Methods Of Mathematical Statistics Research Articles

EXPERIMENTAL JUSTIFICATION INFLUENCE OF SPORTS GAMES ON PSYCHO-PHYSIOLOGICAL INDICATORS OF STUDENTS

Relevance of the research topic. A specialist will be able to compete effectively on the labor market only when he is ready for a specific type of activity and will have a sufficient supply of reserve capabilities of the body. Studying the ways of psychoregulation and increasing the level of development of psychophysiological abilities of students is an important problem of the organization of physical education in higher education institutions. The purpose of the research is to experimentally substantiate the effectiveness of the use of means from sports games on the development of psychophysiological abilities of students. Research methods: analysis and generalization of scientific and methodical literature, dynamometry, spatial orientation test, computer program "Psychodiagnostics", methods of mathematical statistics. Research results. During the year, a set of specific exercises aimed at the development of psychophysiological abilities was implemented in the training of students of optional groups in sports games. In order to determine the differences in the impact of various sports in the pedagogical study, optional control groups from power sports and athletics were selected. The indicators of muscle differentiation, spatial orientation, simple visual-motor reaction and reactions of distinction and choice were studied. In the experimental groups, an increase was obtained in all the mentioned tests, but it differed both in terms of indicators and in different game sports, which corresponded to the features of competitive activity. In the control groups, according to some indicators, there were also positive shifts in the development of psychophysiological abilities, but they were not statistically reliable. Conclusions. The specifics of the impact of various sports on students' muscular, spatial sensations and psychomotor skills have been determined. The developed complexes of special means for sports games have shown their effectiveness and can be recommended for their use in the physical education of students for a purposeful effect on psychophysiological abilities.

RESEARCH OF CHANGES IN THE POWER OF CAR FLOW AT THE SHUTTING STATION DURING THE PERIOD OF MILITARY ACTIONS

It is impossible to solve the problem of improving the system of organizing car flows in trains at the current level of information support without creating an information and management system that will integrate into a single information and computing space the most important optimization tasks covering all levels of managing the process of freight transportation on railway transport, such as such as the calculation of the routing of car flows from loaded and empty cars, the calculation of the plan for the formation of freight trains at the training ground of the main technical stations, the calculation of the plan for the formation of local trains in the areas of local work, and the construction of adjusted operational plans for the operation of stations. The aggression of the Russian Federation against Ukraine fundamentally changed the system of railway transport of Ukraine. The volume of cargo transportation by rail transport during military operations in the east of Ukraine decreased by 37% in 2022, but already in 2023, an increase in the transportation of some types of cargo began, in particular, grain cargo, mineral construction materials, dangerous bulk cargoes, military equipment. Transportation of goods by railways of Ukraine, especially during military operations, is not carried out evenly over a long period of time and has fluctuations in the capacity of car flows. The updated directions of their tracking, which depend on the technical condition of the railway infrastructure for the current period, lead to a change in the direction of tracking of car flows and, as a consequence, their organization into trains according to the formation plan at technical stations. The conducted studies established that the capacities of car flows are random values, therefore it is advisable to use mathematical statistics methods for their description, and modeling methods for forecasting work with them. Those car flows that arrive at the sorting station most of all fall under the geometric law of distribution of a random variable depending on the power of the direction of arrival, which has a significant impact on the accumulation parameter at the station. Fluctuations in the capacity of car flows are quite significant and depend on a sufficiently large number of factors. For the operational planning of the work of sorting stations, it is necessary to take the characteristics of the current state or a sample of data for short periods (a decade, a week), that is, it is necessary to constantly analyze the data from the ASK of the VP UZ - there is, therefore, a study of the capacity of car flows in the technical station during the period of changing their directions is an actual task and can be used to adjust the dispatcher routing and the plan for the formation of single-group and group freight trains.

