Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences

ABOUT TEACHING COMMON FRACTIONS IN MIDDLE SCHOOL IN THE CONTEXT OF EDUCATION DIGITALIZATION

2025-06-18T02:15:59+06:00

This article provides a comprehensive analysis of school curricula and textbooks on teaching ordinary fractions in middle school. Fractions are an important topic that forms the foundation for further mathematical study; however, students often encounter difficulties in mastering it. The use of the numerical axis and the features of the representation of fractions in various educational materials, including normative documents and additional literature aimed at teachers and students, are considered. Special attention is paid to the methods of introducing the concepts of fractions, unit segments and their representation on the numerical axis. The main difficulties faced by students in mastering this topic, as well as limitations in the presentation of material in existing textbooks, are revealed. The article also examines the theoretical foundations of teaching fractions in the context of digitalization, as well as its role in improving the quality of their acquisition in primary school. In conclusion, recommendations are offered to improve teaching methods and representation of fractions on the numerical axis, which contributes to the development of mathematical thinking in schoolchildren with the use of digital tools.

HISTORICAL REVIEW OF THE STATUS OF MATHEMATICS EDUCATION IN KAZAKHSTAN BEFORE THE OCT REVOLUTION

2025-09-03T03:16:09+06:00

This article examines the historical development of mathematical education in Kazakhstan prior to the October Revolution of 1917. The study analyzes the characteristics of arithmetic instruction in Muslim schools, as well as the methods of teaching mathematics in Russian-Kazakh and Russian-native schools. Additionally, the pedagogical transformations of the second half of the 19th century and the role of mathematics textbooks are described. The research methods include historical-comparative analysis, systematization of pedagogical data, and examination of archival documents. The development of mathematical education in pre-revolutionary Kazakhstan was complex and multifaceted, shaped by the influence of diverse educational systems. This study provides insight into the continuity of mathematical education in Kazakhstan and identifies the factors that influenced its evolution.

DEVELOPMENT OF STUDENTS' RESEARCH COMPETENCIES WHEN STUDYING ANALYTICAL AND PROJECTIVE GEOMETRY

2025-09-03T16:28:41+06:00

The article discusses the methods of developing research skills among future teachers of mathematics and physics in the process of studying analytical and projective geometry at the university using interactive learning tools. Let us note that research competencies are a component of the professional competencies of bachelors in the areas of training “Mathematics” and “Mathematics and Physics”. Therefore, in the course of the study, we developed and tested the educational and methodological complex “Analytical and Projective Geometry” using interactive programs, and also proposed methods, forms and criteria for assessing the research abilities of future mathematics and physics teachers. Methods of problem-based learning, practice-oriented learning, methods of analysis and synthesis, and observation methods were used. The relevance of the research topic lies in the problem of developing the research skills of future mathematics and physics teachers, and their use of such interactive programs as living geometry and geogeography can be used by them to create a research lesson. The methodological approach to teaching analytical and projective geometry presented in the article was implemented in the educational process in the course of “Analytical and projective geometry” in Pavlodar Pedagogical University named after A.Margulan during training of future bachelors of “Mathematics”, “Mathematics and Physics” and allowed to achieve positive results in teaching.

IMPROVING THE TEACHING OF INTEGRAL CALCULUS USING THE MAPLE COMPUTER MATHEMATICS SYSTEM

2025-06-23T01:41:50+06:00

This article discusses the features of using the Maple program for studying integral calculus. For students pursuing higher education in the field of science education, it is very important to have a high level of mathematical knowledge. However, the level of mathematical preparation among students entering educational programs in this field is not always sufficient. One effective strategy to bridge this gap is to improve teaching methods in mathematics education. This study presents a new methodology for teaching integral calculus using the Maple computer mathematics system, aimed at expanding students’ mathematical knowledge and improving their understanding of problem-solving techniques among second-year students of the educational program 6B05449 – Mathematics. The effectiveness of integrating the Maple computer mathematics system into practical calculus lessons has been confirmed by the results of the study.

