Methods Of Mathematical Statistics Research Articles

Features of the development of strength and flexibility of middle school children by means of fitness with elements of martial arts

The article is devoted to the study of the peculiarities of the development of flexibility and strength of schoolchildren aged 13-14 under the influence of martial arts fitness. The purpose of the study is to determine the effectiveness of using fitness exercises with elements of martial arts for the development of flexibility and strength abilities of secondary school children. The research involved 20 boys and 20 girls who studied in the 8th grade of a secondary school. The following methods were used to solve the research tasks: studying and analyzing literary sources on the research topic; pedagogical experiment; pedagogical testing of the level of physical abilities development, methods of mathematical statistics. To conduct the pedagogical experiment all participants of the experiment were divided into two groups: experimental (10 girls and 10 boys) and control (the same composition). The essence of the experiment was that for children who were included in the experimental group during 5 weeks during physical education lessons an experimental variable module on fitness with elements of martial arts was introduced. When developing the variable module on martial arts fitness, we adhered to the requirements for variable modules in the current physical education curriculum for schools. Girls and boys in the control group attended physical education classes based on the educational material of the variable module gymnastics. The study proved that the use of a variable fitness module based on the use of classical aerobics exercises and martial arts elements during physical education lessons in middle school contributes to a statistically significant improvement in flexibility (forward bending) and strength (flexion and extension of the arms in a lying position and lifting the torso from a lying position in 30 seconds). At the same time, such exercises are emotional and can have a positive impact on adolescents' functional fitness, well-being, and mood.

Тhe relationship between the level development of motor qualities of female cadets and their performance results exercises with kettles

The article examines the relationship between sports results in exercises with kettlebells and the level of development of motor qualities and the formation of military-applied motor skills of female cadets of the kettlebell sports section of a higher military educational institution under martial law. Research methods: theoretical analysis and generalization of literary sources, pedagogical observation, pedagogical testing, methods of mathematical statistics. It was established that the majority of strength exercises and exercises that require the manifestation of endurance have a close and moderately significant relationship (p<0?01) with high results of female cadets in competitive kettlebell exercises, namely: pull-ups on a low bar, squats with barbell, barbell deadlift, hanging on the crossbar, complex strength exercise, 1 and 2 km run, jumping out in 1 min. Also, a close and average statistically significant relationship (p<0.01-0.05) was found between the high level of formation of military applied motor skills of female cadets and all exercises with weights (p<0,01-0,05) (general control exercise on the obstacle course, throwing a grenade range and 5 km dash march). The results of the study allow us to state that the use of exercises with kettlebells in the process of physical education under martial law conditions will ensure the effective development of motor qualities, the formation of military-applied motor skills in order to ensure the physical readiness of female cadets of higher military educational institutions for educational and future military-professional and combat activity.

SUBSTANTIATION OF THE PROFESSIONAL STANDARD OF "PERSONAL FITNESS TRAINER" IN UKRAINE

Professional staff is needed for the effective functioning of health fitness. There are no professional standards for fitness staff in Ukraine, so there is no single standardized approach to determining the list of job functions, general and special competencies, the required knowledge, skills and practical abilities. The purpose of the study is to substantiate and develop a professional standard of "Personal Fitness Trainer" taking into account international experience. Methods: analysis and generalization of scientific and methodical literature, pedagogical observation, functional analysis, documentary method, method of expert evaluations, methods of mathematical statistics. Results. The development of a professional standard for "Personal Fitness Trainer" was based on regulatory acts and the algorithm formed for the health fitness system. There have been identified 60 necessary labor actions which ensure the performance of 9 labor functions of a fitness trainer. The professional standard takes into account the needs of employers, consumer requirements and will be the basis for the industry standard of higher education in the relevant specialty. Conclusions. The developed professional standard for "Personal fitness trainer" is relevant, complies with regulatory acts and established algorithm, adapted to the system of fitness. The expediency of developing a professional standard "Personal fitness trainer" was based on the study of the actual state and prospects of application of fitness staff. The professional standard provides requirements for the content and quality of professional activity; list of general competencies; requirements for the level of qualification, medical contraindications to work, work experience, level of education of a fitness trainer; a list of labor functions and labor actions and the necessary knowledge, skills and abilities; list of subjects and means of work and definition of professional competencies, etc. The professional standard "Personal fitness trainer" should be the basis for the industry standard of higher education in the relevant specialty.

