Bulletin of Abai KazNPU. Series of Physical and mathematical sciences https://bulletin-phmath.kaznpu.kz/index.php/ped <p>Scientific journal " Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences" is a scientific and educational publication on topical issues of mathematics, mechanics and physics, computer science, as well as informatization of education and methods of teaching physical and mathematical disciplines in school, college and university.</p> <p>International Standard Serial Number ISSN 2959-5886<strong><em><br /></em></strong>ISSN (Online): 2959-5894</p> <p><strong>Contacts</strong></p> <div class="page"> <p>e-mail: <u><a href="https://bulletin-phmath.kaznpu.kz/index.php/ped/management/settings/context/mailto:Vestnik.KazNPU.FMS@gmail.com">Vestnik.KazNPU.FMS@gmail.com</a><br /></u>Shekerbekova Shirinkyz Tileubergenovna</p> <p>Abdulkarimova Glyusya Alimovna<br />Almaty, Tole bi str., 86 office 312</p> </div> КазНПУ им.Абая en-US Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2959-5886 TRENDS IN PERSONALIZED LEARNING AND IMPACT IN ARTIFICIAL INTELLIGENCE: A SYSTEMATIC LITERATURE REVIEW https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2043 <p>Formation of 21st-century skills is one of the most crucial global challenges in contemporary education. It involves overcoming the gap between the achievements of secondary education and the requirements of higher educational institutions, as well as bridging the divide between the needs of employers and learners. In line with the vision of the educational development reform in the Republic of Kazakhstan for 2023-2029, an educational process oriented towards students and their needs has been defined. The article examines the impact of personalized learning and artificial intelligence on the educational process. The challenge of the successful functioning of the educational trajectory, tailored to the student and their potential, personal interests, and needs, is addressed through the transition to personalized learning. This approach contributes to the improvement of knowledge quality by transforming the actions of both learners and teachers. In the era of digital technologies, personalized learning becomes a strategy that captures the attention of the educational community. It proves to be an effective tool for meeting diverse learner needs, strengthening interaction, and enhancing academic performance. The purpose of this article is to provide a systematic review of the literature on trends in personalized learning and the impact of artificial intelligence, highlighting key research, advantages, and disadvantages of personalized education. The objectives of the research were to analyze the main studies of personalized education, to compare the advantages and disadvantages of personalized education. The PRISMA methodology was chosen for a systematic literature review, covering articles from 2014 to 2023 from the Scopus database. The article also analyzes various aspects of the development of personalized teaching methodology, such as Massive Open Online Courses (MOOCs), intelligent mentoring systems, online and adaptive systems, augmented reality, and the development of personalized learning through virtual reality systems. The research findings can be utilized in the development of project systems for transitioning to personalized learning in educational institutions.</p> B. Duisekeyeva S. Koneva T. Sarsembayeva Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.023 ANALYSIS OF POPULAR ARTIFICIAL INTELLIGENCE PROGRAMS IN EDUCATION: STUDENTS PREFERENCES https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2290 <p>In recent years, technologies of artificial intelligence (AI) have become an integral part of the educational process, providing students with new opportunities for training and self -realization. The popularity of AI programs among students is explained by their ability to simplify access to educational materials, automate routine tasks and personalize the learning process. This article presents an analysis of the most popular and tools such as ChatGPT, Grammarly, Quizlet, Canva and Duolingo, which are actively used by students to write essays, prepare for exams, learn foreign languages ​​and create multimedia content. The study reveals which programs are most often selected by students, their main functions, advantages and restrictions.</p> <p>The results of the work allow us to understand how AI programs affect the effectiveness of training, as well as outline the prospects of their further application in the educational environmen</p> А.А. Kanatbekova М.N. Kemelbek М.В. Bereke R.A. Sheraliyeva S.K. Yessirkep Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.024 LEARNING A PROGRAMMING LANGUAGE BY INTEGRATING GENERATIVE ARTIFICIAL INTELLIGENCE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2229 <p>This article discusses the theoretical foundations and practical aspects of the use of generative artificial intelligence technologies as a pedagogical tool in teaching programming. The importance of artificial intelligence in education is growing, and GenAI allows students to increase their motivation to learn, personalize learning materials and develop their practical skills. The article analyzes the main methods, advantages and limitations of integrating artificial intelligence into the educational process. During the research, artificial intelligence tools were used to automate and personalize the learning process. In particular, in the process of students mastering the basics of programming, artificial intelligence was used as a tool to help give dynamic feedback, interpret algorithms and correct errors. In addition, ethical issues and the impact of technology on the quality of education were discussed. The article provides practical recommendations for improving the effectiveness of the use of artificial intelligence in programming courses. This research will contribute to the introduction of innovations in the field of education and the discovery of new opportunities for using artificial intelligence tools. This approach is based on improving the quality of programming education and developing students' creative and technical skills.