ВПЛИВ ІННОВАЦІЙНИХ ПІДХОДІВ НА ФІЗИЧНИЙ РОЗВИТОК ШКОЛЯРІВ З ВАДАМИ СЛУХУ В ПРОЦЕСІ АДАПТИВНОГО ФІЗИЧНОГОВИХОВАННЯ

Introduction. Correcting the physical development of students with hearing impairments requires an individual approach and the use of specialized methods and tools. Each student with hearing loss may have unique needs and capabilities. Therefore, it is important to create individualized physical education programs that take into account the specific limitations and capabilities of each student. It is important to develop and implement innovative approaches for children with hearing impairments that would have an impact on the physical development of schoolchildren along with the correctional and health-improving orientation of the entire process of adaptive physical education. The purpose of the study is to substantiate and implement an innovative methodology of adaptive physical culture for the correction of physical development of children with hearing impairments in the process of adaptive physical education. Research methods: theoretical analysis and generalisation of scientific literature data, sociological research methods, somatometric and physiometric research methods, methods of mathematical statistics. Results. The developed algorithm consisted of comparing two groups of 15-year- old schoolchildren with hearing impairment (boys (n=14), girls (n=12)) (control and experimental groups). Difference of content of classes in two groups of pupils was in means and methodical approaches to solution of correctional tasks in the process of physical education. In the first group, all training sessions were conducted in accordance with the physical education programme. In the second group, the methodology of correction of physical development included the following forms of training: exercises of different structure and focus to improve physical development indicators; increasing the level of functional capabilities of the cardiovascular and respiratory systems; balancing the psycho-emotional state (correctional games, tourist training skills, various types of health and recreational physical activity, improving the development of fine motor skills, exercises aimed at correcting and lagging behind in physical development), as well as an innovative program developed taking into account the needs and capabilities of children with hearing impairments. The innovative programme contained interactive exercises, included video tutorials with subtitles, games and tasks that can stimulate physical development, coordination and joint interaction.Conclusions. As a result, the implementation of the proposed methodology is confirmed by positive changes in the level of physical activity, improvement of general health and correction of physical development in the process of adaptive physical education of schoolchildren with hearing impairments.

STUDYING THE PECULIARITIES OF PHYSICAL ACTIVITY OF STUDENT YOUTH

Statement of the problem. Insufficient motor regime is caused by prolonged staying at home during classes and a large volume of academic subjects has a direct impact on the state of the student's body. Prevention and overcoming of these consequences is possible only through the introduction of a sufficient amount of physical exercises in the educational process of students. The study of various aspects of health has shown that each component is an important on the way to strengthening and improving the performance of college students. The purpose of the study is to analyze the physical activity of first and second year students of different pedagogical specialties. Research methods: pedagogical observation, questionnaire, methods of mathematical statistics. Results. The study established the concept of a healthy lifestyle and its main components. It has been found that physical activity is the most important indicator of a healthy lifestyle, and the lifestyle of student youth is a way to integrate the needs of the student. A questionnaire was conducted to assess the lifestyle of students of pedagogical specialties. The preferences and priorities, motives and factors that motivate students to be active were identified. According to the survey, students assess their health status differently: 33.4 % believe they have no health problems, 36.1 % of students believe they have minor health problems, and 30.5 % of respondents consider their health to be unsatisfactory. Instead, only 25.2 % of all students surveyed engage in health activities outside of class time, while 74.2 % prefer additional tutoring sessions with tutors. Conclusions. It has been established that different sources of information and the environment in which students live directly affect the formation of a healthy lifestyle. That is why it is necessary to reorganize and improve the system of physical education in educational institutions by forming motor activity models of student youth.