Correspondence of self-assessment of physical development according to indicators of physical fitness of higher education acquires

The purpose of the work is to study the correspondence of self-assessment of physical development according to indicators of physical fitness of students of higher education to determine the effectiveness of pedagogical control in the process of motor activity. To achieve the goal, the following research methods were used: data analysis of scientific and methodological literature, regulatory and legal documents, programs on physical culture, pedagogical testing of physical fitness, methods of mathematical statistics, test-questionnaire E.V. Bochenkova "Self-description of physical development". To study the individual profile of the physical "I" of the individual, we used the test-questionnaire of E. V. Bochenkova "Self-description of physical development". The questionnaire included 70 statements related to the field of physical development of a person and an indicator of general self-esteem. The purpose of this technique is to study the peculiarities of self-esteem of boys and girls and to compare the obtained data. Research was conducted on the basis of the Lutsk National Technical University, at the Faculty of Digital, Educational and Social Technologies with students of higher education. The conducted studies revealed the inadequacy of the self-assessment of physical fitness of higher education students, which indicates the importance of theoretical coverage and practical implementation in physical education classes of the section of pedagogical control and self-control of physical fitness, which should be an incentive for self-improvement of boys and girls in the process of physical activity.

Activation of Students' Cognitive Activity through Physical and Health-Improving Activities

The methodology for developing cognitive activity through physical and health-improving activities is thoroughly examined for primary school students. Regarding the methodology for developing cognitive activity through physical and health-improving activities for middle school students, there are practically few developments, and recommendations are often given in a general form. Thus, the issue of the impact of physical and health- improving activities on the cognitive activity of middle school students is still largely unexplored and has not yet received scientific substantiation. The article determines the influence of the level of physical working capacity on the cognitive activity of 6th-grade students. A method for activating cognitive activity through small forms of physical culture is presented. The study involved the analysis of literary sources and internet resources; analysis of students' academic performance; research on physical working capacity; speed of thinking; determination of the average academic score; mathematical statistics methods using the SPSS program: the Kolmogorov-Smirnov one-sample test; Pearson correlation.

Autenthity of the indicators of complex visual-motor reaction for trap shooters

The aim of the study was to determine the validity and stability of choice reaction time testing in trap shooters. The following research methods were used: theoretical analysis and summarization of data from scientific and methodological literature and the Internet, medical-biological methods, pedagogical observation, and mathematical statistics methods. Relevant calculations were conducted using the MS Excel analysis software package and functions from the Statistica software package. The study involved 27 athletes of varying qualifications in trap shooting. Each athlete's reaction time was measured in ten attempts. Satisfactory reliability of choice reaction time testing was found among shooters of average skill level (Candidate for Master of Sports, 1st and 2nd categories) with a reliability coefficient of ICC=0.767. Excellent reliability of the test (ICC=0.933) was found in highly qualified shooters (Master of Sports and International Master of Sports). The tested choice reaction time methodology demonstrated acceptable informativeness (validity) and reliability (stability) for the training process of trap shooters.

Assessment of agroclimatic resources in agricultural landscapes of the Turkestan region of the Republic of Kazakhstan Askha

The article presents the scientific results of a study assessing agroclimatic resources in agricultural landscapes located in various natural zones of the Turkestan region of the RK (Republic of Kazakhstan). The research methods included classical and modern methods of mathematical statistics using digital technology and time series graphs to develop a mathematical model for climatic and hydrological indicators. Assessment of changes in indicators of agroclimatic resources in agricultural landscapes for 1941–2020 showed that the sum of air temperature, evaporation from the water surface and radiation balance of the daytime surface, characterising the energy resources of landscapes, increased by 10–15%, which contributes to increase in the total water consumption of agricultural land by 10–12%. Meanwhile, the decreasing tendency of the amount of precipitation by 5–10% in all natural climatic zones of the region has become one of the factors leading to a decrease in the natural moisture supply of the soil and vegetation cover of landscapes by 10–15%, acting as important environment-forming and ecological functions. The combined impact of these environment-forming factors has become the key reason for the increase in the deficit of agricultural land water consumption by 15–20%, the reduction of solar energy costs for the soil-forming process by 10–15% and the increase of the climate aridisation, and has become a signal for the need in the safety of agricultural activities, requiring the development of a set of adaptive measures to mitigate this process in the region.