</p> N.N. Kerimbayev Zh.G. Menlibay Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.025 MEASURING THE PROCESS OF INTEGRATING ARTIFICIAL INTELLIGENCE TOOLS INTO THE PROFESSIONAL ACTIVITIES OF COMPUTER SCIENCE TEACHERS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2262 <p>This study was devoted to the study of the process of integrating artificial intelligence (AI) tools into the professional activities of teachers. Since the purpose of the study is to identify the relationship between the age of teachers and their approach to the use of AI in educational practice, the results of a pilot study conducted among computer science teachers in Aktobe region schools in the 2024-2025 academic year are analyzed.</p> <p>As determined by the results of the study, the dependence of the problem of using AI on its perception by teachers of different generations, the level of training, and the propensity to allocate time resources is shown. The reason why teachers of the younger generation positively perceive the possibilities of AI, while teachers of the older generation are reluctant to accept them, was based on doubts that technology could reduce the role of teachers or lead to the destruction of the human factor in learning.</p> <p>Therefore, the importance of training future teachers to use AI tools in higher education institutions and the need to organize advanced training courses for school teachers is substantiated, and the amount of choice of respondents that should be covered in the course of research in the future is calculated.</p> A.M. Mubarakov A.D. Duisegaliyeva A.T. Baibaktina A.D. Kaipova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.026 CLASSIFICATION OF EMOTIONAL ARTIFICIAL INTELLIGENCE TECHNOLOGIES USED IN THE EDUCATIONAL PROCESS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2221 <p>This article presents the classification of emotional artificial intelligence technologies used in the educational process according to various criteria, including types of educational activities. The potential of affective computing for personalizing learning, increasing student motivation and improving their well-being is considered. The author analyzes classification approaches by data types, learning methods, types of emotions and ways of interaction. Examples of technologies such as emotion analysis and automatic assessment are presented, as well as their role in optimizing the educational process. The prospects of using emotional artificial intelligence are highlighted, including improving interaction between students and teachers, and the risks associated with data confidentiality and ethical aspects are also noted. The article indicates the need for further research and policy development for the safe and effective implementation of technologies in the educational environment.</p> Zh. Nurbekova R.A. Abduvaliyev Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.027 ARTIFICIAL INTELLIGENCE IN EDUCATION: IMPACT, APPLICATIONS AND FUTURE PROSPECTS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2242 <p>The article explores the use of artificial intelligence (AI) technologies in education, providing examples from Kazakhstan and abroad, and discussing their potential and prospects in this field. It outlines a strategy model for implementing AI in higher education, including planning, implementation, and evaluation of effectiveness. The study highlights positive trends in the adoption of AI in Kazakhstani universities, supported by the Republic's interest and successful integration of advanced technologies in higher education. A survey conducted among teachers of "Informatics" and "Mathematics-Informatics" programs at Zhetysu University named after I. Zhansugurov assessed the use of AI in education and identified factors hindering its application. The research substantiated the stages of integrating AI elements into the training of computer science teachers, demonstrating improvements in education quality and student motivation for learning and scientific research.</p> Y. Smagulov Zh. Zhiembayev M. Bokan Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.028 APPLIED ORIENTATION OF TEACHING STOCHASTIC METHODS TO ENGINEERING STUDENTS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2279 <p>The application of stochastic techniques as a tool for enhancing the quality of the technical specialties' educational process is investigated in this paper. Particularly relevant in the framework of fast technical and digitalization advancements, these approaches enable the modeling of complicated industrial processes and solving of problems under conditions of uncertainty. The research emphasizes the development of strategies for instructing stochastic procedures inside educational curricula designed to cultivate technical specialists. The primary objective of this study is to enhance students' analytical thinking, forecasting, and decision-making skills in unconventional situations, thereby allowing educational processes to align with the requirements of contemporary industrial sectors. The scientific and pragmatic relevance of the research is found in the fact that stochastic approaches enable the combination of theoretical knowledge with practical skills, therefore facilitating the training of highly qualified experts ready to operate in dynamic and complex systems. The study approach called for theoretical modeling, data analysis, and investigation of real-world examples. By means of production scenario modeling, the outcomes were acquired, therefore highlighting the efficiency of stochastic methods in addressing practical issues. The results of the research suggest that using stochastic approaches helps students to acquire their data analysis, process management under uncertainty, and modern digital tool application abilities. The approach significantly helps to create adaptable learning environments meant to solve industrial challenges. The practical relevance of the research findings is in their usefulness for the creation of educational programs meant to equip graduates fulfilling the criteria of digital transformation and modern industries.