Philosophical and practical understanding of the quality of medical education in the Russian Federation: analysis of the opinions of students and practicing doctors

Introduction. The transformation of higher medical education, caused by the rapid development of medical technologies and growing social demands on the healthcare system, requires research into students’ ideas about quality education, their assessments and expectations, since students’ understanding of the learning process can have a significant impact on the development of student motivation and medical professionalism. The purpose of the study is to analyze the current system of higher medical education in the Russian Federation based on survey data from senior students, residents, and practicing doctors. Materials and methods. The survey involved 350 respondents (senior students, residents, practicing physicians) mainly from Moscow medical higher education institutions. Statistical analysis was carried out using the software StatTech v. 3.0.4. Methods of mathematical statistics: U-Mann-Whitney, Kruskal-Wallis, χ2 -Pearson tests. Results. It was revealed that only 52% of respondents consider the amount of theoretical knowledge acquired at a higher education institution under a specialty program to be sufficient. Students and graduates of the pediatric faculty more often consider the amount of theoretical training sufficient compared to respondents from the medical and dental faculties (p < 0.001). Only half of the respondents are satisfied with the quality of the education received. Students and graduates of the Faculty of Pediatrics more often stated that they use the knowledge and skills acquired during practical training in their professional activities (p < 0.001). Students and graduates of medical faculties of non-core Moscow universities and Russian National Research Medical University named after N.I. Pirogov are most satisfied with the amount of theoretical knowledge received within the framework of the specialty program compared to students and graduates of other higher education institutions (p < 0.001). Conclusion. The results of this study may be valuable for government agencies that determine strategies for the development of higher medical education in Russia, as well as for university leaders who plan targets for the development of educational activities with an emphasis on involving students in the educational process.

ASSESSMENT OF PHYSICAL FITNESS OF MATURE WOMEN WITH DIFFERENT TYPES OF POSTURE

Relevance of the research topic. The systematization and generalization of a wide layer of both theoretical developments and practical achievements in the field of physical culture and sports serve as a basis for stating that maturity is the longest period of ontogenesis, characterized by the tendency for a person to achieve the optimal level of development of his spiritual, intellectual and physical potential. Against this background, the age of maturity in women, according to numerous data from representatives of the scientific community, is a period of motor deficit. The consequences of the latter include, first of all, the gradual unfolding of involutional processes, negative changes in the hormonal background, the appearance of excess weight, a decrease in the elasticity of connective tissue, the appearance of the first signs of structural and functional disorders of the spine and joints. The purpose of the article is to determine the level of physical fitness of women aged 36-40 with different types of posture. Methods. Theoretical analysis of special scientific and methodical literature, pedagogical testing, methods of mathematical statistics. The results of the work. The assessment of physical fitness of women in the second half of mature age showed the following. Firstly, it was found that according to tests of strength, endurance and flexibility, women aged 36-38 were more physically fit, performing pull-ups in a lying position mainly at an average level, tilting the torso forward from a sitting position and lifting the torso in a sitting position at a sufficient level. In contrast, the physical fitness of women aged 39-40 years was much worse, in particular, most of them performed lying pull-ups at a low level, torso bending forward from a sitting position and lifting the torso in a sitting position at an average level. Secondly, the comparison of groups of women aged 36-38 and 39-40 years, taking into account the type of their posture, did not reveal any differences in pairs of different ages of each type. At the same time, it was found that women with normal posture performed much better than the other groups in exercises such as flexion and extension of the arms in a lying position, pull-ups in a lying position, and women aged 36-38 years were superior in the test of lifting the torso into a seated position. Accordingly, women with a round, flat back and scoliotic posture were less physically prepared to perform these exercises.