APPLICATION OF COGNITIVE LOAD THEORY TO TEACHING SCHOOLCHILDREN MATHEMATICS

2025-09-02T01:32:05+06:00

Many schoolchildren experience significant difficulties in teaching mathematics. The search for ways to solve this problem has actualized the appeal to the theory of cognitive load, which relates to the field of educational psychology and educational design. The purpose of this study is the theoretical substantiation, development and testing of methods aimed at reducing the cognitive load of schoolchildren when teaching mathematics. The implementation of the designated goal was carried out on the basis of the analysis of scientific literature, synthesis of the information obtained, study and generalization of pedagogical experience, a pedagogical experiment, the results of which were processed using the Mann-Whitney U-criterion. The study revealed the features of how the effects of cognitive load can be taken into account in the methods and techniques of teaching mathematics to schoolchildren. A method of proven geometric construction has been developed, which, along with other methods and techniques aimed at reducing the cognitive load of students, was tested when teaching geometry to schoolchildren in the 8th grade. The results of the pedagogical experiment indicate a positive impact of the introduction of ideas of the theory of cognitive load on the educational results of students. In conclusion, based on the completed study, methodological recommendations are proposed.

MODERN APPROACHES TO TEACHING MATHEMATICS USING SMART TECHNOLOGIES

2025-09-07T01:53:03+06:00

The article examines the use of smart technologies in teaching mathematical disciplines in higher education institutions, which have become one of the main allies of teachers in pedagogical innovation. The main purpose of this article is to determine the impact of smart technologies on the perception of educational material in teaching mathematics at the university. For this purpose, the advantages of introducing interactive, multimedia and smart technologies into the educational process are analyzed. The literature review describes examples of smart technology applications such as interactive whiteboards, mobile applications, online simulators, and virtual labs. It is shown how these technologies contribute to increasing students' motivation and engagement, as well as improving their academic performance in mathematical disciplines. To determine the impact of smart technologies on the perception of educational material in mathematical disciplines, a questionnaire was developed. The questionnaire was tested on 80 students. The processing and analysis of the research data was carried out in the R programming environment. The data obtained showed significant differences in the use of smart technologies by teachers in the process of teaching mathematics between the online platforms Moodle, Canvas and other technologies. The use of interactive smart boards, online resources and educational platforms stood out among other technologies with the highest level of effective use. As a role of smart technologies in class preparation, students associate their presentation with visualization, which facilitates learning, helps visualize problems and mathematical concepts.

THE EVOLUTION OF EFFECTIVE USE OF DIGITAL GAMES IN EDUCATION

2025-09-04T20:35:48+06:00

The article analyzes the rate of use of digital games in the educational process over the past decades. The evolution of the use of digital games in education includes several key stages: from the first educational games created in the 1960s to modern interactive platforms using virtual and augmented reality technologies. The use of digital games in education is characterized by a variety of formats and approaches. Games are used to teach traditional subjects, as well as to develop critical thinking, teamwork and other key skills of the 21st century. An important aspect is also the use of data analysis to monitor student performance and adapt educational content to their individual needs. Thus, the use of digital technologies in education demonstrates significant potential for transforming the learning process, which will help to increase the accessibility, interest and effectiveness of education. In the future, rapid development of technologies and teaching methods is expected, which, in turn, will allow for a deeper integration of games into the educational process. The relevance of the study lies in studying the rate of use of digital games in education. To analyze the research of foreign and domestic researchers devoted to the experience of using games in education in various fields, and to improve the methodology of the appropriate use of games in the educational process based on the study of the advantages of using gaming platforms.

A MODEL FOR TEACHING INFORMATICS TO PRIMARY SCHOOL STUDENTS BASED ON ELECTRONIC HIERARCHICAL STRUCTURES

2025-06-04T23:59:11+06:00

This article shows that the digitalization of education requires a systematic approach to organizing the content of the informatics course in primary school. The relevance of the study lies in the need to develop a pedagogically grounded teaching model based on electronic hierarchical structures. The purpose of the research is to design an original instructional model that provides structured, adaptive, and visual delivery of content, taking into account the cognitive characteristics of younger learners. The study utilized methods of analyzing national and international experiences in teaching informatics, comparing the conceptual framework of V.V. Grinshkun’s model with Bloom’s taxonomy levels, as well as techniques of computer modeling and computational experimentation. As a result, an original three-level teaching model was proposed and implemented in a new information integrator. The validation of the model based on Bloom’s taxonomy and the findings from the computational experiment confirmed the cognitive coherence, pedagogical soundness, and high adaptability of the developed structure. The study substantiates the effectiveness of applying electronic hierarchical structures to optimize informatics education in primary school. Future prospects include the development of the model into an adaptive learning system using digital platforms and artificial intelligence.