</p> A.E. Abylkasymova Е.А. Тuyakov G.A. Rysbekova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.009 FORMATION OF STUDENTS' LOGICAL THINKING SKILLS WHEN TEACHING A SCHOOL GEOMETRY COURSE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1688 <p>The main goal of the school geometry course is to develop students' logical thinking skills. The article discusses the importance of the tasks of the school geometry course for the correct development of the logical thinking of students. In addition, the geometry states that the submitted reports in many textbooks are incorrectly translated or incomplete content elements necessary for the development of the report are presented, and effective approaches that contribute to the formation, development of students' logical thinking skills, purpose and relevance. It is only when students fully understand the content of the given tasks that the skills of imagining the spatial arrangement of geometric shapes are properly formed, that is, the ability to think logically develops with the analysis and comprehensive discussion of a particular desired geometric shape according to the specified elements. In addition, the release of each report includes, in addition to the ability to correctly draw a diagram of geometric shapes, the stages of its preliminary analysis, justification of the correctness of the decision of the report and investigation of the decision. However, the need for students to develop logical thinking skills in teaching the school course in geometry determines the relevance of the issue of teaching geometry calculations.</p> A. Kokazhaeva A. Оspanovа B. Maibasarova G. Bergenzhanova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.010 THE PROBLEM OF THE ANNUNCIATION OF TRUTHS AND FARABI's HERITAGE IN THE HISTORY OF MATHEMATICS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/1892 <p>When talking about mathematics and its history in modern national schools, teachers use literature written during the Soviet era. In those literatures, while acknowledging that the first mathematical data came from the Babylonians and Egyptians, they write that the formation of the science of mathematics should be attributed not to the ancient Greeks, but also not to the Babylonians-Egyptians. The Greeks, who conquered the Egyptians, compared the Babylonians to the Egyptians. Mathematical science was an important branch of civilization in ancient times. Although its information is set forth in one national language, it is known to be the common spiritual wealth of the neighboring ancient peoples surrounding this nation. Because the owners of this wealth are the peoples of this region. In Greek literature there is no mention of the peoples who settled in Babylonian and Egyptian countries, nor of the sages of the non-Greek nations. The worldly and spiritual Babylonians of the country of Bodan are depicted in the pure Greek world. All the wealth was given to Pythagoras and Euclid, and the rest was related to historical truths. The same situation occurred in the history of the medieval period. The mathematical and scientific wealth of the developed Arab civilization was transmitted to the European world in dead Latin. Asian nations and rulers are not mentioned, with the exception of Al-Khorezmi. On the other hand, it is known that the names of European nations and scholars are widely used in the literature. This is a colonial approach to spiritual space. In this regard, we draw attention to the fact that this approach is still very popular and is gaining distribution. The article is devoted to the realistic approach to historical truths in the development of mathematics. In this direction, due attention is paid to the national pride of Al-Farabi's mathematical heritage. In the final part, the problem of inclusion of Farabi's heritage in the textbooks of national schools and measures to promote historical truths was raised. The article is intended primarily for teachers of general education schools. In addition, we believe that it will be useful for physics and mathematics specialists, students and schoolchildren.</p> Zh.A. Sartabanov A. Shaukenbaeva Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.011 MODELING OF NONRECIPROCATIVE DEVICES BASED ON ELASTIC METAMATERIALS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2264 <p>We consider a one-dimensional nonlinear periodic structure that supports the effect of nonreciprocity of elastic wave propagation. It is known that microstructured media have the ability to control wave propagation due to the internal microstructure. Elastic linear lattices consisting of point masses and elastic non-inertial ligaments exhibit dispersive and filtering properties, even if they are homogeneous. To exploit this advantage, it is important to understand the dynamic properties of the structure. The dispersion relation results for different models considered in this paper (monoatomic, diatomic systems with the same and different stiffness) show that the new nonlinear elastic periodic structure has obvious advantages over other types of periodic structures, including greater sensitivity to flexibility in band gap manipulation. The dynamic behavior of the elastic system is investigated analytically and compared with numerical solutions. The results for the dispersion relation model demonstrated obvious advantages related to the manipulation of elastic wave propagation. Based on the obtained results, the design of non-reciprocal device is introduced by including linear and non-linear circuits. The specific non-reciprocal effect for transmitted waves due to coupling effect is verified based on the theoretical concept supported by the calculation of two mutual works between applied forces.