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Development of a mathematical model of the system for collecting and analyzing data
(Faculty of engineering and natural sciences, 2019) Suleizhan T.
This thesis is aimed at developing practical skills of building mathematical svstems for data collection and analvsis. The peculiarity of the work is to learn to self-decision-making. to develop research skills. which is especially iniportant in a dynamic world. Data collection is carried out. in almost all areas of science and technology. Over the past few vears. data collection techniques have been applied to applications and new corporations have emerged to commercialize the technology. Many business and financial problems are successfully solved with the use of big data. Problems of management, classification. pattern recognition, forecasting, inherent in almost all application areas. such as medicine. military Affairs. aviation and space, construction, are increasingly solved with the use of this technology. In this regard. vou will see a fundamental understanding of the basic concepts and models of big data, as well as learn how to apply this knowledge - in practice.
Analysis and the development of a mathematical model of the children mortality
(Faculty of engineering and natural sciences, 2019) Zhumabek D.
The mortality rate depends on many different factors: the socio-economic development of the country, the environmental situation. the well-being of the population. the level of stress and much more. After fertility. it takes the second place in its importance in the processes of reproduction of the population. has a serious impact on the population size. its structure. and is closely interconnected with all socio-demographic processes. The causes of mortality in Kazakhstan are classified by the main groups: infectious discases. diseases of the respiratory system. circulatory system, neoplasms. accidents, poisonings and injuries. Mortality of the population is a mirror reflection of the level of socio-economic development of society.
The Art of Personalized Student-Supervisor Matchings
(ADAL Kitap, 2025) Serek A.G.; Berlikozha B.A.
The process of student-supervisor matching is a critical yet complex task in higher education institutions, directly influencing research productivity, student satisfaction, and workload distribution. The ability to assign students to the most suitable supervisors is essential for fostering strong academic relationships, optimizing institutional resources, and improving research outcomes. However, traditional manual assignment methods often lead to inefficiencies, subjective biases, and an imbalance in workload distribution. As a result, automated recommendation systems have emerged as a promising solution to enhance the efficiency and fairness of student-supervisor pairings. This study evaluates three recommendation algorithms—Singular Value Decomposition (SVD)-based collaborative filtering, graph-based matching using the Hungarian Algorithm, and machine learning via Random Forest Regression—to determine their effectiveness in optimizing student-supervisor assignments. A rigorous empirical analysis is conducted across five key performance metrics: accuracy, fairness, stability, scalability, and computational efficiency. The findings reveal that while collaborative filtering performs well with established datasets, it struggles with novel cases due to its dependence on prior interactions. The Hungarian Algorithm guarantees optimal matching but faces scalability challenges, particularly in large academic institutions with thousands of students and supervisors. Meanwhile, Random Forest Regression effectively captures complex compatibility patterns but requires extensive labeled data, limiting its applicability in cases where historical matching data is sparse or unavailable. To overcome these limitations, the study proposes an adaptive hybrid framework that integrates the strengths of all three approaches. The hybrid model leverages collaborative filtering’s ability to recognize patterns in existing data, the Hungarian Algorithm’s precision in optimal pairings, and the predictive power of machine learning. By combining these methodologies, the proposed system enhances match accuracy, ensures fair workload distribution, and remains computationally efficient for large-scale institutional implementation. Additionally, the framework introduces dynamic adaptation mechanisms that allow the system to update recommendations based on real-time changes in student preferences and supervisor availability, making it more practical for real-world applications. The research contribution is a comprehensive, empirically validated hybrid framework that improves student-supervisor matching by balancing accuracy, fairness, and efficiency. This study provides educational institutions with actionable guidelines for scalable and equitable assignment processes, ultimately contributing to more effective mentorship experiences, improved research collaborations, and enhanced academic outcomes.
Integral power balance method in heat problems with free boundary
(Faculty of engineering and natural sciences, 2019) Kassabek Dina
One of the important areas of application of the free boundary problems is the mathematical modelling of phenomena in the low-temperature plasma of an electric arc and in contacts of electrical devices. Analysis of solutions makes it possible to verify the obtained theoretical results, to test the effectiveness of the developed algorithms for specific evolutionary processes in electrical apparatuses, and to interpret the available experimental data. The evolution of contact bridge and arcing processes is so fast (nano- and microsecond range) that their experimental study is very difficult. In some cases, only mathematical modeling can give an idea of their dynamics. Thus, the need for modeling is required not only for optimization of the experiment, but also due to the impossibility of using a some different approach. One of the most effective methods of solving heat problem is the method of heat potentials, which reduces the initial boundary value problems to integral equations. However, in the case of regions degenerating at the initial time, additional difficulties arise releted to the singularity of these integral equations. These difficulties are compounded in the case when an unknown function appears not only in the boundary condition, but also in the coefficients of the equation. This method enables us to obtain an approximate solution with desirable degree of accuracy and to evaluate the approximation error, using the maximum principle. Analytical methods for solution of heat and mass transfer problems have recently received a new stimulus to their futher development due to the growing need to solve multicriteria problems for which numerical methods are unable to estimate the influence of a large number of input parameters on the behaviour of the solution and especially on its dynamics. In particular, an integral thermal balance method, a perturbation method, and a number of other methods are widely used to solve problems of the Stefan type with a free boundary, describing heat transfer with phase transitions. The main problem with the use of this method is the estimation of the approximation error, which, as a rule, is replaced for applied problems by comparison of the analytical solution with the experimental data.
Laguerre polynomials in axisymmetric heat problems with a free boundary
(Faculty of engineering and natural sciences, 2019) Jabbarkhanov Kh.
The aim of the thesis is to consider solving heat equation with free boundaries using by heat polynomials method, in particular, using by Laguerre polynomials. There are two problems were considered. It is spherical inverse and direct problems the mcthod of thermal polynomials is appropriate. As exactly as the approximate solutions. The inverse two-phase spherical Stefan problem for unknown boundary heat. flux is solved by the method of the heat polynomials. Side by side with exact solution two methods for the approximate solution, collocation and variational methods, convenient for engineering applications are presented and compared.