Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences

FEATURES OF PROBLEM SOLVING IN FUNCTIONAL ANALYSIS

M. Kydyrakyn, А. Birgebaev — Sun, 27 Sep 2026 00:00:00 +0600

It is well known that problem books and exercise collections play a special role in mastering theoretical material in functional analysis and the theory of functions of a real variable at pedagogical institutes and universities. In Russian, there exists a sufficient number of problem collections of various levels in this field. Among the most notable are the works of Yu.S. Ochan, A.A. Kirilov and A.D. Gvishiani, S.A. Telyakovsky, P.L. Ulyanov, A.N. Bakhvalov, M.I. Dyachenko, K.S. Kazaryan, P. Sifuentes, V.A. Petrov, N.Ya. Vilenkin, and M.I. Graev. These collections mainly focus on set theory and measure theory, and provide solutions to a large number of problems. However, the theory of integrals, operator theory, separability, completeness of spaces, compactness, and their applications to problem solving are insufficiently covered. In the Kazakh language, there are almost no problem collections corresponding to university curricula in these disciplines. Among the few published works, one may note G. Akyshev’s book on functional analysis, which covers several sections of the subject and includes solutions to problems, although its circulation is very limited. The aim of the study is to identify and systematize the methodological aspects of solving problems in the core areas of functional analysis, as well as to develop approaches to presenting them in the Kazakh language, taking into account the content of the university course. Since this discipline is one of the fundamental areas of mathematics, future researchers (Master’s and PhD students) cannot engage in scientific work without mastering it thoroughly. Functional analysis is considered a continuation of real analysis, and its problems are studied in close interconnection. From a methodological perspective, many problems were analyzed and their detailed solutions were provided. The study systematizes the main types of problems in set theory, measure theory, the Lebesgue integral, and functional analysis; defines methodological approaches to solving them; and develops a system of exercises of varying difficulty. The results obtained can be used in teaching functional analysis in the Kazakh language and in developing educational and methodological materials.

DIGITAL EDUCATIONAL RESOURCES IN INCLUSIVE MATHEMATICS TEACHING

T. S. Mamadaliev — Sun, 27 Sep 2026 00:00:00 +0600

The study examines the potential of digital educational resources for mathematics teaching in inclusive education and the readiness of pre-service mathematics teachers to integrate these resources into their professional practice. The research was conducted at O. Zhanibekov South Kazakhstan Pedagogical University. The methodological design combines a questionnaire with practice-oriented mathematical tasks. GeoGebra and Desmos were incorporated into the practical component to assess participants’ ability to visualize mathematical content, use digital tools purposefully, adapt mathematical tasks to inclusive learning requirements, and differentiate activities according to learners’ educational needs. The practical tasks were evaluated using five criteria: mathematical accuracy, effective use of digital tools, visualization, inclusive adaptation, and task differentiation. The methodological framework therefore approaches digital competence not merely as technical proficiency but as the ability to integrate technology with mathematical content and inclusive pedagogical practices. The practical significance of the study lies in its potential contribution to mathematics teacher education by supporting the development of learning activities that integrate digital competence with the capacity to design accessible and differentiated mathematics instruction.

USE OF ARTIFICIAL INTELLIGENCE IN INDEPENDENT WORK: THE ROLE OF PEDAGOGICAL SUPERVISION

Sun, 27 Sep 2026 00:00:00 +0600

The article examines the features of using artificial intelligence technologies in students’ independent work and the role of pedagogical supervision in this process. The purpose of the study is to investigate the effectiveness of using artificial intelligence tools in students’ independent work and to determine the influence of pedagogical supervision on learning outcomes. The study employed methods of theoretical analysis, comparative analysis, survey, pedagogical control, pedagogical experiment and statistical processing. The empirical basis of the study consisted of data from 182 students (n = 182) who participated in the pedagogical experiment. The data were processed using methods of comparative analysis of mean values, two-way analysis of variance, and panel regression. The results of the study showed that the use of artificial intelligence tools in combination with pedagogical control increases students’ learning motivation, academic independence, and the quality of task completion. In addition, it was established that systematic feedback and control by the teacher improve the level of responsible use of artificial intelligence and adherence to the principles of academic integrity. The findings confirmed that the positive impact of artificial intelligence on the quality of learning is sustainable only under conditions of systematic pedagogical supervision. In the absence of sufficient control, a tendency toward a decrease in students’ independent cognitive activity and conscious completion of learning tasks was observed. The scientific significance of the study lies in substantiating the fact that the effectiveness of using artificial intelligence in students’ independent work directly depends on the systematic nature of pedagogical supervision.