</p> B.K. Alimbaeva M.Zh. Sakypbekova L.A. Sagimbayeva G.G. Gaziz A.K. Moshkalov Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.001 MIXED-TYPE DIFFERENTIAL EQUATION WITH FRACTIONAL DERIVATIVE IN THE CAPUTO SENSE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2379 <p>The purpose of this paper is to study boundary value problems for a mixed-type differential equation with fractional derivatives in the sense of Caputo and to demonstrate the existence and uniqueness of its solution. Such equations, including fractional derivatives, have significant potential to describe various physical processes in which the effects of memory and heredity are evident, such as abnormal diffusion, heat transfer, and relaxation phenomena. The paper presents an analytical approach to solving the problem based on the method of separating variables by representing the solution as a Fourier series. As a result, the conditions for the uniqueness of the solution were established and strictly proved, which, if certain conditions are met, ensure the ambiguity of the task. Additionally, the uniform convergence of the obtained series of solutions is demonstrated under the specified conditions. The results obtained can be used in the theory of differential equations and further applied research.</p> A.E. Alpysbayeva M.B. Murzambetova A. Ryskan Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.002 ABOUT SOLUTIONS IN THE BROAD SENSE OF NONLINEAR SYSTEMS IN PARTIAL DERIVATIVES OF THE FIRST ORDER https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2086 <p>The article addresses the issues of existence and uniqueness of periodic solutions in some variables in the generalized sense for a nonlinear system of first-order partial differential equations. Mathematical models of physical and other processes are described using partial differential equations. The article provides definitions of solutions in the generalized sense for a nonlinear system of first-order partial differential equations, as well as the main properties of the differentiation operator. The method of characteristics and the method of contraction mappings are applied. The theorem on the existence and uniqueness of a periodic solution in some variables in the generalized sense for a nonlinear system of first-order partial differential equations is proven within a ball. The necessary and sufficient conditions for periodicity in some variables of the solution in the generalized sense are also proven.</p> A. Bekbauova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.003 MODELING THE PROCESS OF STEAM PRESSURE CONTROL IN A BOILER UNIT https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2190 <p>The paper investigates the processes of steam pressure regulation in a boiler unit in order to increase the efficiency and reliability of its operation. The main purpose of the study is to develop a mathematical model that allows to describe the dynamic processes in the system accurately and determine optimal parameters of the pressure regulator. The objectives of the research include development of a model of dynamic processes, analysis of existing control methods and selection of optimal parameters to minimize pressure deviations. The research methodology includes modeling the processes of setting up a PI-controller (Proportional integral controller) by engineering methods, comparative analysis and evaluation of the results obtained during the synthesis of ACS (Automatic control systems) with a PI controller. After setting up and evaluating the qualitative characteristics of the regulator in question, it was concluded that this regulator had an effect on the effectiveness of automatic pressure control system in the drum. Taking into account the obtained numerical values of the quality criteria, it can be concluded that the selected tuning coefficients and the structure of the PI regulator guarantee the necessary properties of the pressure control system and meet all the requirements for industrial regulators. These results are important for improving the efficiency of operation of thermal power plants and reducing their energy and operating costs, which is important for energy sector and automated control systems.</p> S. Bystrova B. Djuzbayeva T. Akishev A. Kydyrbayeva V. Cherdakov Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.004 INEQUALITY OF THE BEST ANGULAR APPROXIMATION https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2180 <p>This paper is devoted to the study of best approximation estimates for generalized Liouville–Weyl derivatives using angular approximation of functions in a multidimensional space. We consider generalized Liouville–Weyl derivatives, which are used instead of classical mixed Weyl derivatives. The concept of general monotone sequences plays an important role in the study. The paper consists of three sections. The first section contains basic definitions and a brief historical overview. The second section presents known statements necessary for proving the key results. In the third section, upper estimates for the best angular approximations of functions of several variables are obtained. The topic considered in this paper is related to the issues studied in the works of A.A. Konyushkov, Stechkin, Timan, M.K. Potapov, B. Simonov, S. Tikhonov.