Browse
Recent Submissions
Item Open Access Integration of Machine Learning for Enhanced Efficiency in Industrial Systems: Analysis, Forecast, and Perspectives(SDU University, 2026) Borangazin T.Contemporary industrial systems exhibit a pronounced dependence on extensive data, thereby requiring sophisticated analytical frameworks to facilitate decisionmaking under conditions of uncertainty. Conventional statistical methodologies are frequently constrained in their ability to encapsulate the non-linear, dynamic, and multi-factorial interactions characteristic of complex industrial ecosystems. This Master’s thesis undertakes an exploration into the integration of advanced machine learning paradigms to augment the efficacy of industrial forecasting and property prediction endeavors, as evidenced by two pertinent case studies. The initial case study undertakes an investigation into the efficacy of supervised learning models for the prediction of international crude oil prices. A suite of algorithms, including linear regression, tree-based ensembles, and recurrent neural networks, were subjected to training and evaluation utilizing historical price data in conjunction with pertinent macroeconomic indicators. The study substantiates that non-linear machine learning models yield superior predictive accuracy relative to traditional baselines, with a notable advantage observed during periods of market volatility. The second case study delves into predicting mineral properties, with a particular emphasis on Mohs hardness, by leveraging tabular datasets that capture chemical composition and physical measurements. The study develops regression models and a basic generative model to evaluate the role of machine learning within materials informatics. The generative model underscores the feasibility of generating synthetic mineral-like feature vectors, representing an early step towards data augmentation and the concept of inverse design. For both case studies, the dissertation outlines a standardized methodology that involves preparing data, crafting features, training models, validating them, and evaluating performance with metrics like MAE, RMSE, and (R2 ) . The findings illustrate how versatile machine learning is for different industrial data types and suggest that data-driven models offer exciting possibilities for integration into current industrial practices.Item Open Access Variety of special Tortken algebras(SDU University, 2026) Baigali M.This dissertation studies special Tortken algebras arising from the symmetrization of Novikov algebras. The main object is the space of symmetric elements in the free Novikov algebra generated by one element. Using the differential realization of free Novikov algebras, the symmetrized product is written as a ◦ b = (ab) ′ , which allows us to expand elements in the ◦-language into differential monomials and study their linear relations by methods of linear algebra. For the homogeneous component Tn of degree n, we describe the dimensions and obtain dim T1 = dim T2 = 1 and dim Tn = p(n − 2) for n ≥ 3, where p(n) is the partition function. Low-degree components are constructed explicitly, and special attention is given to relations in degrees 6 and 7. The computations suggest a recursive structure for the spaces Tn and contribute to the study of free special Tortken algebras.Item Open Access Dynamic Obstacle Avoidance in Autonomous Robot Navigation Using Deep Reinforcement Learning(SDU University, 2026) Parmash A.Existing indoor navigation systems for autonomous robots have proven their success in geometric mapping and avoidance of obstacles in the local environment, but they lack semantic reasoning capabilities; thus, they cannot comprehend instructions issued in natural language. In contrast, utilizing state-of-the-art vision and language foundation models in the robot control loop would create too much computational delay, making the implementation impractical for the purpose of reactive execution of tasks. This thesis attempts to fill this gap through a two-stage hierarchy. During the initial phase, a mobile robot performs an exploration task within the unknown environment by employing an SLAM pipeline based on LiDAR, while the robot’s on-board VLM performs object detection to build a structured, small global 3D semantic database. During the second phase, the robot takes up any natural-language instructions (for example, “go to the bookshelf”), extracts the coordinates of the target from its memory, and performs autonomous navigation. Here, the navigation process is entirely mapless and does not involve any VLM inference cost overhead. Control at the lower level is done by the robot’s DRL-based policy trained using TD3 algorithms. Assessed under ROS-integrated Gazebo simulation, the proposed architecture attains an accuracy rate of 85% in navigation with a lightweight Moondream VLM, substantially superior to cloud-based GPT-4o mini versions and classical approaches. The trained policy for depth proves to have excellent generalization performance with respect to unknown