CONCEPTUAL MODEL OF THE ORGANIZATION AND DIGITAL SUPPORT OF SMART AUDIENCE ACTIVITIES IN THE PEDAGOGICAL EDUCATION SYSTEM

G.B. Kamalova, Sh.P. Turashova, M.E. Yersin — Sun, 27 Sep 2026 00:00:00 +0600

In the context of the digital transformation of pedagogical education, a SMART audience is viewed not only as a technologically equipped learning space, but also as an integrated physical‑digital environment that supports the organization of educational, project‑based, and research activities for future teachers. Despite the progress in research in this field, the scientific literature predominantly presents individual technological solutions and areas of application for SMART audience, while the issues of organizing them as a holistic educational system remain underdeveloped. In this regard, there is a need for a systematic representation of the structure of the SMART audience, its participants, resources, areas of activity, and interconnections, as well as for defining the requirements for digital support of this activity. The aim of the study is to develop a conceptual model for organizing and digitally supporting the activities of a SMART audience within the system of pedagogical education, reflecting its structure, participants, resources, main areas of activity, and interrelationships, and defining the functional structure and information architecture of the digital platform as the technological foundation for digital support. The research methodology included an analysis of scientific sources, systemic and functional analysis, conceptualization of the SMART audience, structural‑functional modeling, and logical‑scenario testing of the developed model. As a result, seven interrelated components of the SMART audience have been identified, the cycle of its activities has been presented from planning to analysis and dissemination of results; requirements for digital support have been formulated; and the functional structure and information architecture of the digital platform have been developed. The proposed conceptual model systematizes the structure and organization of the SMART audience’s activities, establishes the relationships between its components, and defines the requirements for digital support, forming the basis for designing a unified digital platform.

OPERATIONAL LOGIC OF THE EDUCATIONAL PROGRAM ANALYSIS WEB SYSTEM

D. Naimanova, А. Dautova, Zh., N. — Sun, 27 Sep 2026 00:00:00 +0600

This paper presents the development of a web-based system for educational program analysis designed to automate the assessment of educational document content using artificial intelligence technologies. Unlike existing solutions that primarily focus on local processing of individual documents, the proposed system is implemented as a web application based on a client–server architecture comprising a frontend, backend, relational database, PDF document processing module, and an artificial intelligence module. The paper describes the system's operational logic, including interactions among users with different roles (instructors, students, and administrators), data storage organization, and the internal data processing workflow. Natural Language Processing (NLP) techniques and Large Language Models (LLMs) are employed to perform intelligent analysis of educational program content, enabling the automatic identification of soft skills and the generation of recommendations for improving educational programs. The analysis results are stored in a relational database and made available to users through a web interface. The developed web-based system automates the analysis of educational programs, reduces the workload associated with expert evaluation, improves the objectivity of the analysis, and can be applied by higher education institutions to monitor and enhance educational programs in accordance with current labor market requirements.

A METHODOLOGICAL MODEL FOR TEACHING HIGHER MATHEMATICS BASED ON ARTIFICIAL INTELLIGENCE

Sun, 27 Sep 2026 00:00:00 +0600

In recent years, artificial intelligence technologies have been developing rapidly, opening up new opportunities for teaching mathematical disciplines within the higher education system. In this regard, the study aimed to develop a methodological model for teaching higher mathematics based on artificial intelligence, as well as to propose diagnostic and analytical tools for evaluating its effectiveness. In the course of the work, the specific functions performed by the virtual problem set and the intelligent chatbot were identified, the sequence of technology application and its internal structure were established, criteria for measuring learning achievements were formulated, a questionnaire for assessing student satisfaction was developed, a procedure for data collection and statistical processing was established, and the proposed analytical apparatus was tested on model data. The methodological model consists of four closely interrelated blocks — target, content-technological, organizational-activity, and evaluation-result — and three levels of intelligent support were developed: orienting, guiding, and explanatory. Two groups of indicators — learning achievements and student satisfaction — were proposed to evaluate the results, and validation performed on model data confirmed the operability of the proposed analytical protocol. The scientific novelty of the study lies in combining the virtual problem set and the chatbot within a unified learning cycle featuring adjustable levels of AI support and a two-component evaluation system. The practical significance is determined by the possibility of applying the developed model and tools in higher education institutions of the Republic of Kazakhstan.

PEDAGOGICAL ISSUES IN DEVELOPING LOGICAL THINKING SKILLS OF FUTURE INFORMATICS TEACHERS IN THE CONTEXT OF ARTIFICIAL INTELLIGENCE

A.E. Sagymbayeva, K.Zh. Sabrayev — Sun, 27 Sep 2026 00:00:00 +0600

The article examines pedagogical issues arising in the development of logical thinking skills among future informatics teachers in the context of artificial intelligence. The aim of the study is to systematize the subject-specific activities through which future informatics teachers’ logical thinking skills are manifested when mastering informatics content, to identify pedagogical issues arising in the development of these skills in the context of artificial intelligence, and to substantiate the relationship between their underlying causes and possible solutions. The study employed methods of scientific literature analysis, comparative analysis, theoretical generalization, systematization, and pedagogical interpretation. The manifestations of logical thinking skills in learning activities were systematized based on the interrelationship between thinking operations and logical reasoning activities. The analysis of informatics content identified their subject-specific manifestations in such areas as algorithmization and programming, information modeling, data processing, computer systems, network technologies, information security, and computer graphics. An analysis of the capacity of artificial intelligence tools to support or fully or partially perform these logical activities, in relation to preserving learners’ independent logical activity, revealed three key pedagogical issues: preserving learners’ independent logical activity; ensuring that learners independently verify AI-generated results and formulate reasoned conclusions based on them; and preparing future informatics teachers to use artificial intelligence tools in accordance with pedagogical goals. The causes underlying the identified issues and pedagogical approaches to addressing them were systematized. The findings indicate that the pedagogical significance of using artificial intelligence tools in the development of logical thinking skills should be considered not only in terms of their technological capabilities but also in terms of whether they support or substitute learners’ independent logical activity.