</p> A. Jumabayeva А. Zhetpisbayeva Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.005 SOME CONTROL CONDITIONS FOR QUASI-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH IMPULSE INFLUENCE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2265 <p>The study of edge control problems for quasilinear integro-differential systems with pulsed action is an urgent area of modern mathematics, which is used in modeling complex dynamic processes. The main goal of studying the controllability of quasilinear integro-differential equations with pulsed action is to develop methods that allow determining the conditions under which the system is controllable, to develop algorithms that allow you to build control actions to implement the desired trajectory of the system, and to investigate the stability of solutions under conditions of both regular and abrupt external changes. This article discusses some conditions of controllability of the boundary value problem for a qua zilinear system of integro-differential equations with pulsed action. Processes in which pulsed action does not occur at pre-prescribed time points, but in mo time points, which are determined by the state of the system, have been investigated. The article proved some conditions of controllability of quasilinear integro-differential equations with pulsed action in the form of lemmas, a definition of solvability of the control problem is given.</p> R. Seilova M. Talipova A. Turganbayev Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.006 BOUNDARY FUNCTIONS OF NIKOLSKY-BESOV SPACES WITH SMOOTH MIXED SMOOTHNESS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2296 <p>The embedding theory of spaces of differential functions of many variables studies important connections and relationships between smooth and metric properties of functions and has wide application in various branches of pure mathematics and its applications. Earlier, we obtained the embedding theorems of different metrics for Nikolsky-Besov spaces with dominant mixed smoothness and mixed smoothness and mixed metric, and anisotropic Lorentz spaces. In this work, we showed that the conditions for the parameters of spaces from the theorems are unimprovable. To do this, we built the extreme functions included in the spaces from the left sides of the embeddings and not included in the "slightly narrowed" spaces from the spaces in the right parts of the embeddings.</p> Y. Toleugazy K. Kervenev S. Iskakov Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.007 NUMERICAL STUDY OF THE THERMOELASTIC STATE OF THE ROD IN THE PRESENCE OF A HEAT FLUX SPECIFIED BY A QUADRATIC LAW https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2275 <p>This paper considers a computational algorithm for the thermoelastic state of a rod clamped at two ends in the presence of a heat flow on its side surface, varying along the coordinates by a quadratic law. The corresponding computational algorithms developed by the author make it possible to solve a class of engineering problems in determining the elongation of rods of limited length. The corresponding computational algorithms developed by the author make it possible to solve a class of engineering problems in determining the elongation of rods of limited length. Therefore, undoubtedly, the results of this work can be widely used in enterprises where calculations are carried out to determine the distribution laws of temperature fields and elongations of structural rod elements operating in a thermal field and in the presence of mechanical forces. The study of compression of a rod of limited length clamped at two ends under the influence of a temperature field and heat flow that varies along the length is of relevant interest for engineering and technological processes related to the strength of partially thermally insulated structural elements operating under coordinate-variable steady-state thermal fields. The relevance of these problems is also motivated by the fact that many structural elements operate under the simultaneous influence of axial force, coordinate-variable heat flow, heat exchange and thermal insulation. With the simultaneous consideration of the above factors, the analytical solution of steady-state thermoelastic compression and tension of rods becomes very complex. In this regard, there naturally arises the need to develop appropriate mathematical models of universal computational algorithms that make it possible to study the thermoelastic state of partially thermally insulated one-dimensional structural elements in the presence of heat exchange with the environment, a variable coordinate of the heat flow field and axial forces.</p> R. Tuleuova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.008 CREATION OF A PLATFORM FOR INFORMATION SECURITY RISK ANALYSIS AND MANAGEMENT https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2260 <p>This article is devoted to the development of a platform for the analysis and management of information security risks arising from the use of digital twin technology. The study examines the role and importance of digital twins in Industry 4.0, especially in areas such as manufacturing, energy, smart cities, and cyber-physical systems. The risks associated with information security and their causes will be identified, as well as ways to reduce them. Innovative methods such as predictive analysis, artificial intelligence, adaptive security systems, cryptographic technologies and blockchain are being discussed, which will enhance the security of digital twin platforms and ensure information security. These methods are important tools for improving the reliability of Gemini digital systems, and their integration contributes to improving the efficiency and security of the platforms. As a result, digital twins are used to improve the efficiency of system management by ensuring their security, optimizing business processes and opening up new opportunities. In addition, these methods ensure compliance with information security requirements and long-term stability of digital twin platforms.