THE IMPACT OF INTERDISCIPLINARITY ON THE DEVELOPMENT OF STEM SKILLS AMONG FUTURE TEACHERS

2025-09-09T22:54:54+06:00

This study examines the impact of interdisciplinary connections on the development of future teachers’ educational and methodological skills. The research analyzes the effectiveness of interdisciplinary links in enhancing methodological competence and identifies creative and innovative teaching approaches through subject integration. In addition, it demonstrates how interdisciplinary teaching contributes to improving subject competence, enhancing methods of working with students, and enabling the effective organization of the learning process by combining theory and practice through integrative approaches. Future teachers acquire skills in applying interdisciplinary connections through the use of STEM technologies and develop experience in integrating various disciplines. This strengthens their methodological competence and provides opportunities to implement modern technologies and innovative methods in teaching. The study was conducted among 3rd- and 4th-year students of physics and informatics education programs, with the results of surveys and interviews analyzed. The findings revealed that the level of understanding of the significance of STEM among future teachers varies.

MODEL OF INTELLIGENT FORECASTING OF ACADEMIC PERFORMANCE AND CAREER TRAJECTORY OF STUDENTS OF THE IT SPECIALTY

2025-09-09T14:01:03+06:00

In the context of the rapid development of digital educational technologies and the introduction of modular programs in higher education institutions, there is a growing need for intelligent systems capable of performing in-depth analysis of academic data and generating predictive models aimed at improving students' academic performance and career support. This study is designed to develop an intelligent model based on the factor analysis method for predicting the academic performance and career trajectory of students studying in the IT specialty. The model uses grades in the main subjects of modular educational programs as input data. Principal component analysis (PCA) was used to identify a latent factor structure, which is interpreted as two dominant components: "Theoretical preparation" and "Practical preparation". The obtained factor scores are used as features in a logistic regression model, which shows high accuracy in classifying career outcomes (ROC-AUC ≈ 0.95). This allows not only to perform binary predictions (success/failure), but also to quantitatively assess the contribution of educational modules to a student's career trajectory. The results of the study confirm the potential of the proposed model as an educational analysis tool capable of identifying hidden dependencies in academic data, profiling students according to their developmental trajectories, and providing interpretable recommendations to teachers and curriculum coordinators. The proposed approach can be scaled and integrated into learning management systems (LMS), digital career guidance platforms, and student competency support systems.

RESEARCH OF MOTIVATION FACTORS OF PARTICIPANTS IN INFORMAL EDUCATIONAL PROGRAMS IN THE FIELD OF ICT

2025-09-09T21:23:37+06:00

In this article, the motivational factors of the participants of non-formal education programs in the field of information and communication technologies are presented. The main tasks include identifying the features of motivation in non-formal education, especially in the field of information and communication technologies, classification of motivational internal and external factors, analysis of the influence of personal qualities on the choice of non-formal education in the field and development of recommendations for educational organizations to increase student motivation. The research methodology is based on conducting a survey of first- and second-year students using questionnaires through the students' personal offices and subsequent analysis of the answers to the questions. As part of the survey, a special questionnaire was developed with questions, including closed and open questions. As a result of conducting an online survey among the participants, motivational factors and personal qualities were revealed, which contribute to increasing the effectiveness of non-formal education programs in the field of information and communication technologies. The obtained data indicate interest in non-formal education and the prospects of non-formal education programs to improve the quality of education in the field of information and communication technologies.

