3. Articles and Papers
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Item Open Access On the solutions of second order difference equations with variable coefficients(faculty of engineering and natural sciences, 2024) Shynarbekb N.; Shynarbekb N.; Orynbassar A.In this article, we explore solutions to second-order linear difference equations featuring variable coefficients. By imposing mild conditions, we present closed-form solutions through the utilization of finite continued fraction representations. The proof of our results relies on elementary techniques, specifically involving factoring a quadratic shift operator. As a consequential application, we unveil two novel generalized continued fraction formulas for the mathematical constant π 2 .Item Open Access DEVELOPMENT AND OPTIMIZATION OF PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS(Vol. 1 No. 1 (2025): Journal of Emerging Technologies and Computing (JETC), 2025) Sharimbayev B.; Kadyrov Sh.; Kavokin A.This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on one-dimensional and two-dimensional Poisson equations suggests that FDM gives far more accurate results with a relative error of 7.26 × 10-8 and 2.21 × 10-4 , respectively, in comparison with PINNs, with an error of 5.63 × 10-6 and 6.01 × 10-3 accordingly. Besides forward problems, PINN is realized also for forward-inverse problems which reflect its ability to predict source term after its sufficient training. Visualization of the solution underlines different methodologies adopted by FDM and PINNs, yielding useful insights into their performance and applicabilityItem Open Access 2D face recognition using PCA and triplet similarity embedding(Bulletin of Electrical Engineering and Informatics, 2023) Bazatbekov B.; Turan C.; Kadyrov Sh.; Aitimov A.The aim of this study is to propose a new robust face recognition algorithm by combining principal component analysis (PCA), Triplet Similarity Embedding based technique and Projection as a similarity metric at the different stages of the recognition processes. The main idea is to use PCA for feature extraction and dimensionality reduction, then train the triplet similarity embedding to accommodate changes in the facial poses, and finally use orthogonal projection as a similarity metric for classification. We use the open source ORL dataset to conduct the experiments to find the recognition rates of the proposed algorithm and compare them to the performance of one of the very well-known machine learning algorithms k-Nearest Neighbor classifier. Our experimental results show that the proposed model outperforms the kNN. Moreover, when the training set is smaller than the test set, the performance contribution of triplet similarity embedding during the learning phase becomes more visible compared to without it.Item Open Access A novel recommender system for adapting single machine problems to distributed systems within MapReduce(Bulletin of Electrical Engineering and Informatics, 2024) Orynbekova K.; Kadyrov Sh.; Bogdanchikov A.; Oktamov S.This research introduces a novel recommender system for adapting singlemachine problems to distributed systems within the MapReduce (MR) framework, integrating knowledge and text-based approaches. Categorizing common problems by five MR categories, the study develops and tests a tutorial with promising results. Expanding the dataset, machine learning models recommend solutions for distributed systems. Results demonstrate the logistic regression model's effectiveness, with a hybrid approach showing adaptability. The study contributes to advancing the adaptation of single-machine problems to distributed systems MR, presenting a novel framework for tailored recommendations, thereby enhancing scalability and efficiency in data processing workflows. Additionally, it fosters innovation in distributed computing paradigms.Item Unknown Factors Affecting Mathematics Achievement in Central Asian Specialized Universities(International Journal of Emerging Technologies in Learning (iJET), 2020) Sapazhanov Y.; Sydykhov B.; Kadyrov Sh.; Orynbassar A.This study examines variables explaining student’s academic performances in mathematics from the specialized engineering institutions. A survey consisting of 42 items was conducted from 127 students and statistical multiple regression was carried out to analyze the data set. Based on FennemaSherman Mathematic Attitude Scales followed by the result of stepwise linear regression, found a significant impact of high school geometry grades in the mathematics performance. Authors suggest that mathematics instructors in higher education should pay attention to improve their student’s confidence, which in turn would decrease the anxiety level towards mathematics. The high school teachers should not advise their students to go to technical sciences in higher education unless the student’s confidence and high school math grade are sufficiently high.Item Unknown CANTOR SETS AND TOTAL SELF-SIMILARITY(ISCIENCE.IN.UA «Актуальные научные исследования в современном мире», 2025) Kadyrov Sh.; Keulimzhayev A.We study overlapping Cantor sets with parameter and classify the situations when these fractal sets are totally self-similar. More precisely, we consider iterated function system consisting of three functions , and and the fractal set it generates in the real line. We define what totally self-similar means and show for that the fractal set is totally self-similar if and only if it is in the form for some positive integer . We mainly rely on the recent work of Dajani, Kong, and Yao where they consider the analogous problem for .Item Unknown Endemic coexistence and competition of virus variants under partial cross-immunity(AIMS Electronic ResearchArchive, 2025) Kadyrov Sh.; Haydarov F.; Mamayusupov K.; Mustayev K.In this study, we developed a mathematical framework, based on the SIR model, to study the dynamics of two competing virus variants with different characteristics of transmissibility, immune escape, and cross-immunity. The model