; 2) the analytical dependence of the influence of the parameters of one of several structural and functional nodes - digital filters of frequency selection, on the criteria for the synthesis of communication means has been revealed. The paper considers the most common approximating functions - Kaiser, Tukey, Barlett-Khan, Chebyshev, and also shows the influence of the filter order on the equivalent of energy loss in information communication lines of aviation robotic devices.Conclusion. The scientific article presents a method for determining the effect of the uneven frequency response of a symmetrical non-recursive digital filter in devices for receiving and processing radio signals of multicriteria means of communication with the payload of aviation robotic devices. The proposed approach increases the reliability of determining the values of criteria for minimizing electronic computing resources for a given noise immunity, radiation outside the operating frequency band, as well as the use of structural and functional nodes characteristic of the existing information and communication environment.

Scientific and technical ways of reducing quantitative indicators of false alarms during the operation of an airboard radar station on the background of the underlying surface (earth)

The purpose of the research is development of scientific and technical ways to reduce the quantitative indicators of false alarms when operating an on-board radar station against the background of the underlying surface (earth) against the background of passive interference.Methods. When conducting scientific research, methods of probability theory, mathematical statistics, statistical radio engineering and computational mathematics were used. The study identified a number of methods and technical solutions based on them that make it possible to increase the efficiency of the functioning of airborne radar stations against the background of passive interference. The paper proposes a method for expanding the signal spectrum to 1 GHz by reducing the resolved volume of airborne radar stations. Physically, this is determined by the fact that with a decrease in the resolved volume, the size of the underlying surface area from which the signal is reflected decreases. In order to improve the quality of detection of objects against the background of the underlying surface, a method of using polarization modes is proposed.Results. In the course of the research: a technical solution was proposed based on the method of expanding the signal spectrum to 1 GHz by reducing the resolution volume of airborne radar stations designed to convert radio frequency signals into digital form, using a mixed signal receiver with direct digitization at radio frequency, such as the AD6688 ; a design of a low-baseline radar system has been developed, consisting of two positions, the antennas of which are located within the average width of the lobe of the backscattering diagram of the irradiated object; a feature of the antenna is the ability to receive and emit signals of the same linear polarization, but orthogonal to the polarization of the first position (including . horizontal and vertical polarization signals); an important relation was obtained for a lowbaseline polarization measuring system (MPIS) when the distance between two partial antennas can be much less than the distance to the measured object. Conclusion. The scientific article proposes methods and technical solutions based on these methods to reduce the quantitative indicators of false alarms when operating an on-board radar station against the background of the underlying surface (ground) against the background of passive interference. The proposed approach allows us to move on to the synthesis of a low-baseline polarization measuring system.

The Significance of U23 Competitions in Wrestling Career

Background. Designing the training of athletes should be based on specific goals and objectives at each stage of the long-term development. Each age stage in the development of an elite athlete has its own significance. The U23 competitions are organized to facilitate a smoother and more effective transition of wrestlers from junior to senior levels. The aim of the study is to determine the significance of performances in the U23 competitions for the subsequent development process of wrestlers. Materials and Methods. The following research methods have been used in the paper: the analysis of the scientific and methodological literature, the analysis of the official results, and methods of mathematical statistics. We have studied the sports careers of participants in the 2017, 2018, and 2019 World Championships in freestyle, Greco-Roman, and women's wrestling. A total of 1277 wrestlers’ sporting biographies have been analyzed. Results. The majority of participants (73.7 %) in the U23 age category competitions previously competed at the junior level. Moreover, more than half of the athletes (58.4 %) had prior experience of participating in cadet competitions. It is worth noting that 63.7 % of all wrestlers participated in senior-level competitions, and 31.5 % of them achieved podium finishes. Among women, a higher percentage of athletes continue their careers (46.3 %) and achieve success (20.1 %) on the international stage after the U23 competitions. For male freestyle wrestlers, the figures are lower, with only 38.2 % continuing their careers. Conclusion. The analysis demonstrated that the U23 competitions, which serve as a continuation of the cadet and junior age groups, are part of the overall sequence of competitions in the development of wrestlers at the international level. However, the importance of the U23 competitions varies depending on the level of athletes, and they serve both as preparatory and main competitions within the athletes' training system.