objects, dense obstacles, and even multiple rooms, as well as a success rate of 80% in evading moving obstacles without the need for further training. Achieving a processing rate of 10 Hz on board, the framework manages to bypass foundation model delay constraints.Item Open Access 3-nil alternative, pre-Lie and assosymmetric operads(SDU University, 2026) Tekebay A.An algebra is called alternative if it satisfies the following identities: (ab)c − a(bc) = −(ac)b + a(cb), (ab)c − a(bc) = −(ba)c + b(ac). In this dissertation, we consider free alternative algebra with the additional identity x 3 = 0. For motivation, we refer to the dual operad of the alternative operad. Also, we obtain pre-Lie algebra with the identity x 3 = 0 from binary perm algebra. Finally, we consider assosymmetric algebra with identity x 3 = 0Item Open Access Weighted Hardy-type inequalities(SDU University, 2026) Atina A.This thesis is devoted to weighted Hardy-type inequalities and identities obtained by the factorization method. The main focus is on Hardy-type identities in the Baouendi–Grushin setting, where the Euclidean radial derivative is replaced by the radial derivative associated with the Grushin structure. More precisely, we consider the homogeneous distance function ρ and the Grushin gradient ∇γ, and study identities involving the radial Grushin derivative ∇γρ · ∇γu |∇γρ| . Using suitable first-order differential operators and their formal adjoints, we derive an improved weighted Hardy identity with an explicit non-negative remainder term. The result is formulated under the assumption that the weight functions V and W form a Bessel pair adapted to the homogeneous dimension Q. The obtained identity extends classical radial Hardy-type identities with Bessel pairs to the degenerate Baouendi–Grushin framework. Several special cases are also discussed, including power-type and logarithmic weights, which illustrate how the general theorem leads to concrete weighted Hardy-type inequalities.Item Open Access The Euler operator on the space of Lie elements in free Novikov algebra(SDU University, 2026) Yersaliyeva A.This thesis is devoted to the study of special subspaces in the free Novikov algebra, namely the spaces of multilinear Lie and symmetric elements. The main aim of the work is to investigate the intersection of these subspaces and to study conditions for recognizing Lie elements in the free Novikov algebra. The first main result concerns the spaces Ln and Tn. Here Ln denotes the space of multilinear Lie elements constructed by means of the commutator [a, b] = a · b − b · a, while Tn denotes the space of multilinear symmetric, or Tortken, elements constructed by means of the symmetrized product a ◦ b = a · b + b · a. Using the differential realization of the free Novikov algebra and the null Lagrangian criterion in terms of the Euler operator, we prove that for degrees n ≤ 7 this intersection is trivial: Ln ∩ Tn = {0}. The case n = 3 is treated explicitly, while the cases n = 4, 5, 6, 7 are verified by computer computations. The second part of the thesis is devoted to the problem of constructing a criterion for Lie elements. We consider an operator associated with replacing the Novikov product by the Lie commutator and then expressing the result in a basis of the corresponding multilinear component. In small degrees, polynomial conditions satisfied by the elements of Ln are obtained. These computations provide the first steps toward a possible criterion for Lie elements in the free Novikov algebra.Item Open Access Forecasting educational services in Kazakhstan using time series analysis methods: analysis of the growth in the number of children attending schools and universities(SDU University, 2026) Turapbay A.This dissertation develops a reproducible regional forecasting framework for demand indicators for education in Kazakhstan up to 2030. The study considers school enrolment, university enrolment, preschool capacity, technical and vocational education, population dynamics, birth rates and migration inflow at the level of individual administrative regions identified by KATO codes. The key research problem is to make forward-looking quantitative estimates for planning educational infrastructure, but demographic and migration processes vary greatly in the twenty regions of Kazakhstan. The methodology uses four families of forecasting models: Holt's linear trend, damped Holt trend, automatic non-seasonal ARIMA with orders selected by the corrected Akaike Information Criterion and ARIMAX dynamic regression models using lagged birth counts and migration inflow as exogenous demographic covariates. Model selection is performed for each region-indicator pair using three-year holdout cross-validation with mean absolute percentage error as evaluation metric. The empirical results confirm that there is not a single model dominating all regions and indicators. Damped exponential smoothing is effective for stable trend indicators, with ARIMAX specifications being more accurate in areas where predictive demographic covariates exist. Six-year