Use of phygital technologies in improving the level of school students’ physical fitness in sporting games section classes

Introduction. The increasing number of people keeping to sedentary lifestyles highlights the need for innovative and non-standard methods of maintaining physical health. The physical and the digital merge and create exciting new possibilities, transforming sports into a new epoch. This evolution is continuously changing the paradigm of sports, opening up new realities. The research aims to study the effectiveness of a new methodology – using the phygital sports tools in the educational and training process involving sports games based on the school sporting club. Materials and methods. The sample comprised secondary educational school students of Grozny (Russian Federation) aged from 12 to 14. One control group and three experimental groups (a total of 60 people) were formed to carry out the formative pedagogical experiment. Three training groups were formed by phygital sport type: 1) phygital volleyball, 2) phygital basketball, 3) phygital football in which 2 sessions were held within a weekly cycle based on the developed methodology. The used methods of mathematical statistics involved the Student’s t-test. Results. Significant changes were found in the experimental groups in the following indicators: “Running 60 m, s.” – EG1 [t=5.5; p<0.05]; EG2 [t=6.4; p<0.05]; EG3 [t=2.3; p<0.05]; “Standing long jump” – EG 1 [t=5.1; p<0.05]; EG2 [t=3.5; p<0.05]; EG3 [t=2.3; p<0.05]; “Pull-up in suspension on a high crossbar” – EG1 [t=4.9; p<0.05]; EG2 [t=4.6; p<0.05]; EG3 [t=4.9; p<0.05]; “Torso lift in seated position” – EG1 [t=3.5; p<0.05]; EG2 [t=3.1; p<0.05]; EG3 [t=3.1; p<0.05]; “Run 100 m.” – EG1 [t=9.8; p<0.05]; EG2 [t=6.2; p<0.05]; EG3 [t=7.8; p<0.05]; KG [t=0.8; p>0.05]. “Sequential execution of 5 somersaults” – EG1 [t=6.5; p<0.05], EG2 [t=2.4; p<0.05]; EG3 [t=3.3; p<0.05]; “Leaning forward while standing on the gym bench” – (EG1 [t=2.6; p<0.05]; EG2 [t=2.5; p<0.05]; EG3 [t=4.4; p<0.05]. No statistically significant changes were found according to these indicators in the control group. Conclusion. The research results showed that the experiment participants successfully combined computer sports with traditional classes and physical activity. The new format of integrating computer game technologies with active motor activity generates young people’s increased interest and can positively influence their motivation to perform physical exercises and physical activity.

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.

STUDY OF THE EFFECTIVENESS OF THE DEMULSIFIER COMPOSITION ON THE DESTRUCTION OF LOCAL OIL-WATER EMULSION

The effect of the demulsifier composition on the destruction of local oil-water emulsions was studied in this work. One of the urgent problems in the development of deposits is to increase the efficiency of the preparation of hydrocarbons in the fields. The solution of this problem makes it possible to significantly increase the degree of oil preparation, reduce the loss of hydrocarbons with drainage waters, thereby improve the environment and bring additional profit to the enterprise. A complex of theoretical and experimental studies was used, consisting in generalization and analysis of literary data, as well as by analogy, modeling, quantitative and qualitative observation, laboratory tests, conducting a multifactorial experiment, data processing using methods of mathematical statistics. Information processing tools based on computer software products were used. The results of laboratory tests of oil-water emulsion, physico-chemical analysis of water composition, new chemical reagents-demulsifiers recommended for field testing are presented. It can be concluded, based on the research conducted, that the demulsifier EASY-DE03-15 is the most effective reagent for dehydration of oil-water emulsions and desalination of MIX samples.