INCREASE OF TECHNOLOGICAL INDICATORS USED IN THE ENERGY INDUSTRY

When evaluating the suitability of using coal in various industries, it is subjected to technical analysis and a number of special technological studies. The obtained results in combination with elemental and group analysis allow choosing the most rational and economically efficient directions of their use, which plays not the least role in determining the economic significance of coal mining deposits. The work is based on theoretical research methods based on the basics of probability theory and mathematical statistics - to improve the existing methods of processing results and assessing the uncertainty of measurements; theories of accuracy - for the development of procedures for assessing the uncertainty of measurements of the quality parameters of solid mineral fuel during its tests; statistical modeling methods - to check the reliability of the developed provisions. A generalized parameter of the quality of solid mineral fuel has been synthesized, which makes it possible to evaluate its quality based on the results of tests conducted in coal chemical laboratories. improvement of methods of testing solid mineral fuel according to quality parameters by developing uncertainty assessment procedures.

Using Balancing Equipment in Archer Training

Background and purpose The implementation of balance equipment plays an essential role in archery training. It helps develop stability, accuracy, coordination, and muscular endurance, all critical for successful. Balance platforms, exercise balls, and specialized devices add extra load on stabilizer muscles, leading to a more efficient use of the body and assisting athletes in maintaining balance during string tension and targeting. The objective is to evaluate the effectiveness of balance exercises in archers' training. Material and methods Participants: 23 archers (aged 13-14) from the "KOMUNAR" Kharkiv City Specialized Youth Sports School of Olympic Archery Reserve. The experiment was conducted for 2 months from August to October 2024. At the beginning and end of the experiment, an interactive survey was conducted using a Google form. Theoretical analysis, data generalization, questionnaire method, and mathematical statistics Results Developed and implemented in the training process of exercises with fitness balls, balance pillows, boards, fitness trampolines, balancing platforms. In addition to the usual balance exercises, the archers performed stances with bowstring tension with closed and open eyes and archery on balancing devices. The use of an extended set of preparatory exercises in the training process of archers made it possible to change the attitude of athletes to physical training, improve technical skills and develop psychological stability. The introduction of new training tools contributed to increasing the motivation of archers, understanding the importance of a versatile approach in the training process to achieve high results in archery. Conclusions It is shown that the use of special exercises has a positive effect on the psychological state of young athletes, emotionality and self-confidence. Keywords Archery, balancing equipment, balance, young athletes.

Spatiotemporal Evolution Mine Groundwater’s Hydrogeochemical Characteristics Under Influence of Mining and Grouting in Gubei Coal Mine, China

Geological conditions or human activities will affect the hydrochemical characteristics and formation mechanism of mine groundwater to varying degrees. The northern part of the Beiyi mining area of Gubei Coal Mine is taken as the research area in this study. Based on the data of 52 groups of limestone water (Taihui water) samples in the primary environment, in the mining stage and after grouting, the spatial and temporal variation trend of the chemical characteristics of Taihui water was studied by means of constant index mathematical statistics, a Piper diagram, total ionic salinity, correlation analysis, the ion ratio method and the saturation index. The purpose of this study is to analyze the influence of special geological structures, mining activities and grouting treatment on the formation process of the chemical characteristics of Taihui water, and to provide a basis for the identification of water inrush sources and the resource utilization of deep mine water in this area. The results show that in the three stages, the order of cation concentration is Na+ + K+ > Ca2+ > Mg2+, and the order of anion concentration is changed from Cl− > SO42− > HCO3− to Cl− > HCO3− > SO42−. The hydrochemical type is the most abundant in the mining stage, and tends to be unified after grouting. The dissolution of carbonate minerals, gypsum, rock salt and silicate minerals; cation exchange; pyrite oxidation; and the mixing of grouting precipitation liquid mainly occur in the limestone water. These effects are enhanced or weakened due to the influence of pumping and drainage and grouting precipitation liquid. The results of this study may be beneficial to the sustainable utilization of deep groundwater resources in other similar mines, and promote the establishment of data management and identification mechanisms of water inrush sources in deep coal seams.

Психологические основы системы отбора граждан поступивших на обучение в полицейскую академию Никарагуа

The problem of selecting citizens for admission to the police service is being worked out in almost all countries of the world. The process of selection for the internal affairs bodies of the Russian Federation is a fairly widely developed area of ​​science. In Latin American countries, these studies are at the stage of active development. The subject of this article is the optimization of the system of selection of citizens admitted to training at the Nicaraguan Police Academy. The purpose of the study is to develop a program for the psychological selection of citizens for training at the Nicaraguan Police Academy. To achieve the goal of the study, the expert assessment method was used. Mathematical statistics, quantitative and qualitative analysis were used in the processing of empirical data. 30 psychologists of the National Police of Nicaragua (73% were women and 27% were men) acted as respondents in the expert survey. It is shown that the selection of citizens for the National Police of Nicaragua should be optimized in the direction of developing the psychological part of this process. Optimization should be carried out by updating psychometric tests, including methods for assessing the mental health of candidates; inclusion in the interview protocol of parameters for assessing the psychiatric history in the family environment, as well as organizing additional training and feedback on the results of their work for psychologists upon hiring.