INTEGRATION OF INTERNET OF THINGS TECHNOLOGIES INTO EDUCATION AND PROSPECTS OF THEIR APPLICATION IN KAZAKHSTAN

2025-09-11T18:13:54+06:00

In modern education, the Internet of Things (IoT) technologies are considered a promising tool for creating adaptive and intelligent learning environments. However, current research in this field mainly focuses on the development of smart classrooms, automated attendance control, and campus security. Most studies emphasize technical aspects or limited implementation cases, which do not provide a comprehensive understanding of IoT’s potential in education. The aim of the article is to examine the experience of integrating IoT technologies into educational processes in different countries, analyze successful practices and approaches, and identify the potential of IoT for improving the quality of education. The study includes a comparative analysis of international practices as well as a survey conducted among lecturers and students of Abai Kazakh National Pedagogical University. Based on the collected data, practical recommendations for the creation of intelligent learning spaces are proposed, including automation, monitoring, and personalized learning.

EXPERIMENTAL STUDY ON THE EFFECTIVENESS OF ADAPTIVE PROGRAMMING INSTRUCTION FOR FUTURE INFORMATICS TEACHERS

2025-06-21T10:59:00+06:00

This article addresses the organization of adaptive learning in the context of a digital educational environment at a higher educational institution. It presents the VARK learning style model by N. Fleming, which is based on individual psychological characteristics of cognitive structures and predispositions toward different methods of interaction with educational content. The methodology of J. Bruner is also explored, supporting the differentiation of learning according to the primary type of thinking and defining an individual approach to the analytical-synthetic processing of educational information. Based on these theories, a model of adaptive education in programming for students in the «Informatics» field was developed and implemented. As part of the implementation, digital educational modules were created and integrated into the Knan Academy platform. During the experimental trial, students participated in courses where the content was adapted to their cognitive styles, resulting in a 15% average increase in academic performance and improved comprehension of complex topics, such as working with algorithms and data structures. The results of the study demonstrate that the proposed model enhances the quality of the educational process and deepens students' mastery of programming while effectively adapting learning to individual needs. The significance of the study lies in providing a theoretical and practical foundation for the use of digital technologies as a tool for adaptive learning, contributing to the development of the scientific and educational environment in the context of digital education

EXPERIENCE OF INTEGRATING STEM ELEMENTS INTO EDUCATIONAL PROGRAMS

2025-09-04T10:15:02+06:00

This study focuses on analyzing the content and structure of the “Atomic Physics” course in higher education institutions of the Republic of Kazakhstan. Based on university curricula and official documents, a content, statistical, factor, and comparative analysis was conducted. The results revealed significant differences in the way the course is taught across universities, particularly in terms of credit allocation, semester workload, the ratio of lectures, practical and laboratory sessions, as well as in the qualifications of teaching staff and academic opportunities. A survey involving 93 students demonstrated that the structural efficiency of the course, material and technical resources, teachers’ methodological competence, and financial accessibility were evaluated positively (mean values ranged between 4.2–4.4, Cronbach’s alpha coefficient between 0.906–0.944). These findings indicate that, while students generally support the program, there is a clear need for further improvement. In the experimental section, the STEM approach was considered as an effective tool for linking the course content with practice. It was found that the integration of STEM enhances students’ deeper understanding of the discipline, develops their research and project skills, fosters engineering thinking, and strengthens digital technology competencies. In conclusion, the modernization of the “Atomic Physics” course through STEM integration contributes to improving the professional competence of future physics teachers, enhancing the quality of national education, and aligning the educational system with international standards.

THE NEED TO TRAIN FUTURE COMPUTER SCIENCE TEACHERS TO TEACH INFORMATION PROCESSES IN THE CONTEXT OF DIGITALIZATION OF EDUCATION

2025-06-26T07:59:04+06:00

This article highlights the need to prepare future computer science teachers for teaching information and information processes in the context of education digitalization. Particular attention is given to the importance of improving the quality of teacher training under digital transformation. A review of relevant scientific works and literature is provided, outlining the main directions of training future computer science teachers. The paper analyzes the issues of teaching information and information processes within the school informatics curriculum, emphasizing the central role of information representation and measurement in general education. Furthermore, recommendations are proposed for integrating information processes into computer science instruction in digital learning environments. Methodological guidelines are also suggested to help future teachers foster students’ self-directed learning.