Analysis of the Technical and Tactical Characteristics of Li Shifeng in 2023

Objective: To explore and understand the skills and tactics used by the world's top badminton players in the competition, so that ordinary badminton lovers can understand and use the skills and tactics of badminton, improve the level of skills and combat, and expect to provide reference for improving the skills and tactics of the athlete Li Shifeng. Methods: Using the literature method, video observation method and mathematical statistics method, we analyzed the serve, reception, front court ball processing, midfield ball processing, back court ball processing and gain and loss in the competition, and summarized the characteristics of his skills and tactics in the competition. Conclusion: 1) Li Shifeng's serve is mainly backhand ball, and the serve is concentrated in areas 1 and 5 in front court; other areas are involved but not frequently. At present, there is a tendency of men's singles in badminton. 2) Li Shifeng's use of receiving service skills and tactics is mainly to rub and put the net and pick the ball, while the use of other technical balls is involved but not much. He has a high sense of defense, but also actively attack, trying to break free of the control of the opponent, actively strive for the initiative of the game, so the net in the return stage is also particularly important. 3) The use of forward ball skills often requires more energy into dealing with the opponent's return to gain the chance to dominate the game. Li Shifeng's front court attack is more active, like to rub the ball and pick the ball skills and tactics, so as to win the advantage in front of the net. 4) There is no obvious technical and tactical gap in the performance of Li Shifeng and his opponents in the midfield, and all the ball techniques are used. The straight line technology before the net is the most used, followed by the diagonal and pick the ball, and the flat ball is the lowest frequency. 5) Li Shifeng in the back using the ball and kill the ball tactical ability is better, the back is Li Shifeng in the back of the highest utilization technology, using the ball back, facilitate the best time to use the ball, and consciously and accurately control the point and Li Shifeng in the back is given priority to with the ball score, steady, fast, drop ball point precision, to the field of control consciousness is strong, control the rhythm of the tactical intention.6) Li Shifeng loses too much points actively, which is in a phenomenon that he wants to actively grab the advantage but loses points due to poor technical treatment.

STATE SUPPORT OF BUSINESS IN UKRAINE

The article highlights the main directions of state support for small and medium-sized businesses and the functions of the state as a supporter of entrepreneurship development, which consist in providing not only financial, but also informational support, creating and maintaining institutional support and infrastructure. The purpose of the article is to review and analyze the instruments of state regulation and support of entrepreneurship in the countries of the world and the measures and programs introduced by the Government of Ukraine to support and stimulate domestic business. Analysis, synthesis and modeling methods were used to study the state of research. The results of our research was carried out with the help of empirical methods: pedagogical observation, questionnaires, interviews, testing, the method of experimental evaluations. Mathematical statistics methods were used to process the research results. The reasons for the inefficient activity of enterprises are considered, which are connected, among other things, with an unbalanced state policy and the lack of protection from the state. Current areas of support for small and medium-sized businesses are described, including taking into account European programs. State support for small and medium-sized businesses today can be considered insufficiently effective, as evidenced by a number of examples and the consequences of ill-considered decisions by the authorities, which, with the aim of stabilizing the economy in the state, inflict a tangible blow on the activities of small businesses and threaten the existence of a large part of them. The directions of management of small business structures have been determined, the primary tasks of their further functioning and development were outlined, public opinion regarding their activities was formed.

STUDENTS’ INDEPENDENT WORK ON TEACHING METHODS OF UKRAINIAN LITERATURE AS AN IMPORTANT COMPONENT OF PROFESSIONAL TRAINING

The article reveals the essence of the concept “independent work of students on the methodology of teaching Ukrainian literature”, its forms, types, content, and the necessity of independent work. The purpose of the article is to reveal the essence of the concept of independent work, its forms, types, and content. Analysis, synthesis and modeling methods were used to study the state of research. The results of our research was carried out with the help of empirical methods: pedagogical observation, questionnaires, interviews, testing, the method of experimental evaluations. Mathematical statistics methods were used to process the research results. A system of questions and tasks for the independent work of students on the methodology of teaching Ukrainian literature in middle general education and senior specialized humanitarian schools is proposed; the material is structured according to the main problems of methodological science. Special attention is paid to research work in the methodology of teaching Ukrainian literature. In the current stage of educational reforms implementation, the preparation of philology teachers capable of thinking creatively, finding solutions in any pedagogical situation, and developing an individual approach to the learning process in accordance with the demands of the time is crucial. In this context, the problem arises regarding the selection of teaching forms and methods that will facilitate active interaction between the instructor and the higher education seeker, fostering their academic and professional growth. This concerns the system of educational and psycho-pedagogical measures where individualized and differentiated approaches in organizing students' independent work take precedence.