Statistical mathematics in video games

Abstract. Statistics play a crucial role in game design and development, with statistical mathematics being an essential element that developers must carefully consider. The paper introduces how statistical elements can be utilized to develop a creative gameplay mechanism that precisely aligns with the general requirements of players. Since the players gaming experience is considered the most important factor in a game, developers should be open to modifying their game based on feedback from dissatisfied players, which will enable the development team to provide an enhanced experience for all players. For multiplayer online games, the matching mechanism, which determines the teammates and opponents for each player, is just as crucial as the game's basic gameplay mechanism. Through statistical classification methods, we can improve the fairness of this matching process by analyzing players previous behavior and labeling them with their level. Overall, we can conclude that statistics can be used to design games by establishing a general framework and incorporating compelling elements. Additionally, statistics are essential for balancing game attributes and facilitating the perfect matching process.

Покращення рухової активності в учнів 5 класів засобами рухливих ігор

The purpose of the work is to substantiate theoretically and verify experimentally the effectiveness of the method for improving 5th grade students’ motor activity by means of mobile games. Material and methods. The pedagogical experiment was carried out on the basis of the Krolevets Lyceum No. 1 of the Krolevets City Council of the Sumy Region. It enrolled 32 students of 5th grade from the main medical group. They were divided into a control group (CG, n=16, 5-A grade) and an experimental group (EG, n=16, 5-B grade). The term of the pedagogical experiment was September-November, 2023. Pupils of CG and EG studied according to the Model curriculum "Physical culture. 5-6 grades" for institutions of general secondary education. During Physical Education lessons in the CG, the teacher followed the planned tasks and work plan. A developed method of improving motor activity by means of mobile games was implemented in EG. Research methods: theoretical analysis of scientific and methodical literature, pedagogical experiment. The level of motor activity was determined on the basis of a set of indicators: the time of students’ motor activity with a reflection of its content and quality at different moments of the regime, which was determined with the method of individual timing; the amount of motor activity using the pedometry method for quantitative assessment of motor activity; the intensity of motor activity by the pulsometry method (calculation of heart rate in bpm) when various types of muscle activity were performed; methods of mathematical statistics. The results. At the ascertaining stage of the pedagogical experiment, the following indicators of the 5th grade students’ motor activity level were obtained: in CG, 3 students (19%) had a high level, 7 students (44%) had an average level, and 6 students (37%) had a low level. In EG, 3 students (19%) had a high level, 6 students (37%) had an average level, and 7 students (44%) had a low level. It is necessary to note that the indicators of CG and EG were at the same level. At the formative stage of the pedagogical experiment, a method for improving the motor activity of 5th grade students by means of mobile games was developed and implemented. The developed method was implemented into all forms of physical culture and health work in institution of general secondary education. Its content included mobile games directly during Physical Education lessons and during other forms. The developed method was implemented in three directions, in particular with students, teachers and parents. At the control stage of the pedagogical experiment, the following indicators were obtained: in CG, 4 students (25%) had a high level of motor activity, 7 students (44%) had an average level, and 5 students (31%) had a low level. In EG, 6 students (38%) had a high level of motor activity, 7 students (44%) had an average level, 3 students (18%) had a low level. Thus, in CG there is a significant percentage of 5th grade students who have a low level of motor activity, while in EG there are high and average levels of motor activity among 5th grade students. This fact proves the effectiveness of developed method for improving 5th grade students’ motor activity by means of mobile games. Conclusions. The method we had developed for improving 5th grade students’ motor activity by means of mobile games confirmed its effectiveness during the experimental test and can be recommended for use in the practical activities of a Physical Education teacher.