QUASI-OPTIMAL CONTROL OF ONE CLASS OF SYSTEMS WITH DISTRIBUTED PARAMETERS

2025-09-08T23:11:18+06:00

The concept of absolute stability is one of the important phenomena in the study of various processes in reality. Absolute stability of systems with distributed parameters means stable operation of the system under any admissible nonlinearities, which makes it important for practical application. As a consequence, there is a need to study such research methods that would ensure stability in a certain range of changes in the system parameters. Absolute stability of a hybrid system described by hyperbolic partial differential equations can be obtained in the form of a frequency inequality. Since checking the frequency condition in the space of system parameters is a rather complex task, then for its solution it is possible to make a transition from the frequency condition to an algebraic criterion of absolute stability based on the Sturm method applied to quasi-polynomials. This article considers a hybrid system described by hyperbolic partial differential equations. Absolute stability of such a system can be obtained in the form of a frequency inequality, according to the frequency criterion of the V.M. Popov type. But checking the frequency condition in the space of system parameters is a rather complex task. In this regard, the proposed work makes a transition from the frequency condition to the algebraic criterion of absolute stability

ON THE SEPARATION OF A SINGLE OPERATOR IN THE SPACE 〖 L〗_p (R)

2025-09-19T11:36:11+06:00

Most of the physical laws of nature can be formulated in the language of simple and independent derived equations. Examples are the Sturm-Liouville, Navier-Stokes, and Schrodinger equations in quantum mechanics. In all these equations, physical phenomena are described in the language of derivatives of space and time. The presence of derivatives in equations describes important physical quantities. These are speed, acceleration, force, friction, flow, current, and so on. Among the problems posed for differential equations, a class of logically posed problems is of particular importance, which have a solution, are the only ones that are smooth and continuously depend on the initial conditions of the problem. The purpose of this article is to determine sufficient conditions for the existence of a solution to the Sturm-Liouville equation with a weighty coefficient and smoothness of the solution. In the course of achieving the goal, the given differential equation was studied by the method of operators in a functional space. The problem was considered in a Banach space, and the properties of functional spaces were used. It is known that many questions of quantum mechanics are reduced to problems in which the emission of electromagnetic waves in a Hilbert space is determined in the special case by the presence of inverse operators of singular differential operators and separability. One of these operators is the Sturm-Liouville operator with weight at the highest derivative. In this paper, the named operator is investigated by the methods of functional analysis. Sufficient conditions for the existence of a solution and separability of an operator in a Banach space are found.

PROPERTIES OF CATEGORICITY FOR KAISER CLASS

2025-09-05T13:32:33+06:00

In this article we present concrete results on both the countable and uncountable categoricity of some fragments. Our research on the categoricity of these fragments is conducted within the extended framework of normal Jonsson theory. The fragments are derived through the application of the closure operator of a specified pregeometry, and the involved sets are regular. The resulting models in this context constitute the Kaiser class associated with a studied Jonsson theory. These models exhibit distinct and interesting structural properties, making them a subject of extensive study. Furthermore, we analyze how variations in the underlying pregeometry influence the classification of fragments. Such an approach makes it possible to identify broader and deeper connections between categoricity and model-theoretic stability, thereby significantly expanding and refining the understanding of their interrelation in the context of contemporary fundamental scientific research.

NUMERICAL MODELING OF THE SPREAD OF HARMFUL POLLUTANTS IN THE ATMOSPHERE

2025-09-05T12:13:19+06:00

The article considers the equation of transport and diffusion for mathematical modeling of the process of distribution of harmful impurities in the atmosphere. The paper explores an explicit difference scheme for the transfer and diffusion equation, as well as the architecture of physically informed neural networks (PINNS), their principle of operation and application to solving the transfer and diffusion equation. In the course of a practical study, the wind direction was studied in various conditions and their different effects on the distribution of the mixture were discussed. The dynamics of the distribution of pollutants in the urban area in accordance with the north-west and north-east winds observed in the city of Ust-Kamenogorsk is shown. As a result of the study, graphs of numerical solutions to the problem were shown, patterns of the distribution of harmful impurities in the atmosphere were determined, making sure that the direction and speed of the wind have a direct effect on the distribution of harmful substances in the atmosphere.