Spatial Evolution of Sports Tourism Space: A case study of Shandong Province, China

This study adopted the method of literature, mathematical statistics, logic analysis and GIS spatial analysis, taking the spatial elements of sports tourism in Shandong Province from 2009 to 2018 as the research object, clarified the development status of sports tourism in Shandong Province and the distribution status of spatial elements, sorted out the characteristics of the spatial evolution of sports tourism in Shandong Province, and analyzed the influencing factors of the spatial evolution of sports tourism in Shandong Province. To explore the countermeasures for the development of sports tourism in Shandong province, and provide reference for enriching the research plan of sports tourism space in Shandong province and improving the theory of sports tourism space development; It provides empirical reference for optimizing the spatial layout of sports tourism development in Shandong province, balancing the seasonal imbalance of sports tourism in Shandong province, creating high-quality sports tourism brands in Shandong Province, and promoting the development of sports tourism in Shandong province.

Развитие логистической инфраструктуры хранения и сбыта скоропортящейся сельскохозяйственной продукции

The article presents the results of an analysis of the logistics infrastructure for storing and marketing agricultural perishable products in the regions of Kazakhstan. The results of a comparative and cluster analysis of the infrastructure of storage and marketing facilities for perishable agricultural products in the amount of 1056 units are presented based on the methods of mathematical statistics and clustering using the SPSS program based on the data provided by the akimats of all 20 regions of Kazakhstan. Problems in the functioning of their infrastructure have been identified. During the analysis, 6 clusters were identified according to the selected indicators. Cluster analysis made it possible to systematize and identify the logistics infrastructure for storage and sales that is most typical for each cluster. Based on the identified problems, the need to develop storage facilities that provide a range of logistics and marketing services, closer interaction between manufacturers, storage facilities and retail trade on the basis of long-term contracts was determined. Based on the results of the cluster analysis, recommendations were proposed for the modernization of existing and construction of new storage facilities, depending on the needs of each region. It is recommended to increase climate-controlled capacity, leading to a reduction in losses of perishable agricultural products and an increase in the efficiency of storage facilities through the construction of modular storage facilities.

СОЦІАЛЬНО-ПСИХОЛОГІЧНІ ОСОБЛИВОСТІ ДІТЕЙ, ПОСТРАЖДАЛИХ ВІД СІМЕЙНОГО НАСИЛЬСТВА

Purpose. The article reveals the problem of family violence in psychology and the study of socio-psychological characteristics of children affected by family violence. Methods. In order to achieve the goal, the following methods were used in the study: Lazarus coping test, personality orientation method" V. Smekala, M. Kuchera; personal questionnaire FPI (modified form B), method of diagnosis of indicators and forms of aggression by A. Bass and A. Darka; methods of mathematical statistics, in particular (determination of average values, percentage and correlation analysis, Fisher's φ-angle transformation). Results. According to the results of the interviewed teenagers using the selected methods, it was established that teenagers who have experienced family violence or witnessed it: are task- and self-oriented, in difficult life circumstances they are more likely to demonstrate coping behavior: distancing, seeking social support, and escape-avoidance; they are characterized by a high level of: neuroticism, depression, irritability, shyness, openness and emotional lability, verbal aggression, suspiciousness, offensiveness, indirect and physical aggressiveness. On the other hand, adolescents who were not subjected to illegal actions by their parents/guardians and generally did not experience any violent actions (bullying) in social groups were found to be: focused on themselves and on building interpersonal relationships; in difficult situations, they resort to confrontational coping, social support and positive reassessment of the situation; on the one hand, they are more balanced, on the other hand, they demonstrate irritability, emotional lability, negativism, irritation, suspicion, and verbal aggression. Also, a certain level of spontaneous aggressiveness, sociability, reactive aggressiveness, ambiversion and androgynous gender identity was determined in both groups of teenagers. Conclusions. Socio-psychological features of children affected by family violence are characterized by a certain connection among the interviewed teenagers. Namely, in adolescents who have experienced violence, a connection was determined: distancing with depression, escape-avoidance with neuroticism and reactive aggressiveness; self-directedness with coping seeking social support and negative association with shyness. In adolescents who did not experience violence in the family, connections were established: coping, problem solving planning with a focus on interaction, positive reevaluation with sociability; a negative relationship between the search for social support and neuroticism and depression.