METHODOLOGY FOR THE USE OF ARTIFICIAL INTELLIGENCE IN DEVELOPING STUDENTS' FUNCTIONAL LITERACY

Sun, 27 Sep 2026 00:00:00 +0600

This article examines the possibilities of using artificial intelligence in the development of students’ functional literacy in the process of teaching physics. The aim of the study is to demonstrate ways of applying artificial intelligence in the formation of students’ functional literacy, specifically to determine the effectiveness of developing functional literacy through the use of digital educational resources, virtual experiments, 3D models, and situational tasks in physics lessons. The article considers the use of virtual experiments on the platforms foxar.education, efizika.ru, and Corinth in physics instruction. Students were given practical situational tasks on the topics «Atmospheric Pressure. Measurement of Atmospheric Pressure», «Determination of the Size of Small Objects», and «Direct Current». To evaluate the effectiveness of artificial intelligence in physics education, a survey was conducted among teachers. The majority of teachers noted that virtual experiments supported by artificial intelligence have a positive impact on increasing students’ interest in the subject, contribute to a deeper understanding of physical phenomena, and support the development of functional literacy. The results of the study show that the systematic use of artificial intelligence in school physics education contributes to the development of students’ functional literacy, as well as their research and practical skills.

THE USE OF AI-BASED INFOGRAPHICS IN PREPARING FUTURE INFORMATICS TEACHERS TO TEACH INFORMATION PROCESSES

SH.T. Shekerbekova, U.K. Bazarbayeva, B.B Kaldanov — Sun, 27 Sep 2026 00:00:00 +0600

With the rapid adoption of digital technologies and artificial intelligence, the requirements for training future computer science teachers are changing. Not only mastery of digital tools is becoming increasingly important, but also the ability to methodically use them when explaining educational material. The aim of the study was to develop and test an approach to using AI-based infographics in the training of future computer science teachers to teach information processes. The study was conducted as a pedagogical experiment. Sixty students participated: 30 in the control group and 30 in the experimental group. Students' readiness was assessed using cognitive, practical-technological, methodological, and reflective-critical criteria. The experimental group utilized a consistent approach to learning content, including analysis, visual presentation, application of artificial intelligence tools, verification of the resulting material, and methodological refinement. Following the formative phase, the proportion of students in the experimental group with a high level of readiness increased from 16.7% to 50.0%, while the integrated indicator increased from 63.3% to 81.1%. Differences between the control and experimental groups at the control phase were statistically significant (χ² = 6.664; p = 0.036). These results demonstrate the feasibility of incorporating AI infographics into the methodological training of future computer science teachers, provided that the resulting material is thoroughly and pedagogically verified. These numerical results are consistent with those already presented in the "Research Results" and "Conclusion" sections: the high level in the EG increased from 16.7% to 50.0%, the integrated indicator increased from 63.3% to 81.1%, and the final comparison yielded a p value of 0.036.

SYSTEM ANALYSIS OF AUGMENTED REALITY SIMULATORS IN PHYSICS TEACHING

K. Shetiyeva, A. Salykova, A. Yesseikyzy, U.E. ambetakunov — Sun, 27 Sep 2026 00:00:00 +0600

The article presents a systematic analysis of augmented reality simulators used to visualize physical laws and phenomena in educational practice. The research is relevant because a significant part of the concepts of physics are presented abstractly and are difficult for students to perceive when using only traditional teaching methods. In this paper, we conducted a comparative analysis of seven existing AR applications covering the main branches of physics: mechanics, molecular physics and thermodynamics, electricity and magnetism, optics, as well as the "Atom and Atomic Nucleus" block. The assessment was carried out according to a number of criteria, including the level of visualization, interactivity, physical correctness of models, user-friendliness of the interface and pedagogical potential. The results of the study made it possible to classify AR simulators according to their functionality and didactic characteristics, identify their strengths and limitations, and identify the most promising areas of application of augmented reality in teaching physics. It was also found that a greater educational effect is achieved if visualization is combined with the ability to control parameters and receive feedback. As a result, it can be argued that AR technologies can significantly improve the quality of learning physical patterns, provided they are methodically soundly integrated into the learning process.

SENSITIVITY ANALYSIS AND IMPACT ASSESSMENT OF DESIGN AND OPERATING PARAMETERS ON THE EFFICIENCY OF A FLAT-PLATE SOLAR COLLECTOR IN BTES SYSTEMS

Sun, 27 Sep 2026 00:00:00 +0600

Flat-plate solar collectors are crucial in Borehole Thermal Energy Storage systems for bridging the gap between renewable energy supply and consumer heat demand. Because most studies rely on idealized models, this work develops a Python-based transient mathematical model of a "solar collector–heat exchanger" system using energy balance equations and real commercial SchücoSol collector specifications. With this validated model, a parametric and sensitivity analysis (±20%) evaluated how daily efficiency is impacted by optical efficiency, heat losses, heat exchanger transfer coefficient, fluid mass flow rate, and ambient temperature. Results demonstrate that ambient temperature, optical efficiency, linear heat losses, and heat exchanger characteristics most significantly influence efficiency. These findings quantitatively assess the impact of design and operating parameters, offering practical recommendations for designing and optimizing real seasonal thermal energy storage systems.