Comparison of dynamic balance indicators using the Star Excursion Balance Test method in men of various types of martial arts with left- and right-sided motor asymmetry

Purpose: to perform a comparison of the Star Excursion Balance Test indicators in men of various types of martial arts with left- and right-sided motor asymmetry. Material and methods. The results of the study were obtained at the Ivan Boberskyi Lviv State University of Physical Culture at the Department of Fencing, Boxing and National Martial Arts in the period October-December 2023. Qualified male martial artists aged 18-22 in the number of 84 participated in the collection of experimental material: 11 representatives WKF karate (including 1 left-hander), 12 members of fencing (including 2 left-handers), 9 representatives of hopak hand-to-hand combat (including 1 left-hander), 31 representatives of boxing (including 12 left-handers), 21 representatives of Kyokushinkai karate (among whom there was 1 left-handed person). Research methods: analysis of literary sources and materials from the Internet; survey (questionnaire); measurement of anthropometric indicators of athletes (height, body weight, length of arms and legs); measurement of Star Excursion Balance Test (SEBT); methods of mathematical statistics. Results: right-handed martial artists (n=67) had an anthropometric advantage over left-handed martial artists (n=17): height – 178.1 cm versus 177,5 cm, respectively, body weight – 70,9 kg versus 66,8 kg, length arms – 76,7 cm vs. 73,9 cm (P<0,05), leg length – 95,0 cm vs. 91,8 cm. Comparison of SEBT indicators revealed: left-handed group has better SEBT indicators in almost all positions, as on the left side of the body, as well as on the right. When comparing indicators of all 8 positions of SEBT of the left leg in right-handed and left-handed players, it was found that left-handed players had significantly (P<0,05) better indicators in positions 6 and 7. Left-handed martial artists demonstrated significantly (P<0,05) the best SEBT indicators in positions 6, 7, 8 of the right leg than right-handed martial artists. SEBT indicators of both right and left arms showed that positions 7, 8 of both left and right arms were significantly (P<0,05) better than those of right-handers. A separate phenomenal result is the specificity of passing the SEBT test by left-handed athletes: their results are significantly (P<0,05) better in the most difficult positions – 6, 7, 8, and in each of the four limbs of the body, regardless of motor asymmetry. Conclusions. The results of the work demonstrated phenomenal SEBT indicators in left-handed martial artists, compared to right-handed martial artists. This phenomenon is observed in all SEBT indicators of the lower and upper limbs of the left and right sides of the body: indicators of all SEBT positions in left-handed athletes are better than in right-handed athletes. Lefties reliably dominate in the most difficult positions of the test – 6, 7, 8, both in the girdle of the upper limbs and in the balance and flexibility of the lower limbs, regardless of asymmetry. This phenomenon is observed against the background of left-handed athletes lagging behind right-handed athletes according to anthropometric indicators. In view of the above, we assume that left-handed athletes have special properties of neuromuscular activity that require special in-depth research.

Problem-oriented stimulus of teaching foreign-language listening in a secondary school. Part 1

The problem for the research. Listening skills are important for a modern person in many areas of life: at work, at home, travelling the world, etc., when immersed in the social space of culture in the fullness of its spiritual meanings. However, in school teaching of foreign languages, there is a contradiction between the large reserve listening capabilities in achieving students’ personal, metasubject and subject educational results in a foreign language and the established practice of teaching this type of foreign-language speech activity, where there are many difficulties associated with students’ perception and understanding of foreign-language information by ear. Methods of investigation. 50 ninth-graders of secondary school named after S. S. Rakitina in Murashi, Kirov Region (Russian Federation) took part in pilot testing. To obtain personal learning results, the “Methodology for studying the motivation of teaching older adolescents” was used; metasubject – L. F. Tikhomirova’s “Exclude the word” method; subject (in the field of foreign-language listening) – the method for calculating the success rate of V. P. Bespalko and A. N. Shamov. The results were processed using the sign test. The findings of the study. The final control revealed an increase in the level of proficiency in personal learning outcomes in 40% of ninth-graders; metasubject – in 45%; subject – in 61%. The reliability of the presented results is confirmed by the use of mathematical statistics methods for personal, metasubject and subject results. The results of calculating the criterion of G-signs in the experimental group: Gemp. is above ≤ Gcr.: 0 ≤ 3 for personal, 0 ≤ 5 for metasubject and subject results (p < 0.05). Conclusion. The purpose of the study is achieved: the article describes the characteristics and proves the effectiveness of using the problem-oriented stimulus in the process of teaching foreign-language listening in a secondary school (based on materials from the senior stage in secondary school). The theoretical foundation and testing of a set of exercises for teaching students foreign-language listening using the components of the problem-oriented stimulus led us to the conclusion that the presented exercises contribute to the formation of personal and metasubject universal educational actions of students, increases the level of their proficiency in the oral receptive type of foreign-language speech activity.