</p> S.A. Adilzhanova G.A. Abdulkarimova F.R. Gusmanova G.T. Zhubanysheva Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.012 IMPACT OF AI AND LSTM-BASED SCRIPTWRITING PLATFORMS ON BUSINESS-PROCESSES OPTIMIZATION OF CONTROL SYSTEMS IN FILM INDUSTRY https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2270 <p>The optimization of film production through global standards and advanced software remains underutilized in CIS countries due to regional specifics and language barriers. Consequently, inefficiencies in resource management, time allocation, and quality control persist. The film industry's rapid development has led to unstructured business processes that hinder optimization and standardization. This research aims to develop a business process management model utilizing artificial intelligence (AI) and recurrent neural networks (RNNs), particularly long short-term memory (LSTM) networks, to enhance scriptwriting automation. The proposed AI-driven platform facilitates script generation, empowering filmmakers by reducing dependency on experienced screenwriters. This paper presents practical solution for potential impact on filmmaking efficiency</p> A. Aidarbekov A. Ibraiymov G. Murzabekova A. Aidarbekova N. Satybaldy Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.013 АDEVELOPMENT OF A MOBILE APPLICATION FOR DELIVERY IN RURAL REGIONS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2205 <p>The development of a mobile delivery application for rural regions is an urgent topic not only at the current time. This topic has always been relevant and important, because the IT infrastructure in rural regions has always been underdeveloped, compared with megacities and cities. The aim of this project is to improve digital technologies in rural areas for residents so that they have the opportunity to improve their living conditions and have access to more advanced technology. Our article reveals the main problems and achievements in the field of digital technology development in rural regions, using the analysis of academic literature, open sources, technical and practical factors. Our project will help simplify various digital factors, such as the development of your product among local residents, the way from one point to another point, without leaving home to order the right things from another point in the city, find and offer services, and so on. Also, the project is very promising in terms of digitalization and further development. Because our task is not only to collect and analyze large amounts of data, but also to automate routine tasks. Despite significant progress every year, the results of the analysis show that there are significant gaps in digitalization in rural regions, especially compared to large cities that have great access to digital technology. Our project helps to solve this problem, at least partially, so that rural regions have the opportunity to improve digitalization and simplify work processes.</p> A.K. Aitim A.E. Toleukhan Sh.R. Chshir Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.014 GEOINFORMATION SYSTEM FOR THE ANALYSIS AND VISUALIZATION OF GEOSPATIAL DATA IN THE REGIONS OF WESTERN KAZAKHSTAN https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2188 <p>The research is devoted to the development of a geoinformation portal for a comprehensive analysis of the environmental, economic and social situation in Western Kazakhstan. The aim of the work was to create a tool to assess the impact of climate change on the state of water resources and biodiversity in the region. Meteorological data, soil data and socio-economic indicators were used as input data. The developed portal allows for spatial and temporal data analysis, visualization of results in the form of maps, graphs and diagrams. The system is based on Python/Django, PostgreSQL and OpenStreetMap technologies. The portal provides an opportunity to assess the dynamics of vegetation cover changes, analyze the relationship between climatic factors and the state of ecosystems. The developed tool can be used to make informed decisions in the field of environmental management and environmental protection in Western Kazakhstan.</p> <p>&nbsp;</p> Zh. Buribaev Z. Abdirazak A. Yerkos M. Zhassuzak P. Omarova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.015 USING MACHINE LEARNING ALGORITHMS IN CREDIT RISK ASSESSMENT https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2167 <p>This article analyzes current issues in bank credit risk assessment and focuses on the scoring model created using data analysis methods to assess borrower creditworthiness. Credit scoring is chosen as an example to illustrate the data processing process. Credit risk assessment has become an important tool for financial institutions to distinguish between customers who can or cannot repay their loans. This is why machine learning algorithms are successfully used in credit scoring. Credit risk mitigation is an area of ​​growing interest since the financial crisis, with financial institutions collecting large amounts of data. Therefore, risk analysts are faced with the difficult task of processing large amounts of data and adequately determining individual creditworthiness. Financial institutions can use advanced machine learning techniques to develop highly efficient credit scoring models. This paper uses machine learning classification techniques for benchmarking. The results show that regression is the initial best guess, followed by the random forest model. The widely used logit model performed better than vector machines. We also show that other machine learning methods outperform the widely used logit model in terms of classification ability using the Kolmogorov-Smirnov test.</p> D.K. Darkenbayev N.O. Mekebayev Copyright (c) 2024 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.016 APPLICATION OF SWARA AND DNMA METHODS IN RECRUITING SOFTWARE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2148 <p>Personnel selection is a complex, multi-criteria decision-making problem that involves both qualitative and quantitative factors. Despite various techniques being proposed across different industries, a robust method that adequately addresses uncertainty remains needed. This study introduces an integrated approach, combining the Step-wise Weight Assessment Ratio Analysis (SWARA) and the Double Normalization-Based Multiple Aggregation (DNMA) methods. The proposed framework first employs the SWARA method to determine the importance of criteria, followed by the application of the DNMA method to rank candidates based on a sequential evaluation process.