A LEGENDRE–FENCHEL TRANSFORM FRAMEWORK FOR MATHEMATICAL MODELING OF NONLINEAR CAPILLARY FLOW OF GENERALIZED NEWTONIAN FLUIDS

Y. Wang, D. Sydyk, S. Omirbekov — Sun, 27 Sep 2026 00:00:00 +0600

A Legendre--Fenchel transform framework is developed for pressure-driven capillary flow of monotone generalized Newtonian fluids. A monotone nonlinear flow curve defines a convex dissipation potential, and its Legendre--Fenchel transform gives a complementary potential in the stress variable. Since the stress distribution is known explicitly in fully developed capillary flow, the velocity profile can be obtained from this complementary potential without requiring the inverse constitutive relation to be written explicitly. This reformulates nonlinear capillary-flow modeling from a model-by-model constitutive inversion problem into a convex-duality construction. The method recovers the shear-rate-parametrized Carreau--Yasuda solution, gives compact average-velocity relations for circular and planar geometries, and extends to several generalized Newtonian models, including Papanastasiou-regularized yield-stress fluids. In the ideal yield-stress limit, plug formation follows naturally from the subdifferential structure of the dissipation potential and the corresponding flat interval of the complementary potential. The framework provides a unified mathematical structure for analytical and semi-analytical pressure-drop--flow-rate relations in nonlinear capillary flow.

FINITE-TIME STABILIZATION METHODS FOR NONLINEAR SWITCHED SYSTEMS

A. Zhambulatova, K. Alimhan — Sun, 27 Sep 2026 00:00:00 +0600

This paper investigates the problem of finite-time stabilization for nonlinear switched systems under arbitrary switching laws. Such systems play an important role in control theory and are widely encountered in many engineering applications, including robotics, chemical reactors, mechatronic systems, and virtual interaction systems. While classical stability theory focuses on the asymptotic convergence of system states to an equilibrium point, finite-time stability guarantees that the system states reach the origin within a finite time interval. This property improves the response speed of the system and enhances its robustness against external disturbances. The paper considers a mathematical model of nonlinear systems with switching modes and analyzes stability conditions based on a common Lyapunov function. In addition, control design methods based on the adding a power integrator technique are presented to achieve finite-time stabilization. The proposed approaches ensure system stability even when the switching law is arbitrary. To verify the effectiveness of the developed methods, several numerical examples are investigated and simulated in the MATLAB environment. The obtained results demonstrate that the state variables converge to zero within a finite time. Numerical simulations confirm the effectiveness of the proposed control strategies and indicate their potential applicability in practical engineering systems.

QUASILINEAR INTEGRAL HARDY-TYPE INEQUALITIES

N. Zhangabergenova, A. Temirkhanova — Sun, 27 Sep 2026 00:00:00 +0600

The introduction of a kernel into quasilinear Hardy-type operators is an important direction. However, obtaining results for the general type of kernel is an undefined problem, so researchers study Hardy-type operators for certain kernel classes. Generalizing the research, we obtained the criteria for the validity of quasilinear integral Hardy-like inequalities belonging to the classes and in the parameter ranges . That is, necessary and sufficient conditions for the validity of quasilinear operators involving the kernel Hardy operator in weighted Lebesgue spaces were determined. This allows us to study generalized bilinear operators. In particular, the results of quasilinear inequalities with kernels provide alternative method for estimating bilinear inequalities. This study contributes to the theory of integral operators in functional analysis and can be used in finding solutions to differential equations.

ULYANOV-TYPE INEQUALITY FOR MIXED MODULI OF SMOOTHNESS OF GENERALIZED LIOUVILLE–WEYL DERIVATIVES

A. Zhetpisbayeva, A.А. Jumabayeva — Sun, 27 Sep 2026 00:00:00 +0600

The paper proves an Ulyanov-type inequality for the mixed modulus of smoothness of a generalized Liouville--Weyl derivative of a function of two variables in mixed metrics. The derivative is defined by transforming the two-dimensional Fourier series by a positive general monotone sequence of the class and by phase parameters. The main estimate relates the mixed modulus of the derivative in the metric to an integral operator involving a dyadic functional constructed from angular best approximations of the original function and differences of the multiplier. The proof combines the mixed Ulyanov inequality, an inverse estimate of the modulus through angular approximations, and a two-dimensional Abel transformation for multipliers. Particular cases include the classical Weyl derivatives and logarithmically modified multipliers.

PPO-BASED RESOURCE ALLOCATION FOR FIFTH-GENERATION NETWORK SLICING

D. Marlambekov, S. Mukhambetzhanov, Sh. Ibraheem — Sun, 27 Sep 2026 00:00:00 +0600

This paper presents a deep reinforcement learning approach to service-level-agreement (SLA) aware network slicing in 5G radio access networks. We formulate the dynamic allocation of Physical Resource Blocks (PRB) among three coexisting slices — enhanced Mobile Broadband (eMBB), Ultra-Reliable Low-Latency Communications (URLLC), and massive Machine-Type Communications (mMTC) — as a Markov Decision Process and develop a Gymnasium-compatible simulation environment in which per-slice SLA requirements follow the 3GPP TS 28.530 framework. A Proximal Policy Optimization (PPO) agent is trained with a composite reward that jointly rewards aggregate throughput, penalizes SLA violations, and encourages resource utilization. The agent is evaluated over 100 episodes against three classical baselines: Static Equal, Static Priority, and Greedy Proportional allocation. The PPO agent reduces the aggregate SLA violation rate to 2 × 10⁻⁵, three to four orders of magnitude lower than the Static Priority baseline (0.46), while sustaining a mean aggregate throughput of 74.7 Mbit/s and a resource utilization of 98.6%. A throughput-versus-violation analysis confirms that the learned policy occupies an operating point that no single static rule attains. The complete environment, training pipeline, and evaluation scripts are open-source and reproducible using the Stable-Baselines3 library.