Вікові особливості олімпійських чемпіонів в спортивній боротьбі

Purpose: determine the age characteristics of Olympic champions in three styles of sports wrestling (Greco-Roman, freestyle and women's). Material and methods. The age of Olympic champions from 1896 to 2024 in three styles of sports wrestling: Greco-Roman (29 Olympiads), freestyle (27 Olympiads) and women's (6 Olympiads) was studied. A total of 455 athletes were analyzed: Greco-Roman (n=214), freestyle (n=211) and women's (n=30). The raw data of the wrestlers' performances is taken from the UWW website. The research used the following methods: analysis of scientific and methodological information and Internet sources; analysis of competitive activity protocols; methods of mathematical statistics. Results: the analysis of the age characteristics of Olympic champions during the research period showed that in Greco-Roman wrestling, the average age of athletes varies from 24,1 years to 32,8 years; in freestyle wrestling - from 23,0 years to 29,6 years; in women's wrestling - from 20,3 years to 27,5 years. The youngest champion in Greco-Roman wrestling was 18 years and 8 months, and the oldest was 41 years and 11 months. The youngest freestyle champion was 19 years and 8 months, and the oldest was 40 years and 4 months. In women's wrestling, the youngest and oldest champion was the same wrestler who took part in four Olympics and won four gold medals. She was 18 years and 2 months old at the first Olympics, and 32 years old at the fourth. The most decorated wrestler is Cuban heavyweight Mijain Lopez, who participated in six Olympic Games and won five gold medals. Seven stages of the evolutionary development of wrestling were identified. The youngest average age is observed among athletes at the first stage both in Greco-Roman wrestling (25,39 years) and in freestyle wrestling (23,92 years). The greatest average age of the athletes was at the second stage in the Greco-Roman style (29,36 years) and freestyle (27,52 years) wrestlers. Women's wrestling has been included in the program of the Olympic Games since 2004, so it is only in the last two stages. The average age of the wrinkles does not have a significant difference at these stages. It should be noted that at the last stage, Greco-Roman wrestlers have an average age of almost four years more than representatives of freestyle and women's wrestling. Conclusions. The conducted research made it possible to determine the age characteristics of Olympic champions in three styles of sports wrestling. The results of the study showed that the athletes competed in a wide age range (18-42 years), the average age was 27,82±9,77 years. The majority of athletes were between 22 and 32 years old, which accounted for 80 % of the total number. It was established that in Greco-Roman wrestling, the average age of athletes of all Olympiads is significantly higher (p<0,05) than in freestyle and women's wrestling. It was found that women were younger than men. There was also a weight category effect, with lighter wrestlers being younger than heavier wrestlers.

Модель змагальної діяльності зв’язуючого гравця високої кваліфікації у волейболі

Increasing the competitive performance of Ukrainian volleyball players requires scientific support of the educational and training process and the use of modern methods of scientific research, one of which is modeling. Indicators of technical and tactical actions obtained by analyzing official competitions are the basis for creating models of competitive activity. The aim of the study is to develop a model of a high-skill link player on the basis of statistical data from the games of the Ukrainian Volleyball Championship among men's teams of the Super League. Material and Methods. The data of 18 qualified volleyball players who perform the function of a linking player in their teams were used for the study. We analyzed statistical data of link players of 8 teams participating in the Ukrainian Super League championship of the season 2023-24. To create a model of a linking player of Ukrainian Super League teams, 10 athletes were selected from the total sample, the main criterion was quantitative indicators of participation in the championship games (at least 80% of official matches). Research methods: analysis of literary sources and data in the Internet, pedagogical testing, analysis and generalization of statistical data of competitive activity, methods of mathematical statistics. Results. The analysis of game technical and tactical indicators of qualified volleyball players allows to understand more clearly the peculiarities of competitive activity of players of different roles. In accordance with the purpose of the study we analyzed the game activity indicators of linking players (number of matches and sets, total number of assists, effective assists, satisfactory assists, number of errors). It should be noted that all game indicators indicated the heterogeneity of the group of highly skilled binders, which is explained by different experience, players' participation in matches, and the variety of tactical actions of the teams. Conclusions. The developed model of competitive activity of highly skilled liaisons contains general data (height, age), indicators of physical abilities (height of block and attack), technical and tactical indicators (execution of passes, number of errors). In addition to the average data, the model presents a variation series from the lowest to the highest results.