</p> <p>The goal of the study is to select the most suitable candidate from five applicants for a vacant position in a company within the participatory software sector. The criteria weights were primarily determined by the decision-maker using the SWARA method, with computer and software skills, work experience, teamwork adaptability, foreign language proficiency, and problem-solving skills identified as the five key criteria. The DNMA method was then used to assess the candidates' performance, and the results indicated that one of the candidates was the best fit for the position.</p> <p>When compared with similar studies in the literature, it was found that while many multi-criteria decision-making methods have been employed, the combination of SWARA and DNMA methods is novel. This study demonstrates the effectiveness of these methods in personnel selection, offering a new approach to the literature on decision-making processes.</p> G.N. Kazbekova N.M. Zhunissov A.N. Amanov A.A. Abibullayeva A.B. Aben Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.017 DEVELOPMENT OF A METHOD FOR GRAPHICAL DESTRUCTIVE CONTENT ANALYSIS https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2269 <p>Social media platforms play an important role in facilitating the spread of extremism by influencing people's views, opinions and perceptions. These platforms are increasingly being used by extremist elements to spread propaganda, radicalize and recruit youth. Therefore, research on identifying extremism on social media platforms is necessary to prevent its impact and negative consequences. A comprehensive and comparative study of datasets, classification methods, and screening methods using an online extremism detection tool is essential.</p> <p>The purpose of this research is to create a system for identifying ISIS and Al-Qaeda flags from images. Dataset augmentation and training were performed using image augmentation using CNN deep learning networks.&nbsp; A solution has been found to increase the size of the dataset. The complete dataset contains 1,400 images, half of which are the Al-Qaeda flag and half are the ISIS flag. Additionally, 2 convolutional and one fully connected layer were used to recognize ISIS and Al-Qaeda flags. A method for recognizing ISIS and Al-Qaeda flags was proposed.</p> <p>As the relevance of the work, it should be noted that the CNN convolutional network model was trained using deep learning, that is, based on neural networks. The novelty of the work is that the model obtains the highest value of the accuracy indicator using the new data set using the classification method.</p> <p>The study is devoted to the study and application of machine learning methods aimed at solving the problems of identifying potentially dangerous information on the Internet.</p> Sh. Mussiraliyeva M. Bolatbek Sh. Temirgaziyeva Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.018 PREREQUISITES FOR CREATING AN ADAPTIVE LEARNING PLATFORM BASED ON ARTIFICIAL INTELLIGENCE https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2357 <p>This article discusses the prerequisites for the need for an adaptive learning platform based on artificial intelligence. The purpose of the article is to substantiate the need to develop an adaptive learning platform based on AI for comprehensive schools by analyzing existing educational platforms. The study used observation, interviewing and document analysis methods. The results of the study showed that the process of improving the platform requires close interaction between experts in the field of technology, education and user experience design. Users - teachers and students - noted the overall positive effect of using existing platforms. The study also found that adaptive platforms contribute to increased motivation, activity and learning outcomes of students, which indicates the need for their further improvement. However, to improve adaptive learning platforms, it is necessary to create a database, develop AI algorithms, and ensure data security. More research and applications are also needed to support learner development.</p> <p>Keywords: adaptive learning, personalized learning, artificial intelligence, educational platforms, digitalization.</p> N. Ogan D.N. Issabayeva S.N. Issabayeva J. Caiko Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.029 INTRUSION DETECTION USING MINI-VGGNET-BASED CONVOLUTIONAL NEURAL NETWORK AND FEATURE REDUCTION https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2152 <p>In the context of the rapid growth of cyber threats and an increase in the volume of network traffic, the detection and prevention of network intrusions are becoming urgent tasks to ensure cybersecurity. The purpose of this study is to develop an effective Mini-VGGNet model for detecting anomalies in unbalanced network traffic. The study also aims to analyze time dependencies in the data, which allows for more accurate identification of potential threats. The work uses a deep learning methodology based on the Mini-VGGNet architecture, which includes convolution layers and pooling layers to extract features from network data. To improve detection efficiency, data preprocessing methods are used, including removing unnecessary values and normalization, which improves the quality of model training. The model is trained on a dataset containing various types of network attacks, which allows you to identify anomalies in real time and adapt to changes in network traffic. As a result of the conducted research, high accuracy in detecting network intrusions has been achieved, which confirms the effectiveness of the proposed model. The results show that the Mini-VGGNet model is significantly superior to traditional methods in terms of speed and accuracy of anomaly detection. The significance of the work lies in its contribution to the development of cyber defense methods and improving the security of information systems, which is critically important in the context of constantly changing cyber threats. The results can be used for further research in the field of cybersecurity and the development of more advanced models for detecting network attacks.