EQUATIONS OF MOTION IN OSCULATING VARIABLES WITHIN JACOBI COORDINATES

M.ZH. Minglibaev, M. Saparova — Sun, 11 Oct 2026 00:00:00 +0600

This paper addresses the description of equations of motion in Jacobi coordinates using osculating elements as an effective method for solving many-body problems. The equations of motion are formulated via osculating elements using Jacobi coordinates for the TRAPPIST-1 seven-planet exoplanetary system, characterized by variable masses and non-isotropic reactive forces. In many-body problems, the use of conventional heliocentric coordinates often complicates calculations. Jacobi coordinates consider the motion of each body relative to the center of mass of the preceding bodies, thereby allowing the problem to be decomposed into independent two-body problems. The bodies interact according to Newton's law of universal gravitation. Due to the variable mass, reactive forces are present, which further complicate the problem. The primary objective of this research is to establish a system of differential equations describing the evolution of osculating elements, treated as time-varying variables. While Jacobi coordinates simplify the mathematical framework, osculating variables provide a geometric representation of the motion (changes in orbital shape and orientation). Based on the equations of motion derived in Jacobi coordinates, a canonical perturbation theory has been developed, and equations for perturbed motion in analogues of Jacobi and Delaunay elements have been obtained. This approach enables high-precision modeling of the dynamics of multi-planetary systems. Based on the derived equations, the problem can be analyzed within a barycentric coordinate system using perturbation theory.

SOLVING A SYSTEM OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS FOR HYPERGEOMETRIC FUNCTIONS

A.R. Ryskan , B.K. Abdrahman, N.Zh. Ainakeyeva — Sun, 27 Sep 2026 00:00:00 +0600

This research focuses on the analysis of a second-order system of partial differential equations linked with the four-variable hypergeometric functions . These specific functions play a critical role in numerous branches of contemporary mathematics and theoretical physics, notably in quantum mechanics and string theory. By treating multidimensional hypergeometric functions within the framework of differential systems, this work explores their structural properties and evaluates solution behavior under specific boundary constraints. The subject of this inquiry involves the function classes and originally proposed by Exton. Throughout this investigation, distinct differential operators were established for the aforementioned functions, enabling the derivation of exact analytical expressions for their fundamental solutions. The outcomes highlighted in this paper underscore the significance of multivariate hypergeometric functions in addressing contemporary applied problems and open up new avenues for mathematical modeling. Ultimately, the validity of the computed data is rigorously verified through classical techniques of differential equation theory.

BAYESIAN CAUSAL DEMAND MODELING WITH LATENT RANKING FACTORS IN E-COMMERCE

K.M. Shapen, А.Т. Рахымова, A. Akhmedov, Zh.D. Baishemirov — Sun, 27 Sep 2026 00:00:00 +0600

E-commerce demand forecasting is complicated by the effects of latent ranking factors and deliberate price changes that distort observed sales relative to true demand. This paper presents a systematic review of modern approaches to demand modeling from the perspective of integrating probabilistic forecasting, Bayesian uncertainty assessment, and causal analysis. Three key areas are considered: probabilistic deep time series models (DeepAR, Temporal Fusion Transformer, N-BEATS, PatchTST, foundation models Chronos and TimesFM); Bayesian neural networks and ensemble methods for uncertainty assessment; and methods for causal modeling of price effects, including double machine learning and structural causal models. A comparative analysis of methods is conducted based on the criteria for accounting for uncertainty, ranking, and causality. A fundamental gap is identified: the absence of architectures that jointly account for Bayesian uncertainty, position bias, and causal price effects under conditions of unobservable product visibility. A direction for further research is proposed related to the development of integrated Bayesian-causal models with latent ranking variables for reconstructing true demand in e-commerce conditions.

LEAKAGE-CONTROLLED RESIDUAL-CALIBRATED HYBRID MODEL FOR ONE-HOUR-AHEAD PHOTOVOLTAIC GENERATION DURING ACTIVE HOURS: AN EXPERIMENTAL EVALUATION

A.А. Abdildayeva, G.Zh. Taganova, A.A. Tazhibeyev, A.Zh. Kural, S.S. Askarov — Sun, 27 Sep 2026 00:00:00 +0600