HYBRID SNTHERM-MACHINE LEARNING APPROACH TO SNOWPACK AND MELT MODELING IN EAST KAZAKHSTAN

2025-07-01T15:16:58+06:00

This study presents the integration of the physically based SNTHERM model with machine learning methods to simulate and analyze the seasonal dynamics of the snowpack in the foothill zone of East Kazakhstan. The modeling framework was applied to the case of the Shemonaikha meteorological station, located in a flood-prone area with a sharply continental climate. Meteorological forcing was provided by hourly ERA5-Land reanalysis data, enabling high-resolution simulation of snow accumulation, metamorphism, and melt processes throughout the 2022–2023 winter season. The model outputs-including snow water equivalent (SWE), snow depth, and temperature profiles-were interpolated to daily resolution and analyzed to extract key snow cycle indicators. These included the date of maximum SWE, the onset of sustained melt under positive air temperatures, and the timing of snowpack disappearance. Time series analysis and machine learning techniques were used to identify and quantify melt phase characteristics. Results demonstrate that the SNTHERM model, when combined with data-driven analysis, effectively captures the snowpack evolution at Shemonaikha and offers a promising approach for snowmelt modeling and hydrological risk assessment in similar continental environments.

SYSTEMS FOR COMPARING MATRICES IN THE STABILITY OF SOFTWARE MONIFOLD

2025-09-02T01:25:45+06:00

The results of the research conducted within the framework of the grant project MSHE RK AP23488811 are presented. The article examines the stability of program manifold within the main control system. To investigate the stability properties of the control system, a comparison system has been constructed. A Lyapunov function is formulated for both autonomous and non-autonomous systems. Sufficient conditions for the absolute and asymptotic stability of the program manifold are derived with respect to a function defined by the Lyapunov function. The spatial positioning of auxiliary cartographic systems is based on their representation within a given system space. These methods address various theoretical and applied problems and are also widely used for studying the dynamic properties of multi-image representations in space. Differential equations are employed to analyze comparison systems. The reduction of the order of the considered system of equations demonstrates the principal advantage of the comparison method. The stability of diverse program manifold components within automatic control systems is investigated. From the matrix comparison equations, sufficient conditions for the stability of program manifolds are obtained. Sufficient conditions for the stability of the program manifold are derived from the matrix comparison equations. Sufficient conditions for the stability of the program manifold are derived from the matrix comparison equations.

ASSESSMENT OF FISH POPULATION DYNAMICS IN LAKE ZAISAN USING A COHORT APPROACH BASED ON RESEARCH AND COMMERCIAL CATCH DATA

2025-09-05T12:07:58+06:00

This paper proposes a new approach for estimating changes in the abundance and biomass of fish populations in water reservoirs based on sample data from research and commercial fishing. The developed approach takes into account the age structure and dynamics of changes by cohort, without requiring additional information on absolute fish abundance. To reduce the influence of fluctuations and uncontrolled factors, pre-processing of the data using third-degree polynomial regression is used. A mechanism for conditionally accounting for sex composition in biomass calculations is also implemented, allowing for increased estimation accuracy. The presented formulas provide a flexible and adaptive analysis method suitable for conditions with limited or incomplete data. The new assessment approach provides reproducible and comparable results, enabling monitoring of population status and tracking trends in the abundance and biomass of fish resources. The proposed mathematical model is an alternative cohort method for estimating fish populations and their biomass, which should be considered in conjunction with other approaches to stock assessment and applied jointly to management decision-making in fisheries.

DEVELOPMENT OF METHODOLOGICAL APPROACHES AND TOOLS FOR THE MANAGEMENT OF MEDICAL WASTE USING INTERNET OF THINGS TECHNOLOGIES

2025-06-11T09:55:11+06:00

The article discusses the issues of developing methodological foundations and mechanisms for collecting, structuring and analyzing data for medical waste management. This article discusses the use of Internet of Things (IoT) technologies to optimize the collection, transportation, and disposal of medical waste. Methods of modeling business processes using intelligent sensors are proposed. The methods of designing databases that ensure reliable storage, systematization and analysis of information on the types, volumes and routes of movement of medical waste are described. The developed model makes it possible to increase the efficiency of waste management, minimize environmental risks and reduce logistics costs. The authors offer recommendations for improving waste management based on digital technologies. The proposed solutions are aimed at improving environmental safety, reducing health risks and optimizing resources in the healthcare sector.