Correlations and Variations Between the Major Biochemical Parameters of the Blood of Hybrid Swine.

In modern animal husbandry, increasing attention is given to mathematical modeling and statistical methods, especially for evaluating commercial hybrids. Our aim was to evaluate the phenotypic and genetic variability of biochemical parameters of blood serum of the 56 hybrid boars (Large White × Landrace × Duroc) raised in feeding stations (Russia) through mathematical modeling. The particular variances and covariances of traits were calculated using the limited maximum likelihood model and the REMLF90 programs. A narrow range of variability was found for major biochemical parameters in relationship with the "FFG-factor" ("fattening period × final live weight × gain"), including the majority of the metabolites (p ≤ 0.05). The highest values of the genetic correlations were observed for the "total protein" parameter with albumins (0.78), globulins (0.94), creatinine (0.99), and enzymes: AST (0.98), ALT (0.80), etc. Phenotypic and genetic relationships showed fairly high correlation coefficients (0.5-0.8). It is important to emphasize that most of the studied amino acids (alanine, arginine, aspartic acid and asparagine, glutamic acid and glutamine, glycine, isoleucine, leucine, serine, threonine, tyrosine, valine) were significantly associated with the "FFG-factor" (p ≤ 0.05). The proposed approach provides reliable data on metabolite variability and correlations.

The Integral Assessment of Playing Tactics in National Football Teams

Objectives. The objective of the study was to determine the features of competitive activities among national football teams based on the integral assessment of playing tactics. Materials and methods. The study was conducted during the 2024 European Football Championship. The competitive activities of national football teams from European countries (Germany, Spain, England, Switzerland, France, Portugal, Netherlands, Turkey) were analyzed, focusing on the playing tactics in 50 halves. In order to carry out the study, the following methods were used: theoretical analysis of literature sources; pedagogical observation of competitive activities; analysis of video materials of competitive activities; methods of mathematical statistics. The statistical analysis of the research results was conducted using descriptive mathematical statistics. The sample was characterized by determining the arithmetic mean, standard deviation (S), and coefficient of variation (V). The significance of observed differences in the indicators was assessed using the parametric Student’s t-test for independent samples. Prior to this, the data’s conformity to a normal distribution was verified using the Shapiro-Wilk W-test. Results. A methodology for the integral assessment of the tactics undertaken by national football teams was developed. The integral assessment of team tactics consisted of 10 specific coefficients that reflect the main components of football players’ competitive activities in the phases of ball possession and recovery. The competitive activities in 50 halves of the 2024 European Football Championship were analyzed. The average value of the integral assessment of the tactics in national football teams was determined to be 5.62 ± 0.43 points. The findings revealed significant tactical variations between the teams, with Spain’s use of high pressing and creative play contributing to their championship victory. A ten-point scale for evaluating the tactics of national football teams was developed, on the basis of which the level of competitive activities is interpreted. Conclusions. The developed methodology for monitoring and analyzing the tactics of football teams allows for targeted management influences on the competitive activities of football players at the operational, current, and stage levels.

Numerical method for forming an alternative opinion in coalitions of highly qualified specialists using relative usefulness indicator

Subject of research: the formation of an alternative opinion in coalitions of highly qualified specialists. Purpose of research: development of a numerical method for the formation of an alternative opinion in coalitions of highly qualified specialists using a relative utility indicator and its subsequent implementation in the form of a computer program. Methods of research: survey, formalization, system analysis, correlation analysis, Hamming criterion, natural experiment, object-oriented programming. Main results of research: 1. The approach proposed by the author, based on combining methods of mathematical statistics and taking into account the individual competencies of experts, provides new opportunities for the formation of an alternative opinion in coalitions of experts and allows for increased efficiency in decision-making. 2. Verification of the developed numerical method was carried out using the example of a survey of police officers regarding violators of security systems in the field of critical information infrastructure. 3. A computer program has been developed that implements the created method. 4. The study revealed that the relative usefulness indicator of the j-th expert provides an opportunity to form alternative expert positions that have a reliable generalized opinion. 5. The practical significance of the work lies in the development of a computer program that can be used to conduct expert surveys and obtain reliable expert assessments based on them.