This experimental research study evaluates a leakage-controlled residual-calibrated hybrid model for sequential one-hour-ahead photovoltaic generation forecasting during active station-hours. A source audit of operational records from three solar power plants identified 28,296 raw hourly rows but only 11,736 unique station-hour keys; 16,560 redundant source rows were collapsed only when known plan and actual values were identical, and no conflicting known plan/actual values were found. After restricting supervised modelling to unique station-hours with positive planned generation and known actual output, 4,848 observations remained and were chronologically divided into 3,038 training, 819 calibration, and 991 held-out test observations. The proposed Residual-Calibrated Neural Hybrid (RCNH) combines a two-hidden-layer Tabular MLP with a HistGradientBoosting residual calibrator trained exclusively on the calibration period. On the held-out test period, RCNH achieved MAE = 2,591.80 kWh, RMSE = 3,906.53 kWh, and R² = 0.908609; 95% three-day block-bootstrap intervals were 2,372.75-2,961.81 kWh, 3,537.16-4,505.29 kWh, and 0.848489-0.932518, respectively. Against the train-only Tabular MLP, RCNH reduced MAE by 11.36% (95% block-bootstrap interval 6.98-14.95%; Holm-adjusted two-sided p = 0.003998). However, a matched-label-budget diagnostic favored an MLP refitted on train plus calibration data (MAE = 2,464.63 kWh), and rolling-origin validation showed substantially stronger temporal stability for tree ensembles, with ExtraTrees attaining mean RMSE = 3,064.51 kWh versus 6,106.74 kWh for RCNH. These results show that residual calibration is competitive and beneficial in the final held-out regime but is not uniformly dominant; its effectiveness depends on calibration-window representativeness and temporal regime. The contribution is therefore an experimentally validated, leakage-controlled forecasting protocol and a quantified assessment of where residual calibration helps and where its robustness is limited.

A DATASET AND BENCHMARK FOR FINE-GRAINED CLASSIFICATION OF GAME WATERFOWL

R. Abdrakhmanov, A. Alimova, S. Sokolov, N. Chalova, D. Nurseitov — Sun, 27 Sep 2026 00:00:00 +0600

Identifying birds by species and sex is essential for recording game harvests, monitoring the status of game resources, and ensuring compliance with established hunting regulations. However, existing datasets and digital applications primarily focus on species identification and do not account for the sex of individual birds, which limits their applicability to game management. This paper presents GameWaterbird-41, a specialized dataset designed for the joint classification of species and sex in game waterfowl and shorebird species classified as game species. Compiled from images obtained from the iNaturalist platform, the dataset contains 18,851 images representing 38 bird species and is organized into 41 classes, with sex-specific classes defined for species exhibiting pronounced sexual dimorphism. Modern computer vision models were comparatively evaluated under zero-shot classification, linear probing, and full fine-tuning settings. The evaluated architectures included convolutional neural networks and vision transformers, encompassing both general-purpose models and models pretrained on biological images. The results demonstrate that full fine-tuning on the target data yields the highest classification performance. The developed dataset and comparative evaluation results can be used to improve game harvest recording and provide information support for game resource management.

BENCHMARKING HANDOVER CONTROL IN MULTI-USER 5G NETWORKS

S.Zh. Aibagarov, A,A, Mukhanbet — Sun, 27 Sep 2026 00:00:00 +0600

Handover management is an important issue in mobile 5G networks. A controller must decide when each piece of user equipment (UE) should switch its serving base station to maximize throughput while minimizing handovers, ping-pong switching, and connection failures. This paper presents a reproducible simulation environment and a systematic review of handover strategies in a multi-user scenario with four base stations and ten mobile UEs, using a 3GPP Urban Macro channel model with log-normal shadowing. We evaluate four controllers over 100 independent episodes: the 3GPP A3-event algorithm with hysteresis and time-to-trigger, an ideal Strongest-Cell rule, a No-Handover lower bound, and a learned controller trained with Proximal Policy Optimization (PPO). The results show that the standardized A3-event policy provides the best overall balance. It achieves the highest mean system throughput at 89.1 Mbit/s, the fewest handovers per episode at 21.7, and the lowest ping-pong rate at 0.098 among all methods assessed. The Strongest-Cell rule offers similar throughput but results in about 2.6 times more handovers. The learned controller shows stable training but does not reach the performance of the tuned A3 baseline based on the current reward and observation design. We discuss why the hysteresis-and-TTT logic remains a strong baseline and outline the conditions where a learned policy could outperform it. The entire environment and evaluation process are available for others to reproduce.

PASSENGER TURNOVER MAXIMIZATION STRATEGY FOR SOCIALLY SIGNIFICANT RAILWAY ROUTES UNDER DETERMINISTIC TARIFFS

Sun, 27 Sep 2026 00:00:00 +0600

This article examines methods for enhancing the capacity utilization efficiency of long-distance passenger trains operating under state-regulated tariffs. Unlike traditional revenue management systems based on dynamic pricing, socially significant passenger rail services are constrained by fixed tariffs and cannot employ price mechanisms to regulate demand. Under these conditions, intelligent management of seat allocation across various Origin–Destination (O&D) city pairs becomes the primary instrument for increasing operational efficiency. We propose a comprehensive capacity management methodology based on train classification by occupancy level, route segmentation by contribution to passenger turnover, application of Virtual Nesting, unconstrained demand estimation, and Route Splicing technology. Control algorithms were developed for five train categories based on predicted load factors. An empirical analysis using real-world operational data from JSC "Passenger Transportation" (Kazakhstan) for the 2022–2025 period, combined with simulation modeling, demonstrates a potential 6–12% increase in passenger turnover compared to the baseline static bucket allocation method. The findings show that maximizing passenger turnover can improve the efficiency of subsidized rail operations without altering existing tariff policies.