THE STRUCTURE OF DOMAIN KNOWLEDGE IN ONTOLOGY

2025-09-03T20:07:56+06:00

This article addresses the issue of formally representing algorithmic knowledge in computer science through the modeling of algorithms in the form of ontology. The main goal of the study is to structure algorithmic concepts and adapt them for use in information systems, artificial intelligence, and the educational process. The methodological framework relies on the widely recognized Protégé ontology editor and the OWL (Web Ontology Language). In constructing the ontology, the “Algorithm” class was chosen as the core, with subclasses identified as SortingAlgorithm, SearchingAlgorithm, GraphAlgorithm, OptimizationAlgorithm, CryptographicAlgorithm, and MachineLearningAlgorithm. Object properties such as hasComplexity, hasDataStructure, hasApplication, usesAlgorithmType, and hasStep, as well as data properties including hasName, hasTimeComplexity, hasSpaceComplexity, hasAuthor, and hasYearIntroduced were defined. These properties make it possible to describe algorithms in terms of efficiency, application domains, and historical context in a formalized manner. The results demonstrated that structuring algorithmic knowledge within an ontology not only enables automated processing but also improves its practical application in education, artificial intelligence, semantic web technologies, and intelligent information systems. The developed ontology provides a new level of formal knowledge representation in informatics and serves as a foundation for further expansion and adaptation to specific applied domains.

ADVANCES IN PATH PLANNING AND OBSTACLE AVOIDANCE FOR AUTONOMOUS MOBILE ROBOTS

2025-09-03T19:36:25+06:00

This article delivers an extensive review of path planning and obstacle avoidance methods in mobile robotics, covering their theoretical principles, algorithmic progress, and real-world applications. Path planning techniques are grouped into four main categories—classical, sampling-based, optimization-oriented, and learning-based—each discussed in terms of advantages, shortcomings, and suitability for diverse operational contexts. Obstacle avoidance is analyzed through reactive, predictive, and learning-focused approaches, with particular attention to sensor technologies and real-time decision-making. The paper also considers integrated navigation systems that merge global and local planning, utilize layered control structures, and operate on embedded platforms to ensure safe and efficient mobility in complex, dynamic environments. Practical examples, such as the ROS Navigation Stack, autonomous delivery systems, and robotic cleaners, illustrate real-world implementations. Additionally, the article highlights persistent challenges and open research directions, including planning under uncertainty, real-time adaptability, socially aware navigation, coordination of multiple robots, and transfer learning for generalization. The discussion is reinforced with figures and tables comparing algorithmic trade-offs and system designs. Overall, the review provides researchers and practitioners with a structured taxonomy, comparative analysis, and forward-looking perspectives to support the creation of more reliable, adaptive, and intelligent navigation systems for future autonomous robots.

CASE STUDIES OF COLLECTING AND PROCESSING DATA ON DETECTING PEOPLE IN URBAN TRANSPORT

2025-09-03T12:37:28+06:00

In the context of increasing urban mobility, the task of accurate passenger counting becomes critically important for transportation infrastructure planning. The aim of this study is to develop an automated system for detecting and counting people in urban transport using the YOLOv8 model and depth cameras. The objectives included collecting and annotating video data, training the model, and evaluating its effectiveness. A specialized dataset was created (4,047 images, 8,918 objects), and the model was trained to achieve an F1-score of 0.90. A series of experiments with different tracking algorithms was conducted. The results confirmed the system's high accuracy and real-time applicability. The developed solution can be used for monitoring passenger flow, optimizing routes, and improving the efficiency of urban transport management.