Capacity analysis of short-distance continuous diversion areas on mountainous urban expressways.

The short-distance continuous diversion area plays a crucial role within mountainous urban expressway systems, significantly enhancing the efficiency of specialized road sections through capacity analysis. This study develops a capacity calculation model tailored to the diversion area's unique characteristics and principal capacity-influencing factors. Initially, the research focuses on a specific short-distance continuous diversion area of a mountainous urban expressway, employing video trajectory tracking technology to gather trajectory data. This data serves as the basis for analyzing road and traffic characteristics. Subsequently, the model computes the capacity influenced by eight variables, including diversion point spacing and deceleration lane length, using VISSIM simulation experiments. A gray correlation analysis identifies key factors, which guide the establishment of the model's fundamental structure through two-factor surface fitting results. Mathematical statistical methods are then applied to resolve the model's parameters, culminating in a robust capacity calculation model. The findings reveal that diversion point spacing, along with primary and secondary diversion ratios, significantly influence capacity. Notably, the capacity exhibits a marked quadratic polynomial relationship with the primary diversion ratio and diversion point spacing, and a linear relationship with the secondary diversion ratio. The model's validity is confirmed through a case study at the diversion area north of Huacun Interchange in Chongqing Municipality, where the discrepancy between calculated and actual capacities is under 5%, underscoring the model's high accuracy. These results offer valuable theoretical and methodological support for the planning, design, and traffic management of diversion areas.

A dimensional design of tractor seat based on Iranian anthropometric characteristics.

The dimensional seat design process should consider both the users' tasks and their physical characteristics. To use an approach for the design and evaluation of seat dimensions based on the anthropometric characteristics of the Iranian population and the requirements of tractor operators. Some existing equations relating the seat dimensions to anthropometric characteristics were modified according to logical justifications and international standards. A new mathematical-statistical method was used to extract the equations estimating the constant seat dimensions based on the theoretical maximizing of the accommodation level. In addition, an Overall Seat Accommodation Score (OSAS) was developed to represent the mean of seat dimensions accommodation level and dimensional accommodation equality, simultaneously. The dimensional seat design can be affected under different conditions of adjustability, esthetic, and space limitations. However, it was shown that it is possible to improve the design of tractor seats without any significant increase in the final cost and complexity. A new approach was used for tractor seats for a sample of Iranian operators and can be used for the design and evaluation of tractor seats for other target populations.

Detailed Late Pliocene-Quaternary sedimentation history and diagenesis processes in the eastern part of the Norwegian-Greenland Basin based on mathematical statistical methods

As a result of univariate regression analysis, quantitative parameters on the distribution of Mn/Al and Mn/Fe ratios in the sections of the studied holes of ODP Leg 151 were obtained. On the basis of correlation analysis data with Pearson matrix construction and classical factor analysis with varimax rotation, a division of rather homogeneous Upper Pliocene-Quaternary sediments was carried out with the allocation of 3 main factors that characterize the history of sedimentation and diagenesis in the Norwegian-Greenland Basin. The boundaries between lithostratigraphic subdivisions are drawn on a strict mathematical basis. It is established that the nature and degree of intensity of diagenesis processes in this region were influenced by the following main factors: sedimentation environments in the Norwegian-Greenland Basin in the Late Pliocene-Quaternary time; grain-size and chemical composition of the studied sediments; total organic carbon content in the sediments; sedimentation rates.

Safe-Enhanced Autonomous Driving Technology Using Conformal Prediction Results

Abstract Autonomous driving technology significantly improves road safety, mitigates traffic congestion, and paves the way for a more efficient and connected transportation future. However, the uncertain driving scenarios poses a great challenge to the safe control of autonomous vehicles (AVs). Therefore, this paper proposes an enhanced safety control framework by integrating the quantified prediction results of human driving behaviors into the path-planning process. First, a Long Short-Term Memory (LSTM) network is employed for driver behavior prediction, based on which, the conformal prediction, a mathematical statistical method, is introduced to quantify the uncertainties of the prediction results with a probabilistic presentation. Then, a model predictive model controller (MPC) is designed to enable the path-planning ability. By using the Lipschitz constant, the inequality for obstacle avoidance is reformulated as a hard constraint in the MPC optimization framework while considering the conformal prediction results. Finally, some simulation test cases are conducted to validate the proposed method. The results demonstrate the effectiveness to guarantee the safety of AVs with uncertain prediction results.