lagged birth counts provide statistically significant leading indicators for school enrolment in several regions and migration in-flow helps explain urban enrolment pressure. The aggregate national forecasts indicate continued growth in total school enrolment and demand for preschool. There is strong regional heterogeneity in the rates of change. The scientific contribution ofthis work is a region-level comparative forecasting pipeline that includes the official demographic and educational statistics of Kazakhstan, uses uniform standards of model evaluation, and generates visual and tabular outputs for planning purposes. The practical contribution is a set of regional forecast grids, model aсcuracy heatmaps, demographic pipeline analyses and summary tables that can directly support school construction, teacher recruitment and higher education capacity allocation decisions.Item Open Access Қазақстандағы биометриялық технологиялардың интеграциясы: инновацияларды, тәуекелдерді және құқықтық аспектілерді талдау(SDU University, 2025) Тортай Е.К.Қазақстандағы биометриялық технологиялардың интеграциясы елдің цифрлық трансформациясының негізгі бағыттарының біріне айналуда. Ақпараттық технологиялардың қарқынды дамуы және мемлекеттік қызметтердің қауіпсіздігі мен тиімділігін арттыру қажеттілігінің артуының негізінде беттерді, саусақ іздерін және басқа да бірегей биометриялық параметрлерді тануға негізделген жүйелерді пайдалану қоғамдық өмірдің әртүрлі салаларын оңтайландырудың маңызды әлеуетін білдіреді. Алайда, бұл инновацияларды енгізу бірқатар маңызды сын-қатерлермен байланысты. Олардың ішінде дербес деректерді қорғау, құпиялылықты қамтамасыз ету және технологияларды теріс пайдаланудың алдын алу мәселелері шешуші болып табылады. Биометриялық ақпарат көлемінің өсуімен инновациялық мүмкіндіктер мен азаматтардың жеке өміріне қол сұғылмаушылық құқықтары арасындағы тепе-теңдікті қамтамасыз етуге қабілетті нормативтік-құқықтық базаны құру және жетілдіру қажеттілігі туындайды.Item Open Access Creating the Integrative STEM Lesson Unit Plan for 10th Grade Students(SDU University, 2025) Zhumashev A.This master's thesis examines the creation and implementation of an integrative STEM method in the educational process based on 10th grades through the use of a Unit Plan/Curriculum. The main purpose of the master's thesis is to introduce and evaluate the effectiveness of STEM methodology as a methodology capable of being integrated in educational institutions in Kazakhstan. Additionally evaluate and comprehensively study the aspects of the methodology based on the work of other authors in the literature review section. The study contains traditional teaching methods such as the use of modern teaching technologies, the use of digital tools, and practical processes during the lesson. In order to understand how familiar students are with the concept of STEM, a survey was conducted among 179 students of Colleges in Almaty. Also, based on the students' responses, a methodological guideline for teachers on the implementation of STEM with an emphasis on chemistry was created and a comparative analysis of two groups was conducted, one of which was taught the STEM methodology (experimental group) based on the methodological guideline and the group that was trained according to the traditional system. At the beginning and end of the training, two groups were tested to compare changes in the results. The results of the test study showed a positive trend in the assimilation of material and memorization in the experimental group, which was trained using the STEM methodology, as well as higher motivation for lessons and full involvement of students. As a result, this work can serve as a practical guide for integrating STEM methodology into the learning process and subsequent improvement for teachers who want to change the teaching format and try new things in teaching, thereby increasing student engagement in the learning process. According to the hypothesis, the introduction of STEM methodology will cause high student engagement and improve the quality of educationItem Open Access Research on a UAV Distance Prediction System Based on Acoustic Data and Deep Learning(SDU University, 2025) Yembergenova A.Unmanned aerial vehicles (UAVs), also referred to as drones, have become increasingly popular in recent years, posing serious security and privacy issues. Concerns have been raised by their growing presence in public areas and civilian life as a result of incidents involving disturbances, privacy invasion, and unauthorised surveillance. This study aims to address these issues by creating an intelligent, sound-based system that can identify drones and determine how close they are to people or sensitive areas. The primary objective of this study was to assess the viability of classifying drone distance based on sound emissions using deep learning models and audio signals. Three zones—Zone 1, Zone 2, and Zone 3—each denoting varying degrees of proximity—were created from the drone sounds. Convolutional neural networks (CNNs), bidirectional long