ENHANCING AUTOMATIC SPEECH RECOGNITION FOR KAZAKH PEDIATRIC SPEECH THROUGH TRANSFER LEARNING AND FINE-TUNING

Zh. Duisenbekkyzy, А. Tursynkhan, G Gaziz, B. Ilessova — Sun, 27 Sep 2026 00:00:00 +0600

This study aims to improve automatic speech recognition for children aged 5–12 by accounting for the acoustic and phonetic characteristics of the Kazakh language. The objective is to adapt OpenAI’s Whisper-tiny architecture to Kazakh through fine-tuning on a specialized children’s speech dataset. A two-stage fine-tuning strategy was applied: the model was first trained on 235 audio samples and then on an expanded corpus of 1,936 samples. The audio recordings were standardized to a sampling rate of 16 kHz, and the text transcriptions were normalized. Model performance was evaluated using Word Error Rate (WER) and Accuracy. The experimental results showed that WER decreased from 0.80 to 0.42, representing a relative improvement of 47.5%, while Accuracy increased from 20.43% to 57.95%. These findings demonstrate that increasing the amount of data and applying domain-specific fine-tuning improve the recognition of children’s speech. The proposed approach can support the development of educational and intelligent speech systems for low-resource languages.

A MODIFIED SECRET SHARING SCHEME FOR PROTECTING FACIAL BIOMETRIC TEMPLATES

N.S., N.A. Kapalova — Sun, 27 Sep 2026 00:00:00 +0600

A facial biometric template is a permanent identifier: once a stored template is exposed it cannot be reissued, so single-node storage is a critical point of failure. This work continues the authors' line of research on protecting facial templates with threshold secret sharing and develops a modified algorithm oriented specifically to facial biometrics. The starting point is a share-verifiable secret sharing scheme based on multivariable linear functions, originally proposed for general confidential data and not designed for biometrics. Its mathematical rule is changed: the pseudo-random coefficient matrix is replaced by a structured Vandermonde rule; blockwise packing of the protected facial record and masking are introduced; and the hash-based check is replaced by an unconditionally secure algebraic authentication code. The resulting block-packed secret sharing scheme is MDS (maximum distance separable - any k of n shares reconstruct the secret), perfectly secret up to the privacy threshold t, has exactly bounded ramp leakage and unconditional share verification; all properties are proven. Experimentally, with n = 7, k = 5 all 6300 subsets reconstructed without error; over a small field the modified scheme produced no singular subsets versus 0.41 % for the original; ramp leakage matched theory. For a 256-byte protected record, packing reduces total share storage 64-fold and halves verification metadata; unconditional share verification runs in 0.0012 ms. Recognition accuracy is inherited from the front end and is left unchanged by the protection layer: it reaches an EER (equal error rate) of 0.30 % in deep-embedding mode and 0.02 % in high-quality mode.

MACHINE LEARNING FOR RESERVOIR ANALYSIS AND FORECASTING IN KAZAKHSTAN

M. Junussova, D. Rakisheva — Sun, 27 Sep 2026 00:00:00 +0600

This paper explores the application of machine learning methods for the analysis, classification, and forecasting of the dynamics of small reservoirs in Kazakhstan based on long-term satellite observations. The study covers 71 water bodies for which archival satellite imagery from the Landsat 7, Landsat 8, Landsat 9, and Sentinel-2 missions was collected and processed from 2000 to 2024. The water surface area was estimated using the Modified Normalized Difference Water Index (MNDWI) combined with image segmentation algorithms implemented in Matlab, ArcGIS, and Python environments. Based on the derived estimates, time series reflecting seasonal and interannual variations in reservoir surface area were constructed. To identify characteristic types of water-body dynamics, the time series were classified according to seasonal patterns, long-term trends, and interannual variability. In addition, time series analysis was performed using forecasting models, including Prophet and Long Short-Term Memory (LSTM) recurrent neural networks, enabling short-term predictions of water surface area changes for reservoirs of different sizes. The results demonstrate the potential of integrating satellite data with machine learning methods to develop automated monitoring systems and decision-support tools for water resource management in the Republic of Kazakhstan.

DEVELOPMENT OF A MODEL AND APPLICATION FOR KAZAKH-LANGUAGE TEXTS EXHIBITING SIGNS OF SUICIDAL BEHAVIOR

G. Ziyatbekova, Sh.N. Shekerbaeva, A.I. Akzholova, М. Sydykova, Zh. Polatova — Sun, 27 Sep 2026 00:00:00 +0600

This article aims to develop a model for Kazakh-language texts exhibiting signs of suicidal behavior. Computational linguistics encompasses natural language processing—that is, natural language processing (NLP). The results of this study will undoubtedly be used to address natural language processing tasks—for example, in the analysis of text corpora, in specific subject domains, in data retrieval systems, in machine translation, and in other areas. The main problem addressed in the article is the prompt detection of suicidal tendencies based on data from open sources using machine learning and deep learning methods. The goal is to develop and compare effective classification models based on the analysis of Kazakh texts. Differences in the adaptation of texts in the state language will be taken into account, including morphological difficulties and the phenomenon of agglutination. The research focuses on developing machine learning models tailored to identify patterns of suicidal behavior in our national language, as well as on examining the interplay between them. Improving the monitoring of online sources using artificial intelligence will enable a rapid response to crisis situations