ON THE EFFECTIVENESS OF USING AN ELECTRONIC TEXTBOOK IN FORMING THE READINESS OF FUTURE PRIMARY TEACHERS FOR INTEGRATED LEARNING

The article presents a theoretical review and experimental study of the problem of using an electronic textbook in the process of developing the readiness of primary education teachers for integrated learning. The aim of the article is to determine the effectiveness of the electronic textbook in the process of developing the readiness of future teachers for the integrated education of primary schoolchildren.The research materials were tested during the 2023-2024 academic year on the basis of the Pavlodar Pedagogical University named after Alkey Margulan, where 78 students of the educational program “Pedagogy and Methods of Primary Education” were involved at the stage of testing and implementation of the electronic textbook. To achieve the goal ofthe study, theoretical (analysis, synthesis, generalization and systematization of scientific publications) and empirical (testing, pedagogical experiment, expert assessment) methods were used. The validity of the results of experimental pedagogical work was confirmed using the methods of mathematical statistics -the Pearson criterion.The educational results of the participants in the experimental pedagogical work demonstrated the obvious effectiveness and significance of the developed and tested electronic textbook, the content of which ensured the completeness and systematic assimilation of theoretical knowledge and the development of practical skills of students in the educational program “Pedagogy and Methods of Primary Education” for the successful implementation of integrated education for junior schoolchildren.

PSYCHOLOGICAL SUPPORT OF THE DEVELOPMENT OF THE REHABILITATION POTENTIAL OF EMPLOYEES OF THE FORCE

The article the main approaches to the psychological support of the process of development of rehabilitation potential of specialists of law enforcement agencies. The purpose of our article is to study the peculiarities of social functioning and the leading factors of mental trauma in specialists of law enforcement agencies with depressive disorders of neurotic origin. During the research, the following methods were used: analysis of special, scientific and methodological literature, analysis of documentary materials, observation, testing, experiment, methods of mathematical statistics. Factors of development of rehabilitation potential of personality are characterized. The peculiarities of the systemic structure of mental phenomena and the concept of psychological support of the process of development of rehabilitation potential are considered. The need to implement a systematic approach based on empirical data, which includes research aimed at harmonizing the psychological state of law enforcement officers, is emphasized. Empirical research has revealed the peculiarities of the social functioning of specialists in law enforcement agencies with depressive disorders of neurotic origin. There are differences in the psychological well-being of professionals with depressive disorders of neurotic origin and people without mental disorders, namely: people without mental disorders are characterized by a predominance of interest in life, reflecting their interest in everyday life, enthusiasm for what is happening; in people with mental disorders, the indicators of "consistency in achieving goals" and "consistency between goals and their achievement" are such that indicate inadequate assessment and inability to use their own strength to achieve the goal.

The effectiveness of interactive online courses for the speech competence development in non-language-major students

Interactive online courses are becoming increasingly popular among students studying foreign languages. The aim of the article is to analyse the effectiveness of interactive online courses in the speech competence development of non-language-major students. Research methods included student surveys, testing before and after the interactive online courses, mathematical statistics methods (t-test, Likert scale). The testing showed a significant improvement in the results of the experimental group (EG) that studied using interactive online courses (B2 – 43.5% of students, C1 – 21.7%, C2 – 21.7%). Online courses were found to provide valuable opportunities for real language practice with an average score of 3.6. The user interface and features were found to be user-friendly and easy to navigate, with an average score of 3.5. The variety of topics covered in the interactive online courses was identified as beneficial for general language skills, with an average score of 3.6. Flexibility in study planning was consistent with the benefits, receiving a high mean score of 3.8. The practical value of these results is their ability to improve the practice of foreign language learning. The results provide important insights into the effectiveness of interactive online courses.

The specifics of integrating distance learning technologies with traditional classroom instruction: How to design educational curricula in modern education?