short-term memory networks (BiLSTMs), and a hybrid CNN-BiLSTM model were among the deep learning models examined in the study. With an average classification accuracy of 90%, the hybrid CNN-BiLSTM model outperformed the others. This model is very accurate at predicting drone distance zones because it successfully captured both spatial and temporal features from the audio recordings. These results imply that drone detection systems can be greatly improved by combining deep learning with audio-based classification. Such systems could significantly increase responsiveness and accuracy in detecting unauthorised UAV activity when paired with other sensory inputs in bimodal or multimodal frameworks. All things considered, this research advances acoustic sensing technologies to protect critical infrastructure and public safety from the increasing threat of rogue drone usageItem Open Access Fractal dimension of exceptional sets in semi-regular continued fraction(SDU University, 2025) Duisen S.This thesis investigates the interplay between Diophantine approximation, continued fraction representations, and fractal geometry. We begin by exploring the classical notion of badly approximable numbers-real numbers whose continued fraction expansions have bounded partial quotients. These numbers, while forming a set of zero Lebesgue measure, exhibit full Hausdorff dimension, highlighting their rich geometric structure. Building on this foundation, we introduce and analyze a generalization known as semi-regular continued fractions, wherein a fixed sequence of signs modifies the classical expansion. For such expansions, we define the class of σ-badly approximable numbers and study their distribution and fractal properties. We demonstrate that these generalized expansions preserve many of the geometric complexities of their classical counterparts, while offering new degrees of arithmetic freedom. In the second part of the thesis, we shift our focus to Lehner expansions of real numbers and examine how the statistical behavior of the associated digit sequence (bn) influences the fractal geometry of the corresponding number sets. Specifically, we investigate the impact of the average value of bn on the box dimension-a quantitative measure of geometric complexity. Employing the box-counting method, we perform numerical experiments to estimate the box dimension and uncover how variations in the digit sequence relate to the irregularity and structure of the expansion. By synthesizing the analytical and numerical approaches, this thesis provides a comprehensive view of how modifications to continued fraction representations influence the fractal characteristics of real number sets, contributing to the broader understanding of number-theoretic and geometric interrelations.Item Open Access Mitigating Bias in AI-Based Loan Approval Systems through Fairness-Centric Techniques(SDU University, 2025) Raziyeva S.As artificial intelligence (AI) becomes increasingly embedded in high-stakes decision-making systems, ensuring fairness in algorithmic outcomes has emerged as a critical concern. This thesis investigates bias and fairness in AI-based credit scoring systems, with a particular focus on gender disparities. Using the German Credit Dataset as a case study, the research evaluates the performance and fairness of several supervised machine learning models, including Logistic Regression, Decision Tree, Random Forest, XGBoost, Support Vector Machine, and Neural Network. The study applies fairness metrics such as Statistical Parity Difference (SPD) and Disparate Impact (DI) to assess group-level inequalities in predicted loan approval outcomes. Results reveal a consistent trade-off between model accuracy and fairness, where high-performing models like Random Forest and XGBoost demonstrate notable biases against female applicants. Even interpretable models, such as Logistic Regression, exhibit fairness issues due to historical and structural biases embedded in the training data. To address these challenges, the thesis highlights the importance of incorporating fairness-aware strategies across the machine learning pipeline, including data pre-processing, fairness evaluation, and potential post-processing mitigation. The use of tools like AIF360 and stratified sampling further strengthens the analysis. This research contributes to the growing discourse on responsible AI by demonstrating that achieving fairness is not merely a technical goal but a sociotechnical imperative. It calls for an interdisciplinary approach that combines ethical reasoning, regulatory compliance, and algorithmic transparency to ensure equitable access to financial services. The findings advocate for the development of AI systems that are not only accurate but also accountable and inclusive.Item Open Access Conservative extensions of NIP non dp-minimal theories(SDU University, 2025) Rassayeva N.This dissertation explores conservative extensions in the context of dependent theories (NIP) that are not dp-minimal. We study the model-theoretic properties of the special Cartesian