Міграція в спортивній боротьбі: аналіз виступів на Олімпійських Іграх 2024 в Парижі

Purpose: to analyze the achievements of migrant wrestlers at the 2024 Olympic Games in Paris. Material and methods.The following methods are used in the research: analysis of scientific and methodical sources, analysis of the results of sportsmen's performances and methods of mathematical statistics. The study was conducted to analyze the number of migrant athletes, their results in competitions, as well as age and weight characteristics in each style of wrestling (women's wrestling, Greco-Roman wrestling, freestyle wrestling). The data is taken from the official website «United World of Wrestling» (https://unitedworldwrestling.org). The percentage of migrants, their average age, weight categories and places they occupied were analyzed, with further processing of statistical indicators to identify patterns in their performance. Results: the results of the study showed that 34 migrant athletes participated in the 2024 Olympic Games, with the largest number (24,0 %) observed in freestyle wrestling, while the figure was the lowest in women's wrestling at 2,1 %. The analysis also found that migrant athletes have an average age of 29,5 years, indicating their experience.Almost a third of them won prizes, in particular, 8,8 % became winners, and 29,4 % won prizes. Despite the high achievements, 35,3 % of the athletes ranked 10 and below, which indicates a wide variety of results among migrants. A comparison with previous studies confirmed the tendency of athletes to change their citizenship after the peak of their career. Migrant athletes aged 24-27 make up the largest group, indicating their strategy to achieve international success after achieving the best results in their careers. Conclusions. Migrant athletes participating in the 2024 Olympic Games showed a high level of results, especially in freestyle wrestling. Their participation and success confirm that changing citizenship is an important strategy for further achievements in international competitions, especially after the peak period of a sports career.

Дослідження впливу фаз менструального циклу на функціональний стан кваліфікованої ветеранки спорту з дзюдо

Purpose: to investigate the influence of menstrual cycle phases on the functional status of a qualified female veteran judo athlete. Material and methods. The following methods were used in the study: analysis of scientific and methodological information and Internet sources; generalization of advanced practical experience; measurement of sensorimotor reactions and determination of heart rate variability indices; methods of mathematical statistics. A qualified veteran female judo athlete (Master of Sports of Ukraine) in the age category F2 (1983-1979) took part in the study. We performed 84 measurements of heart rate variability (n=42, HRV in the supine position; n=42, heart rate variability during the test task dedicated to measuring the choice reaction). The measurement was performed using two computer programs for mobile devices running iPadOS «Research HRV» and «HRV SR+CR» during morning hours (7-8 hours) and afternoon hours (17-18 hours). Results: analysis of the dynamics of changes in heart rate variability parameters obtained in the supine position indicates an increase in sympathetic activity in the follicular phase of the menstrual cycle. Analysis of comparisons of heart rate variability parameters in different phases of the menstrual cycle indicates that the greatest number of statistically significant (p<0,05) differences is observed in the first half of the day. These changes indicate the dynamics of the decrease in the tone of the sympathetic part of the autonomic nervous system in the follicular phase when performing test tasks provided by the computer program «HRV SR+CR». Analysis of the study results indicates that the indicators of heart rate variability are also influenced by the measurement conditions. The test tasks of the computer program «HRV SR+CR» provide cognitive load and concentration of attention, especially in the second stage, where it is necessary to choose the sought-after figure. During cognitive tasks there is an increase in the activity of the parasympathetic nervous system, which leads to an increase in heart rate variability. High level of heart rate variability is associated with better cognitive functions and adaptive response to stress. Consequently, these differences in heart rate variability obtained using the «Research HRV» and «HRV SR+CR» programs may be the result of interactions between physiological changes during the menstrual cycle as well as the influence of measurement conditions. Understanding the changes in heart rate variability indices during test tasks related to the manifestation of the choice reaction provides information about the influence of cognitive load and attention concentration on the functional state of the female athlete. This will allow to plan the training process of wrestling taking into account the phases of the menstrual cycle and functional capabilities that are inherent in high-skilled female athletes. Conclusions. The parameters of heart rate variability and sensorimotor reaction time provide information about the functional state of martial artists. Understanding of metabolic and hormonal processes in different phases of the menstrual cycle of qualified wrestlers will allow to optimize their training loads and recovery measures.

Students' ideas about life and professional success in relation to career orientations and life satisfaction