The active and widespread transition to distance learning modalities was prompted by the COVID-19 pandemic and is currently considered a prospective paradigm for the development of the education system. This shift necessitates the creation of corresponding curricula and programs capable of fostering student competencies through online and blended learning. The purpose of this research is to examine the specifics and formulate an algorithm for the development of educational programs incorporating distance and blended learning technologies. Analytical, sociological (utilizing semi-structured surveys administered to 96 educators and 128 students on the subject of distance and blended learning and its methodological support), modeling, and mathematical-statistical methods (Student's t-test and analysis of variance ANOVA) were employed in this study. The survey confirmed the hypothesis of differences in attitudes toward distance learning among students and educators. Educational needs and challenges were identified, leading to the development of an algorithm for designing educational programs integrating distance and blended learning technologies. An algorithm has been devised for the development of educational programs based on the integration of distance and blended learning technologies. The study underscores the importance of continuity across educational levels and the early cultivation of distance learning skills. Prospective research endeavors are intended to be directed toward the examination of the organization of distance and blended learning for students with special educational needs.

SOCIAL AND ENVIRONMENTAL FACTORS DETERMINING THE HEALTH STATE OF YOUTH STUDENTS IN UKRAINE

One of the bases of sustainable development of mankind is the health of the young generation. The priority of this issue is especially important in the perspective of European integration processes in Ukraine. Youth is an important component of the human resource that every state should take care of. Preserving, restoring and improving the psycho-physiological condition of young people is the key to the survival and further progress of mankind. The purpose of our research is to analyze the importance of individual factors and their combinations that can affect the health of students. Analysis, synthesis and modeling methods were used to study the state of research. The results of our research were 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. This study explores the social and environmental factors affecting the health of university students in Ukraine, emphasizing the importance of promoting a healthy lifestyle among youth. The research highlights the role of education in shaping health culture, noting gaps in the current system's approach to instilling necessary attitudes toward health. The study draws on data from student health assessments and reveals a high prevalence of chronic diseases, especially among students from radiation-contaminated areas. The investigation further examines the genetic and immunological markers influencing students' health, finding that prolonged stress, radiation exposure, and physical inactivity significantly impact immune responses. Additionally, the research explores the link between thyroid and lipid metabolism issues and students' exposure to ionizing radiation. The findings suggest that moderate physical activity and immunomodulators may help mitigate stress-induced immunosuppression. The study concludes that addressing these social and environmental health determinants is critical for improving the well-being of Ukrainian youth and calls for tailored physical education programs and preventive health measures.

THEORETICAL PRINCIPLES OF THE FORMATION OF SPIRITUAL CULTURE IN FUTURE TEACHERS OF ARTISTS

The problem of spirituality, spiritual culture and their role in the formation of the creative personality of student youth is quite relevant. The process of forming spirituality is an important aspect of the modern humane educational paradigm. According to the scientific community, it is spirituality that expresses the degree of "humanization" of the pedagogical process. Questions of spirituality have interested humanity at all times and have been studied by many sciences: philosophy, pedagogy, psychology, sociology, ethics, aesthetics, etc. In the New Ukrainian School Program in the Progress to Values, it is stated that now it is important to intensify efforts to raise the spiritual level of Ukrainian youth, to form a stable system of deep moral and spiritual values in them. The purpose of the article is to describe the concept of spiritual culture and the formation of artistic ideas in future teachers during the study of Ukrainian folk art. 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. In the research, we used a complex of general scientific and pedagogical methods. To ensure an objective and comprehensive study of the researched phenomenon, an analysis of scientific, scientific-methodical, and art sources was carried out; the state of development of the problem and prospects for further research were determined; generalization of pedagogical experience in teaching art in a higher education institution. The formation of a spiritual personality takes place in the interconnected process of education and training. An important role in the formation of the spiritual sphere of the individual belongs to education. Its tasks are classified according to the following directions: formation of a scientific outlook; education of a conscious attitude to learning, development of cognitive activity and culture of mental work; education of political consciousness and development of civic activity; education of a creative attitude to work, preparation for a conscious choice of profession; education of morality and culture of behavior; formation of legal awareness and education of civil responsibility; education of aesthetic culture and development of artistic abilities, etc.