product of ordered structures, focusing on how the dprank and definability of types behave under such constructions. It is shown that the product of two o-minimal or two weakly o-minimal structures yields a theory of dp-rank 2, which remains NIP but is no longer dp-minimal. Further, we analyze the behavior of 1-conservative and n-conservative extensions in these theories. For o-minimal structures, 1-conservativity implies nconservativity for all finite n, ensuring strong definability of types. However, for weakly o-minimal structures, this implication fails; we construct an explicit example where a 1-conservative extension does not extend to a 2-conservative one. The results provide new insights into how model-theoretic complexity measured by dp-rank affects definability and extendability in NIP theories, contributing to the classification and understanding of dependent but non-dp-minimal structures.Item Open Access Expansion of models of DP-minimal theories(SDU University, 2025) Nurlanova A.This study investigates expansions of models of DP-minimal theories, a main subclass of dependent theories in model theory distinguished by well-controlled combinatorial complexity. Finding the circumstances in which DP-minimality is maintained when structures are extended by more predicates, functions, or relations is the main goal of the project. Following a thorough explanation of fundamental ideas like DP-rank, definability, and quantifier elimination, the study examines several extensions of the group of integers (Z, +, 0) and associated ordered algebraic systems. Expansions by linear orders and additional unary or binary predicates are important instances. The findings show that while some expansions lead to superstable but non-DPminimal expansions, others, like those corresponding to Presburger arithmetic (Z, +, <, 0, 1), preserve DP-minimality. By emphasizing the harmony between increased expressive power and minimality condition preservation, these results advance our knowledge of the relationship between model expansions and classification theory. The final section of the dissertation outlines possible avenues for future study, such as applications to ordered structures and broader classes of expansions.Item Open Access Expansion of models of DP-minimal theories(SDU University, 2025) Nurlanova A.This study investigates expansions of models of DP-minimal theories, a main subclass of dependent theories in model theory distinguished by well-controlled combinatorial complexity. Finding the circumstances in which DP-minimality is maintained when structures are extended by more predicates, functions, or relations is the main goal of the project. Following a thorough explanation of fundamental ideas like DP-rank, definability, and quantifier elimination, the study examines several extensions of the group of integers (Z, +, 0) and associated ordered algebraic systems. Expansions by linear orders and additional unary or binary predicates are important instances. The findings show that while some expansions lead to superstable but non-DPminimal expansions, others, like those corresponding to Presburger arithmetic (Z, +, <, 0, 1), preserve DP-minimality. By emphasizing the harmony between increased expressive power and minimality condition preservation, these results advance our knowledge of the relationship between model expansions and classification theory. The final section of the dissertation outlines possible avenues for future study, such as applications to ordered structures and broader classes of expansions.Item Open Access Estimation of Vaccination Price through Mathematical Epidemic Models to Optimize the Government Cost(faculty of engineering and natural sciences, 2021) Dauzhanov Zh.; Avgustov B.; Shakuova D.These days, humanity is faced with a global Coronavirus pandemic problem, which entails a financial crisis, so the governments want to minimize their financial loss. In this project work by using the epidemic mathematical model we consider on the basic reproduction number, which is important parameter in the epidemiology and also on the optimization problem about how much should be a discount for the vaccination to optimize the government revenue. During this study, we get acquainted with the following topics: mathematical modelling, dynamical systems, epidemic models, stability analysis, optimization methods, simulations on software and etc. Initially, we constructed the epidemic model for COVID-19 and separated infectious individuals by two groups, based on the compartmental SIR model and after that by using two different approaches to analyze the model, namely, Linearization (Hartman-Grobman) and Next Generation matrix method, we obtained the most important formula in epidemiology: the basic reproduction number 1.3. To solve the government cost, we constructed the government cost function which takes into account the cost of vaccination, the cost of treatment, the average wage of citizens. By using the software we solved numerically the system of nonlinear differential equations of our epidemic