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Item Open Access Applications of Otelbaev's Abstract Theorem to singular ODES(SDU University, 2026) Zhumabayeva A.This research focuses on analyzing well-posedness of a singular hyperbolic equation with time-varying coefficients, defined on a multidimensional cylindrical domain. Using the spectral decomposition method, the original problem was reduced to a family of one-dimensional singular differential equations. Furthermore, a comprehensive matrix representation of all regular regular boundary conditions is derived through the M. Otelbaev’s abstract theorem and the Riesz theorem. Finally, the existence and uniqueness of the solution for the original two-dimensional equation is established in the within weighted Sobolev space.Item Open Access Investigating Knowledge Graphs for Context-Aware Search in Financial Transactional AI Agents(SDU University, 2026) Baisenkul N.This thesis presents an empirical evaluation of a hybrid knowledge-graph and largelanguage-model (KG–LLM) architecture for financial transactional compliance reasoning. The architecture was proposed in a companion conference paper [1] that established the design and demonstrated it on a small worked example; the contribution of this thesis is the quantitative, ablation-based, robustness-aware empirical study that completes the proposal. A deterministic synthetic dataset of 500 transactions across eight compliance-rule scenarios plus a clean negative class is generated under two complementary disciplines: a crossrule labeling pass that mirrors how real anti-money-laundering pipelines assign overall compliance, and an explicit per-channel audit of base-context fields for label-correlated content (which uncovered, and fixed, a substantial description-field scenario-leakage problem in the dataset’s earlier versions; the empirical impact of the leakage and the corrected results are reported throughout). A four-arm ablation matrix isolates the contribution of structured KG relations by varying only the grounding mode supplied to the language model. A parametric fifth arm sweeps per-transaction KG coverage from 100 % down to 0 % to characterise the architecture’s degradation under realistic incomplete-graph conditions. On the corrected, description-neutral dataset, the KG-augmented arm achieves accuracy 0.891 with perfect precision (1.000, zero wrongly-cleared violations across 1500 predictions), recall 0.691, and F1 0.817 across three independent repeats. Both no-KG baselines—a vanilla LLM and a rule-text-grounded LLM—collapse to majority-class-default behaviour at F1 of approximately 0.01, so the architecture roughly fifty-fold lifts F1 relative to the baselines while never wrongly clearing a violation. The KG-augmented arm’s accuracy advantage degrades smoothly with KG coverage and disappears at coverage below approximately 20 % (the dropout sweep crosses the no-KG baseline at p ∗ ≈ 0.81). The methodological contributions of the work include the rule-name neutrality discipline—a previously-undocumented prompt-design pitfall whereby loaded rule identifiers override structured per-rule relations in language-model reasoning, identified during the project’s first benchmark and described in detail as finding F-001 in the project record—and the description-channel audit protocol (F-007) that the thesis argues should be a default hygiene step in any synthetic-data pipeline feeding a language model.Item Open Access Solving fractional differential equation with Riemann-Liouville fractional derivatives using the Laplace transform(SDU University, 2026) Zhamalbekova K.Thanks to their ability to capture memory effects in different phenomena, fractional differential equations have become a widely used method in many areas of physics, engineering and applied sciences. This thesis investigates the application of the Laplace transform technique for solving fractional differential equations involving the Riemann–Liouville fractional operator. The study begins with a concise review of fractional calculus theory, with particular emphasis on the definition and properties of the Riemann–Liouville fractional derivative. The Laplace transform is then described as a convenient tool to handle operators of non-integer order. The integration of these two tools enables the development of a systematic technique that transforms the original fractional differential equation into an algebraic equation, thereby facilitating its solution. Solutions to several classes of fractional linear equations are found using Laplace transformations.Many examples show the efficiency of the approach proposed. The results indicate that employing the Laplace transform technique facilitates the solution of fractional differential equations involving the Riemann-Liouville fractional derivative. All things considered, this thesis makes a contribution to the theory of solving fractional differential equations analytically and highlights the effectiveness of Laplace transformation in this case.Item Open Access Moduli of smoothness and growth properties of Hartley transform(SDU University, 2026) Ozbek U.This study analyzes how the moduli of smoothness of functions influence the behavior of their Hartley transforms. While harmonic analysis has historically centered on the Fourier transform, the Hartley transform offers a computationally efficient, real-valued alternative for processing real data. The analysis establishes key results, including variants of the Riemann–Lebesgue lemma adapted to the Hartley transform context, the Parseval identity, and the proof of the Hausdorff–Young inequality applicable in Euclidean spaces. By employing the symmetric difference operator, we derive weighted estimates that link the smoothness properties of a function, measured by higher-order moduli of smoothness, to the decay rates of its Hartley transform. Additionally, the investigation extends to Hartley series on the torus, where conditions for convergence and decay of coefficients are formulated through the corresponding moduli of smoothness..Item Open Access Collaborative Multi-Agent Chatbot Framework for