Introduction. Studying ideas about success among young people studying at a university can help identify their life goals, expectations, and values, which in turn will ensure more effective preparation of future specialists for professional activities. The purpose of the study was to identify ideas about professional and life success in relation to career orientations and life satisfaction among students. Materials and methods. The study, in which 111 students took part, was conducted at the University of Architecture and Civil Engineering (Russian Federation, St. Petersburg). Projective methods were used, including the method of unfinished sentences, the «Study of Career Orientations» test by E. Shein, the «Life Satisfaction» test (LS) by N.N. Melnikova. Methods of mathematical statistics: frequency analysis, cluster analysis (Ward's method), correlation analysis: Spearman correlation coefficient, factor analysis (Varimax method). Results. Data analysis showed that for students, success in life includes not only material, but also psychological well-being, as well as self-realization, recognition and the opportunity to help people. Professional success lies in social status, material wealth, professional competence, the presence of useful connections and the opportunity not to engage in work. Examples of life success for modern students are relatives (30%), professional success – representatives of the business sphere (34%). Students show a desire for self-realization, while wanting to maintain harmony between their personal life and career (r=0,26; p≤0,001). Respondents who attach great importance to social status tend to perceive their life as more harmonious (r=0,23; p≤0,01). Orientation towards «autonomy» (r=0,21; p≤0,01) and «entrepreneurship» (r=0,23; p≤0,01) increase life satisfaction. Conclusion. The practical significance of the study lies in the possibility of creating programs aimed at developing skills to achieve professional and personal well-being and helping students. Knowledge about the needs and expectations of future specialists will allow employers to create a motivating environment for comfortable cooperation and achieving goals.

Факторна структура підготовленості тхеквондистів 15-17 років

Purpose: to investigate the factor structure of preparedness of taekwondo players of 15-17 years old. Material and Methods. The following methods were used in the research: analysis of scientific and methodical literature, pedagogical testing, medical and biological methods, methods of mathematical statistics. Results: in the course of the research the factor structure of preparedness of taekwondoists of 15-17 years old by the general sample was studied and 9 orthogonal factors were separated in which the sum of loading variables ranges from 9,571 to 1,736, describing 84,804 % of the total variance. The contribution of the first factor, «morpho-functional», to the total variance is 22,788 % and consists of 10 indicators. The second factor accounts for 13,068 % of the total variance, which reflects the special high-speed abilities of taekwondo players of 15-17 years old in the structure of which 7 indicators are included. In the third factor, which accounts for 11,334 % of the total variance, 7 indicators were the main ones. The fourth orthogonal factor has a contribution of 9,259 % of the total variance, the highest correlation was found in 3 indicators. This factor is characterized as a manifestation of coordination abilities with a combination of high-speed endurance (coordination high-speed endurance). The most significant indexes of the fifth factor (6,868 %) are the power index on the left hand (r=0,529) and performance of a side kick with the left (r=0,682) and right (r=-0,569) foot with a deployment on 360° for 15 s. This factor determines the manifestation of strength and the performance of complex coordination kicks and is interpreted by us as «coordination strength». The structure of the sixth factor «Frequency of movements» with a total variance of 6,431 % includes 3 indicators. The seventh factor «ability to control movements» with a total variance of 5,720 % consists of 2 indicators with the highest correlation of lateral kicks with the left foot in the body for 15 s (r=-0,596) and fencing in motion before losing balance with the left foot (r=0,500). The eighth factor «keeping balance»has 2 indicators: fencing for 15 s in the upper level with the left foot (r=0,559) and tilt of a trunk forward from a sitting position (r=-0,514) with a contribution to the general variance of 5,203 %. This is due to the fact that when performing fencing for 15 s in the upper level with the left foot, the athlete stands on one leg and performs blows to the head with the other, to perform this technical technique, the taekwondo player needs a good display of flexibility. The ninth factor reflects reactivity of muscles of hands and has a contribution of 4,133 % of the general dispersion and is characterized by throwing a tennis ball on a distance (r=-0,519). Conclusions. The research has established a dependence between components of preparedness of taekwondo fighters of 15-17 years old, also the most significant factors which reflect morpho-functional indicators, a manifestation of special high-speed abilities, power, coordination and high-speed endurance have been established. With the help of factor analysis, 9 factors were separated, out of 42 considered indicators, the contribution of which is 22,788-4,133 % and is 84,804 % of the total variance. The largest contribution of 22,788 % to the total variance of the sample of taekwondoists of 15-17 years old has morphological and functional indicators.

Зміни у показниках периферійного зору баскетболісток 11–12 років під впливом спеціально підібраних вправ