PYTHON CONCURRENCY FOR HIGH-LOAD MULTICORE PROCESSING

2025-06-03T22:32:58+06:00

Python's concurrency techniques for processor-intensive activities on multicore computers are thoroughly evaluated in this article. For workloads that are CPU-bound, I/O-bound, and mixed, we contrast multithreading, multiprocessing, and a hybrid threading + multiprocessing strategy. Execution time, CPU utilization, memory consumption, and realized speedup were measured against a sequential baseline in experimental benchmarks on a multi-core computer. The Global Interpreter Lock (GIL) prevents Python threads from providing any speedup for CPU-bound applications, according to the results. In contrast, numerous processes obtain near linear speedup (3.7× on 4 cores) at the expense of increased memory utilization. Both multiprocessing and multithreading greatly increase throughput (by more than 3× speedup) for I/O-bound tasks by overlapping I/O delays, while threading has a smaller overhead. By overlapping computation and I/O, a hybrid concurrency technique outperforms pure multiprocessing by 3.3×, providing the best performance in a hybrid workload that combines compute and I/O. We examine the findings in light of Amdahl's Law and talk about how Python thread parallelism is essentially constrained by the GIL. Future attempts to eliminate the GIL and its effects on Python's concurrency environment are also discussed in the article. The results emphasize the trade-offs in speed and resource utilization for each strategy on multicore processors and offer recommendations for choosing efficient concurrency strategies in Python.

ON THE ISSUE OF MODERN APPROACHES TO CRYPTOGRAPHIC KEY MANAGEMENT AND APPLICATION OF DIGITAL SIGNATURE

2025-06-26T22:20:40+06:00

The article presents the results of the analysis of existing problems in key management and digital signature, and also develops and describes the algorithm of the modified Schnorr scheme. It is proposed to create a PGP-like system, proving that the use of a non-positional polynomial number system opens up significant opportunities for increasing the reliability and efficiency of cryptographic procedures in the development of non-traditional algorithms for managing key certificates and digital signatures in cryptographic systems. This system requires a solution that ensures key security at all stages of the key life cycle, minimizes the role of trust, and automates key management. To achieve this, it is important not only to use cryptographic algorithms, but also to effectively manage encryption keys. The theoretical significance is that the reliability of the proposed scheme is shown, and the practical significance is in the possibility of using it to create effective and easily expandable cryptographic systems, showing that the proposed approach can well protect data from possible quantum attacks.

DEVELOPING AN EXTRUDER FOR MAKING 3D PRINTER FILAMENT AS A STEAM PROJECT

2025-09-09T10:28:13+06:00

The article discusses the experience of implementing a STEAM project on the development of an extruder for recycling plastic bottles through its integration into the higher education system. As part of the research, a plastic recycling extruder for the production of 3D printer filament was developed. The main focus was on integrating engineering, technological and pedagogical aspects that allow combining scientific knowledge, digital skills and creative thinking of students. The development of an extruder is considered not only as a technical task, but also as an educational tool that forms competencies in the field of 3D modeling, digital control of parameters and sustainable development. During the study, the technical characteristics of the device were analyzed, experiments on filament production were conducted, and the effective educational effect of using digital tools for data processing and visualization was assessed. The results justify that the implementation of such projects contributes to the development of digital literacy, teamwork and practice-oriented skills that are in demand in modern society.

ANALYSIS AND IMPROVEMENT OF NOISE REDUCTION ALGORITHMS IN CHILDREN'S SPEECH RECOGNITION SYSTEMS

2025-08-31T11:22:44+06:00

This paper presents a hybrid noise reduction algorithm for improving the quality of children's speech recorded in a real acoustic environment. The algorithm combines traditional spectral analysis methods such as fast Fourier transform (FFT) and Wiener filter with deep learning approaches, including recurrent neural networks (RNN) and long-term short-term memory (LSTM) networks. To evaluate the effectiveness of the proposed method, an audio corpus of children's speech in the Kazakh language was collected using the specially developed Telegram bot "Dataset Loader". The experimental part of the study showed a significant improvement in speech recognition performance after applying the noise reduction algorithm. In particular, the word recognition error rate (WER) decreased from 32.4% to 18.7%, and the F1-score increased from 0.72 to 0.88. Analysis of spectrograms showed a significant decrease in the background noise level and improved speech readability. The research results confirm the effectiveness of the hybrid approach for improving the quality of speech data and improving the accuracy of automatic speech recognition systems in complex acoustic conditions.