Intelligent Tutoring and Feedback(SDU University, 2026) Myrzaliyeva Zh.Intelligent Tutoring Systems (ITS) seek to deliver a personalized approach akin to one-on-one human tutoring. The advent of large language models (LLMs) makes it possible to create conversational tutoring systems at a reasonable scale. Nevertheless, despite some recent advances, single-agent LLM-based tutoring still suffers from problems such as inaccuracies, varying quality of the pedagogical content, and low self-correction ability. In this dissertation, a Collaborative Multi-Agent Chatbot Framework (CMACF) for ITS and assessments is presented and evaluated. The system includes three agents: Tutor Agent, which generates adaptive explanations; Feedback Agent, which detects and corrects any potential misunderstandings; and Verifier Agent, which validates and optimizes responses prior to their delivery to the learner during Java programming lessons. For testing, the framework was used to perform 40 different Java tasks in the following domains: loops, conditionals, arrays, object-oriented programming, exceptions, and typecasting. A comparison between three frameworks was conducted based on three scenarios: single-agent system (SA), multi-agent system without verification (MA-NV), and the proposed multi-agentsystem with verification (MAV). The criteria applied included correctness, clarity, pedagogy, actionability, and consistency of responses. It can be concluded that the proposed model resulted in the best scores (4.52 points) and surpassed both the single-agent solution (4.165) and the multi-agent solution without verification (4.215). In addition, 25% of generated responses were subject to changes due to the verification component and improved task completion rate from 17.5% to 52.5%. Although the response generation time of MA-V (11.1 seconds) exceeded the single-agent solution (3.66 seconds), its quality is sufficient for intelligent tutoring purposes.Item Open Access Numerical Methods for HJB Equations in Option Pricing with Greek Sensitivities(SDU University, 2026) Berikbayev K.Usually, optimal control problems in financial mathematics are solved by maximizing profit and using the Hamilton-Jacobi-Bellman equation. This leads to nonlinear PDE, the solution of which is based on numerical methods. In this paper, we use the method described in the article by Christara and Wu: second-order finite differences on a non-uniform grid. However, instead of the long position discussed there, we study the short position. Therefore, here too we use the same time step, calculated using the Crank-Nicolson-Rannacher method, and we employ an iterative solver with a penalty term. The nonuniform grid puts more nodes near the strike price. This is important for keeping second-order convergence when the straddle payoff is not smooth. Rannacher smoothing at the first time steps helps remove unwanted oscillations from the kink in the initial condition. The nonlinear penalty-like term comes from the optimal control in the stock borrowing fee model. We solve it at each time step with a Newton-type iterative algorithm that uses two stopping criteria. Our numerical tests show secondorder convergence for the short position. The results agree with the benchmarks of Forsyth and Labahn and also Christara and Wu. The main result of this work is the numerical calculation of the Greeks for this nonlinear HJB model: Delta, Gamma, and Theta. As far as we know, there is no other full numerical study of the Greeks for the short position using finite differences on HJB problems. This is the main applied result of our work.Item Open Access Quality-Adaptive Multimodal Face Recognition with Streaming Prototype Learning and CrossModal Evaluation(SDU University, 2026) Anarbayeva D.While state-of-the-art face recognition systems achieve near-perfect accuracy under ideal conditions, their performance degrades significantly in real-world conditions when the input images are blurred, noisy, have partially-occluded faces, or are of low resolution. Multi-modal face recognition systems that combine visible-spectrum, near-infrared (NIR), and depth sensor inputs tend to exhibit even greater performance degradation under these conditions because each sensor modality suffers degradation in different ways. In this dissertation, we consider three main problems with current multi-modal face recognition systems: estimating the quality of the input images from each sensor modality, weighting the inputs according to their estimated quality, and maintaining the identity galleries within the recognition systems in an efficient manner. A new quality estimation function Q(I)is proposed for each input image I that utilises noisecorrected sharpness, noise level, face coverage, and contrast to provide a score that represents the quality of the image without requiring training data. When evaluated on the LFW face dataset with synthetic image degradations, the quality estimates have a Spearman rank correlation coefficient ρ of 0.90 or higher for all four types of image degradation, while the baseline method based on the variance of the Laplacian kernel has a negative correlation with certain types of degradation. When incorporating the quality score estimates into the fusion of visible-spectrum, NIR, and depth sensor recognition results, the system achieves up to a 4.4 percentage point improvement in Rank-1 recognition accuracy under degraded NIR inputs. A streaming framework for updating the identity galleries that utilises an exponential moving average with a momentum value of 0.9 and reservoir sampling achieves the same accuracy as full retraining of the model using only 49% of the computational cost, and utilises only the embedding vectors of the faces rather than the raw face images. A fairness audit of the system on the FairFace dataset reveals a null result in relation to the fairness metric, suggesting future work on this topic. All experiments utilised publicly available datasets and models, and the code for implementing the proposed methods is provided as a publicly available repository.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.