РЕСУРСИ РЕЗИЛЬЄНТНОСТІ ОСІБ З ТРАВМАТИЧНИМ ДОСВІДОМ

Purpose. Theoretical study of resilience and the resources that determine the difference in its manifestation after critical situations, as well as empirical research on the mechanisms and resources that promote the development of resilience in people with traumatic experiences because of the war in Ukraine. Methods. Methods of theoretical analysis of scientific literature on the problem; methods of empirical research using a set of psychodiagnostic techniques; methods of mathematical statistics. Spearman's rank correlation coefficient was calculated for statistical data processing. Results. According to the results of theoretical analysis, the concept of "resilience" is considered as both a process and an outcome of successful adaptation to difficult life situations, especially through mental, emotional, and behavioral flexibility and adaptation to external and internal challenges. The empirical study revealed positive correlations of psychological resilience with resources (crisis coping strategies) "B – Belief & values" (r=0.591), “C – Cognition, thought” (r=0.540). A directly proportional correlations was also found between the overall impact of the event, the level of intrusion and avoidance with the crisis coping strategy "I – Imagination" (r=0.505; r=0.607; r=0.506), between the level of avoidance and the resource “S – Socialization” (r=0.632), between the level of intrusion and “C – Cognition, thought” (r=0.491). Conclusions. Individuals whose crisis coping strategies are based on faith (in God, in people, in miracles, or in themselves and their mission), belief systems, values and meanings, the activation of mental abilities, the ability to think logically and critically, assess situations, learn new ideas, plan, gather information, analyze problems, and solve them rationally, exhibit higher resilience indicators. Those who have higher level of impact of event and manifestations of specific PTSD symptoms more frequently use imagination, memories, and creativity to cope with crises. The level of avoidance positively correlates with the use of social ties, social support, and communication to cope with crises, and the level of intrusion positively correlates with the use of cognition and cognitive strategies.

The Effect of Balance Training on Physical Motor Functions TO 11-12 Year Old Female Football Players

The aim of this study was to investigate the effect of balance training on the physical motor function of adolescent female football players. Thirty female football players aged 11-12 years were selected from Ausheng Football Club as the study subjects, and they were divided into a test group and a control group of 15 each using experimental testing and mathematical statistics methods. The experimental group received balance training intervention for a period of 5 weeks while the control group did not receive any intervention. The Y-Balance test and FMS test were used as assessment indicators to evaluate the balance and body movement function of the athletes respectively. Differences in performance between the two groups before and after training were compared and the relationship between balance ability and physical motor function was analyzed by methods such as paired samples t-test and independent samples t-test. The results showed that compared with the control group, the experimental group showed significant improvement in all balance indicators, especially in medial back and overall balance. In addition, the experimental group showed significant improvement in hurdle stride, linear lunge, and rotational stability indicators. The overall motor function of the experimental group improved significantly as assessed by the Functional Movement Screen (FMS), which indicated that the balance training was very effective. The Y-balance test further confirmed that the experimental group showed a substantial improvement in balance, while the control group showed little change. In addition, the results of the Y-balance test showed a moderate positive correlation with the results of the FMS test, suggesting a relationship between balance and functional movement. These findings emphasize the positive impact of balance training on the physical motor function of young female footballers, demonstrating the importance of balance training in motor development and injury prevention.