</p> Bauyrzhan Omarov A. Serdaly A. Ydyrys Батырхан Омаров Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.019 TANBA-SPHINCS+ - POST-QUANTUM CRYPTOGRAPHIC HASH-BASED DIGITAL SIGNATURE ALGORITHM https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2257 <p>The paper considers the TANBA-SPHINCS<sup>+</sup> digital signature algorithm, which is a modification of the SPHINCS<sup>+</sup> post-quantum hash-based scheme. The algorithm uses the TANBA cryptographic hash function developed on the basis of a modified Sponge scheme, where instead of one internal function, many internal functions with a pseudo-random choice of their sequence are used. This approach provides increased resistance to cryptanalytic attacks and adaptability to various security and performance requirements. TANBA-SPHINCS<sup>+</sup> retains the key properties of SPHINCS<sup>+</sup>, including resistance to quantum attacks and independence from complex cryptographic assumptions. The new scheme opens up additional opportunities for building reliable post-quantum digital signature systems.</p> R.M. Ospanov Ye.N. Seitkulov B.B. Yergaliyeva K.A. Utebayev S.K. Atanov Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-04-01 2025-04-01 89 1 10.51889/2959-5894.2025.89.1.020 DEVELOPMENT OF AN AUTOMATED CONTAINERIZED MODEL USING BLOCKCHAIN TECHNOLOGY IN THE EDUCATION SYSTEM https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2292 <p>The relevance of the study is determined by the implementation of automated containerized models based on blockchain technologies, which open up new directions for the transformation of the education system. Blockchain technologies contribute to increasing transparency, security, and efficiency in managing educational processes. Currently, digital technologies are rapidly integrating into the education system, transforming traditional teaching and management methods. In this regard, one of the most promising directions is the development and implementation of automated containerized models using blockchain technologies. This approach ensures a high level of transparency, security, and efficiency in the educational environment, while also establishing a foundation for adapting to the challenges of digital transformation.</p> <p>The aim of the study is to conduct a comprehensive analysis and develop the fundamental principles for creating an automated containerized model in the education system using blockchain technologies. To achieve this goal, a specialized educational platform is being developed. The main significance of the platform lies in the creation of an electronic database, the effective use of distance learning technologies, and the implementation of decentralized monitoring to optimize network interaction.</p> <p>The research results have made it possible to define the objectives, tasks, and key principles for developing an information system aimed at automating and optimizing the learning process. This paper examines the advantages of implementing blockchain technologies in higher education and proposes methods for their application to enhance transparency and operational efficiency in educational institutions.</p> <p>The scientific novelty of the study lies in the development of informational tools to support educational activities, improve their efficiency, and integrate traditional methods with new digital technologies. Based on the analysis of the results, the goals and directions for integrating blockchain technologies into the development of the educational platform have been identified. Furthermore, combining blockchain with gamification, big data processing, and artificial intelligence enhances student and teacher motivation, optimizes the learning process, and creates opportunities for personalized development and academic achievement</p> G. Sabyrkhanova O. Sembiyev B. Esmagambetov Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.021 COMPARATIVE STUDY OF MACHINE LEARNING ALGORITHMS FOR PHISHING SITE DETECTION https://bulletin-phmath.kaznpu.kz/index.php/ped/article/view/2294 <p>Phishing attacks on websites are a type of cyberattack in which attackers create fraudulent websites that imitate legitimate platforms such as social media in order to deceive unsuspecting users and disclose confidential information. This includes passwords, credit card data, user ID, and other personal data. These phishing websites look real and often use various methods such as URL swapping, social engineering, and email or text phishing to attract victims to reveal their sensitive information. Web applications are becoming more and more complex and difficult to detect at first glance, especially when using encryption and obfuscation methods. Machine learning needs to be developed to effectively detect and prevent phishing web applications from being uploaded to the server in real time. In addition to analyzing machine learning algorithms to detect attacks based on web applications, the study calibrates new analyses by executing machine learning algorithms and validating the results. The study uses unique and categorized results from machine learning data sets. According to the results obtained from the experimental and comparative analysis of the classification algorithms used, the random forest model showed the highest accuracy, with an impressive 97%, followed by the decision tree model of 94% and extreme gradient amplification (XGBoost).</p> D.A. Sultanova Copyright (c) 2025 Bulletin of Abai KazNPU. Series of Physical and mathematical sciences 2025-03-27 2025-03-27 89 1 10.51889/2959-5894.2025.89.1.022