model, also we optimized the governmental cost function depending on a vaccination discount and obtained the main result of applied part of our project work 1.6, that the government cost is minimized with making the vaccination fully free of charge for citizens. The study will be useful for the Government of Kazakhstan in predicting the number of infectious individuals as well as in planning the income revenue. By changing the initial parameters in our epidemic model, it is easy compute the basic reproduction number and Government cost function for any country.Item Open Access Решение дифференциальных уравнений с помощью исскусственных нейронных сетей(faculty of engineering and natural sciences, 2013) Газизов Т.We should note the special role of differential equations in the solution of many problems in mathematics, physics and engineering, as it is not always possible to establish a functional relationship between the data and the variables, but it is often possible to derive a differential equation that allows you to accurately predict the course of a particular process under certain conditions. Differential equations have great practical importance, being a powerful tool for exploring the many problems of science and technology: they are widely used in mechanics, astronomy, physics, in many problems of chemistry and biology. This is because very often the laws that govern certain processes are recorded in the form of differential equations, and the equations themselves act as a mean of quantitative interpretation of thus laws. To solve thus equations we take the most well suited networks belonging to a class of Hopfield neural networks. These networks have a way of transmitting output signals to the inputs, and the response of such networks is dynamic, i.e. after receive a new input the output is calculated and transmitting by feedback network modifies the input. Then the output is recalculated, and the process is repeated again. For the network, which can be considered as stable, the sequence of iterations lead to smaller changes in outputs, and at the end the output does not become permanent. There is also an unstable network, for which the process of selection of the output may never end. That's the essence of the network settings for gaining the desired result. Of course, there is also a classical numerical methods. But there are situations where these methods may not lead to a solution, or it can be obtained for a very large number of iterations. The neural network is much more flexible in this respect, and generally, an algorithm based on them is more efficient.Item Open Access JORDAN ELEMENTS IN ASSOSYMMETRIC ALGEBRAS(faculty of engineering and natural sciences, 2022) Kudaibergen Y.We consider Jordan brackets in a free assosymmetric algebra. We investigate expansions of left-normed Jordan brackets in free assosymmetric algebra and give a conjecture. In general, we show the proposition and some examples then the proof. For associative algebras P.M. Cohn gave a criterion for Jordanian elements generated by three elements, but we further advanced to assosymetrical algebras not with three elements, but with four, and we showed five elements, but we have the degree and the elements are equal. In general, we have shown a special case, but in the end, there are assumptions that it can work on any dimension n.Item Open Access Cardinality of survivor sets in open dynamical systems(faculty of engineering and natural sciences, 2020) Aitu N.In this thesis, our goal is to learn about open dynamical systems corresponding interval maps. We study the class of dynamical systems with holes: Expanding maps of the interval. In detail, We consider symbolic dynamics with holes. Let H-hole lies in the interval [0, 1) and let T : [0, 1) −→ [0, 1) be a self map. The survivor set Ω(H) := {x ∈ [0, 1) : T nx /∈ H, n ≥ 0}. Depending on location and size of the holes we will characterize and study the survivor set Ω(H) infinite or finite, uncountable or countable and survivor set Ω(H) has positive entropy.Item Open Access The prediction of information security level in the enterprise(faculty of engineering and natural sciences, 2020) Khashimova D.This thesis presents the results of an analysis to identify groups of threats specific to the infrastructure and systems of an enterprise, which is one of the main stages in forecasting. The state of information security at enterprises is considered, the qualifications of security threats and classification methods based on attack methods and the impact of threats are analyzed. Threats for the safe use of the Internet and hacking sites, data theft, phishing attacks and social engineering are assessed; Identification of cloud computing security threats that are encountered in the enterprise's Internet networks. The advantages and disadvantages of Web Application Firewall, which are used to protect attacks, such as DDoS attacks, SQL injections, cross-site scripting, and others, are studied. Works for providing protection using artificial intelligence and machine learning are presented.