A REPRODUCIBLE 5G SA TESTBED FOR O-RAN MACHINE LEARNING

D. Lebedev, Zh. Otarbay, A. Kyzyrkanov — Sun, 27 Sep 2026 00:00:00 +0600

Data-driven control of the radio access network through O-RAN RAN Intelligent Controllers depends on labelled, stack-wide measurement data, which is scarce and costly to obtain on commercial equipment. This paper describes a fully software-defined 5G Standalone (SA) testbed and an automated pipeline that turns it into a generator of labelled machine-learning datasets. The testbed integrates the srsRAN gNodeB, the Open5GS core, a GNU Radio plus ZeroMQ radio emulator with runtime-controllable channel impairment, and a FlexRIC Near-RT RIC, all on a single commodity server with CPU isolation and per-user network namespaces for repeatability. A Monte-Carlo orchestrator runs up to one thousand 20-second iterations, randomizing user count, per-user path loss, traffic type and rate, and parallelism, and a synchronized parser assembles one-second snapshots into a 37-feature table spanning the PHY, MAC, RLC/PDCP, and operating-system layers, augmented with five-second rolling statistics, an energy-efficiency index, and forward-looking regression and classification targets at a five-second horizon. We describe the architecture, the feature engineering, the labelling methodology, and the resulting dataset structure, and we discuss how the dataset supports predictive xApps for proactive congestion and degradation control. The platform and pipeline are designed for reproducibility and are intended as a reusable resource for the O-RAN machine-learning community.

OPTIMIZING CHUNKING STRATEGIES AND INFERENCE ACCELERATION FOR KAZAKH LOW-RESOURCE RAG SYSTEMS

A.G. Ospan, T.S. Sarsembayeva, A.Zh. Sailau, A.B. Temirkhanova, I. Felde — Sun, 27 Sep 2026 00:00:00 +0600

Retrieval-Augmented Generation (RAG) has emerged as the dominant paradigm for grounding large language model (LLM) outputs in external knowledge, yet its systematic application to morphologically rich, low-resource languages remains largely unexplored. This paper addresses two under-studied problems for Kazakh-language RAG: the design of semantically coherent document chunking strategies and the acceleration of multi-stage inference on GPU hardware. We construct a corpus of 201,202 preprocessed news documents from the national newspaper Egemen Qazaqstan (2017–2025, 129 thematic categories) and propose three chunking strategies – Fixed-size (baseline), Semantic (cosine-similarity boundary detection), and Adaptive (joint semantic and length-regularized scoring) – evaluated under a four-dimensional quality framework measuring coherence, document coverage, boundary accuracy, and length regularity. The Adaptive strategy achieves an integrated of 0.879, outperforming the Fixed-size baseline by 0.045 absolute, and improves retrieval F1@5 by 0.067 and end-to-end answer accuracy by 4 percentage points (92%) on a 50-query factual test set. For inference acceleration, we deploy an exact GPU-resident index (FAISS-GpuIndexFlatIP) on an NVIDIA H200 GPU, achieving 2.4 ms retrieval latency – a 70.8× speedup over ChromaDB – without accuracy degradation. Combined with INT4-quantised generation (), KV cache residency in HBM3, and an attention-based self-evaluation mechanism, the pipeline achieves a mean end-to-end response time of 0.92 ± 0.06 s under cold-cache conditions and approximately 0.20 s with full KV cache reuse (4.3× speedup), on a single GPU without external API dependencies. These results demonstrate the feasibility of high-accuracy, sub-second Kazakh RAG and establish reproducible baselines for future low-resource retrieval research.

CORPUS AND BASELINE MODELS FOR KAZAKH TOXIC COMMENT DETECTION

M. Sakypbekova, R. Aubakirova — Sun, 27 Sep 2026 00:00:00 +0600

Public discourse in Kazakhstan is moving online and into the Kazakh language, yet resources for detecting toxic comments in that language remain scarce. The Kazakh corpora that exist were assembled from lists of hostile keywords within an extremism or model-safety frame, few of them are openly released, and fewer still document how they were annotated. This paper presents Kaz-ToCo, a corpus of 84,940 comments in Kazakh and in mixed Kazakh-Russian code-switched text. The comments were retrieved in May 2026 through the YouTube Data API v3 from beneath 30 Kazakhstani talk-show videos, with no keyword-based filtering at any stage of collection, and were labelled on a binary toxicity scale by an open-weight large language model deployed on local hardware. Agreement between the machine labels and the annotations of a native speaker of Kazakh, measured on a stratified sample of 100 comments, reached a Cohen kappa coefficient of 0.602, with a 95 percent confidence interval from 0.446 to 0.758. The training, validation and test splits were built at the level of the source video, which prevents comments from one video from appearing in more than one split. Two baseline classifiers are established on the corpus: term frequency and inverse document frequency features over word and character n-grams combined with logistic regression, and a fine-tuned Kazakh conversational encoder of the RoBERTa architecture. Macro-averaged F1 on the held-out test set reached 0.8086 and 0.8198 respectively. These figures fall well below the near-ceiling accuracies published on keyword-collected Kazakh corpora, and are offered as a realistic reference point. The labels, per-comment metadata, splitting protocol, random seeds and hyperparameters are released without restriction. The comment texts cannot be redistributed under the YouTube API Services Developer Policies and are available from the corresponding author upon reasonable request for non-commercial research use.