The Mediation Role of Mobile Phone Addiction to the Relationship between Physical Activity and Autistic Traits among College Students

This study taking physical activity (PA) as the independent variable and autistic traits (AQ) as the dependent variable, we explored the relationship between the three in depth, further verified the mediating role of mobile phone addiction (MPA ) between the two , and constructed a hypothesized mediation model of mobile phone addiction in the relationship between physical activity and autistic traits.Method: This study takes the characteristics and correlations of physical activity (PA), autistic traits (AQ) and mobile phone addiction (MPA) as the research objects, follows the principle of convenience sampling , and uses questionnaire survey method and mathematical statistics method to conduct a survey on Zhanjiang City, Guangdong Province. Three universities conducted stratified sampling , and finally conducted a survey and research on 382 college students . The " International Physical Activity Scale -Short (IPAQ -SF)", "Autism Trait Scale(AQ)" and "Mobile Phone Addiction Tendency Scale(MPATS)" were used. An electronic questionnaire produced by "Questionnaire Star" was used to conduct an online survey on college students' physical activity, autistic traits and mobile phone addiction tendencies, etc., and SPSS24.0 was used for statistical processing and analysis.Result:1. The BMI difference between PAand AQ of college students was significant (p < 0.01). 2. There was a significant difference between the PA level and the level of college students with high and low AQ (p < 0.01). 3. The results of correlation analysis showed that there was a significant negative correlation between PA and AQ (r = -0.48**, Sig.000) and MPA (r=-0.22**, Sig.000), and a significant positive correlation between AQ and MPA (r=0.37**, Sig.000). 4. PA had a significant mediating effect on AQ through MPA, and MPA had a significant mediating effect between PA and AQ; the direct effect of PA on AQ was significant; the total effect of PA on AQ was significant.Conclusion:1.Physical activity can significantly and negatively predict autistic traits and mobile phone addiction; 2. Mobile phone addiction significantly and positively predicts autistic traits ;3. Mobile phone addiction ranks between physical activity and autistic traits has a significant mediating effect.

Online course as a means of developing master's professional competencies: results of a pedagogical experiment

The article proposes a solution to a scientific problem, which is to substantiate the feasibility of using online courses in the professional training of masters in the pedagogical university, to develop an online course and experimentally test its effectiveness as a means of developing the professional competencies of masters in the speciality 014~Secondary Education (Mathematics). The author used the following methods of scientific research: pedagogical experiment, observation (for systematic perception and analysis of learning activities, motivation and personal growth of students in the context of blended learning), testing (to determine the level of logical thinking and development of students’ professional competences), questionnaire (to monitor the ergonomics and efficiency of the online course and the Mathematics teacher’s e-portfolio), expert evaluation of the developed online course, and methods of mathematical statistics (for proper processing of experimental data and verification of the online course’ effectiveness). The results of the control stage of the study indicate a positive trend in the development of mathematical, information and educational, methodological, psychological and pedagogical, and professional and technological competencies of students in the experimental group. The final test of the online course was chosen as a tool for determining the level of mathematical competencies of the masters in the experimental group. The reliability of the assessment of the masters’ professional competencies was confirmed by testing the hypothesis of the normal distribution of test results according to the Shapiro-Wilk test. In addition, a close correlation between students' academic achievement level in an online course and the level of logical thinking development was substantiated using the Student’s t-test. Prospects for further research include the development of online courses on Mathematics teaching methods with an emphasis on methodical, professional, and technological competencies; a detailed study of the impact of the latest information technologies (artificial intelligence, virtual and augmented reality, web programming, etc.) on the development of students’ information and educational professional competences in distance and blended learning.

Building Test Batteries Based on Analyzing Random Number Generator Tests within the Framework of Algorithmic Information Theory.

The problem of testing random number generators is considered and a new method for comparing the power of different statistical tests is proposed. It is based on the definitions of random sequence developed in the framework of algorithmic information theory and allows comparing the power of different tests in some cases when the available methods of mathematical statistics do not distinguish between tests. In particular, it is shown that tests based on data compression methods using dictionaries should be included in test batteries.