In team game sports, peripheral vision can be useful for simultaneously tracking the movements of opponents and teammates. The purpose of the study: to experimentally test the effectiveness of specially selected exercises aimed at changes in the peripheral vision of basketball players aged 11-12 years. Research methods: theoretical analysis of scientific and methodological literature, pyrometry method, pedagogical experiment, methods of mathematical statistics. The device ‘Forster's Perimeter’ was used to determine the index of peripheral visual field. The field of vision was determined for the left and right eyes separately for the white and green colours of the two main meridians - horizontal outward (to the temple) and to the middle (to the nose) and vertical - upward and downward. The study was conducted at the research laboratory of the Kharkiv State Academy of Physical Culture. The study involved 30 female basketball players from Kharkiv aged 11-12 years. In order to establish the effectiveness of using specially selected exercises during training, young basketball players were divided into control and experimental groups, each of which consisted of 15 girls. For 4 months, the training process of the experimental group was based on the standard training programme for basketball for children and youth sports schools and was supplemented by specially selected sets of exercises aimed at developing peripheral vision and improving the condition of the eye muscles. Special sets of exercises aimed at developing peripheral vision. Results of the study. The ‘Forster Perimeter’ device does not allow to set the field of vision in the selected direction by more than 90º. It should be noted that the index of peripheral vision horizontally outward, both with the right and left eyes, for both colours in all basketball players exceeded this index. Thus, it was not possible to establish the indicators of peripheral vision in the horizontal outward direction and to study the influence of specially selected exercises on these indicators. The analysis of indicators in the direction up, down and inwards revealed the highest indicators along the vertical meridian with the right and left eyes downwards, both in the CG and EG. Comparing the indicators of peripheral vision of the right and left eyes to white, it was found that in the EG there were significant differences in the indicators upwards (t=2.54, p<0.05) and in the middle (t=4.47, p<0.05), in the CG - in all three directions (t=2.43, p<0.05; t=2.27, p<0.05, t=3.56, p<0.05. In indicators of peripheral vision of the right and left eyes for green colour significant differences are observed only in EG in the upward direction (t=2.19; p<0.05) After the pedagogical experiment the repeated testing was conducted, the results of which indicated a significant improvement of indicators of peripheral vision of basketball players of EC of the right eye both for white and green colour in all three directions (p<0.005). Significant changes in the indicators of peripheral vision of the left eye occurred only for white colour along the vertical meridian downwards (t=2.06; p<0.05) and upwards (t=2.04; p<0.05). For other indicators, the changes were positive, but not significant. Conclusions. The use of specially selected exercises positively influenced on indicators of peripheral vision of sportswomen of 11-12 years old of EG. Thus, the improvement in the right eye was 5.08% upwards, 6.08% downwards, 9.58% in the middle of white colour; in green colour - 11.82%, 5.86%, 5.91%, respectively. In the left eye, the improvement was 6.58% for white, 7.57% for blue, and 1.08% for green; 7.38%, 7.81%, 5.70% for green, respectively.

Development of mathematical models of power consumption at coal plants

The object of research is coal enterprises where powerful electrical equipment is used (underground installations up to 3000 kW, tunneling complexes of 500–1500 kW, technological complexes of 6–10/0.4 kV, etc.). The deficit of generated capacities, caused by growing energy consumption, can be reduced by regulating power consumption modes. The relevance of this issue is determined by the need to conduct a research of the electricity consumption system, to determine the qualitative and quantitative characteristics of electricity consumption using mathematical models. The lack of mathematical models makes it difficult to analyze energy intensity and consumption modes of each technological operation in the overall balance of electricity consumption of coal enterprises. The article considers the structure and classification of the main technological groups of energy consumers, the development of mathematical models for each type of load modes, as well as a generalized model of electricity consumption of coal enterprises, with the use of mathematical apparatus of probability theory and mathematical statistics. As a result of the work, mathematical models of the electricity consumption process for the main technological groups and for models of daily electricity consumption of coal enterprises as a whole were developed, and it was also established that technological objects of electricity consumption are divided into three different values, in terms of power consumption modes: constant, uniform and pulse. For each class of consumers their statistical characteristics were obtained. The work results can be applied for managing power consumption modes of coal enterprises

Effective use of the tools of probability theory and mathematical statistics in solving the problems of the professional orientation of physicists and mathematicians: an interdisciplinary approach

ABSTRACT The use of methods of mathematical statistics for teaching students carries the task of determining mathematical abilities, formalizing the choice of a professional orientation and the potential choice of solutions. In higher education, the use of the mathematical apparatus allows students to form the ability to multiple choice and assess the conditions of the choice. These include not only the choice of training courses, but also the areas of knowledge in which each student can fulfil themself. For mathematicians, this is especially true, since in most cases mathematics is used to solve purely applied problems. The novelty of the study is determined by the fact that the methods and tools of probability theory cannot be applied exclusively on an individual level. To determine the effectiveness of the methods used, it is necessary to determine the possibilities of group application of the used methodological apparatus and identify areas of assistance to the student in choosing a professional orientation. In terms of the use of ubiquitous distance education, the authors demonstrate the possibility of group work with mathematical support through the use of clusters and network techniques, when each individual is the host of the training programme.