includes variant-specific transmission and recovery rates and enables flexible parameterization of partial and waning cross-immunity. We conducted stability and bifurcation analyses and numerical simulations to explore the conditions of coexistence, dominance, and extinction of the variants, studying variations in epidemiological parameters that affect endemic prevalence and infection ratios. Our results indicated that transmission rates, levels of crossimmunity, and immunity waning rates are critical in determining disease outcomes, which influence variant prevalence and competitive dynamics. The sensitivity analysis provided the relative importance of these parameters and provided valuable insight into designing intervention strategies. This work contributes to furthering our understanding of multi-variant epidemic dynamics and lays the bedrock for tackling complex interactions involving arising virus variants, finding applications in real-world public health planning.Item Unknown Exceptional sets in homogeneous spaces and Hausdorff dimension(Dynamical Systems An International Journal, 2015) Kadyrov Sh.In this paper, we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable flows in compact homogeneous spaces X to show that the Hausdorff dimension of set of points that lie on trajectories missing a particular open ball of radius r is at most dim X + C rdim X log r , where C > 0 is a constant independent of r > 0. Meanwhile, we also describe a general method for computing the least cardinality of open covers of dynamical sets using volume estimates.Item Unknown Plagiarism types and detection methods: a systematic survey of algorithms in text analysis(Frontiers in Computer Science, 2025) Makhmutova A.; Turan C.; Amirzhanov A.Plagiarism in academic and creative writing continues to be a significant challenge, driven by the exponential growth of digital content. This paper presents a systematic survey of various types of plagiarism and the detection algorithms employed in text analysis. We categorize plagiarism into distinct types, including verbatim, paraphrasing, translation, and idea-based plagiarism, discussing the nuances that make detection complex. This survey critically evaluates existing literature, contrasting traditional methods like string-matching with advanced machine learning, natural language processing, and deep learning approaches. We highlight notable works focusing on cross-language plagiarism detection, source code plagiarism, and intrinsic detection techniques, identifying their contributions and limitations. Additionally, this paper explores emerging challenges such as detecting cross-language plagiarism and AI-generated content. By synthesizing the current landscape and emphasizing recent advancements, we aim to guide future research directions and enhance the robustness of plagiarism detection systems across various domains.Item Unknown Semi-Regular Continued Fractions with Fast-Growing Partial Quotients(MDPI Journal, 2024) Mashurov F.; Kadyrov Sh.; Kazin A.In number theory, continued fractions are essential tools because they provide distinct representations of real numbers and provide information about their characteristics. Regular continued fractions have been examined in great detail, but less research has been carried out on their semi-regular counterparts, which are produced from the sequences of alternating plus and minus ones. In this study, we investigate the structure and features of semi-regular continuous fractions through the lens of dimension theory. We prove a primary result about the Hausdorff dimension of number sets whose partial quotients increase more quickly than a given pace. Furthermore, we conduct numerical analyses to illustrate the differences between regular and semi-regular continued fractions, shedding light on potential future directions in this field.Item Unknown Unified computational approach to nilpotent algebra classification problems(Sciendo Journal, 2021) Kadyrov Sh.; Mashurov F.In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.Item Unknown IMPACT OF THE ACTIVE LEARNING STRATEGIES ON STUDENT’S ACHIEVEMENT WITH RESPECT TO DOUBLE INTEGRALS IN MATHEMATICAL ANALYSIS(Қазақ ұлттық қыздар педагогикалық университетінің Хабаршысы № 3, 2019) Almas A.; Kadyrov Sh.; Kaymak S.Active learning is useful to engage and make an interest for the students in learning of mathematics, where the educators face many difficulties in teaching mathematics. This paper aims to address how to apply active learning strategies on the subject of double integral in advanced mathematics. We chose some suitable active learning strategies for using in the subject of double integral to show its designs. We also applied the active learning strategies which is shown in the introduction part for two groups from second year students in the faculty of science education at Suleiman Demirel University to reveal the of impact of achievement on the students. Comparing the achievement of experimental group to the control group, the authors deduce that the experimental group significantly outperform than the control group in the subject of double integral in mathematical analysisItem Unknown Diophantine approximation with restricted numerators and denominators on semisimple groups(Journal de Théorie des Nombres de Bordeaux 29, 2017) Kadyrov Sh.; Gorodnik A.We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.Item Open Access Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems(John Wiley & Sons, Ltd, 2020) Kashkynbayev A.; Skrzypacz P.; Kadyrov Sh.; Kaloudis K.; Bountis A.We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n>1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS modelsItem Open Access Application of ROC Curve Analysis for Predicting Students’ Passing Grade in a Course Based on Prerequisite Grades(MDPI Mathematics, 2022) Orynbassar A.; Sapazhanov Y.; Kadyrov Sh.; Lyublinskaya I.Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course in a sequence. This method was tested on a dataset of Calculus 1 and Calculus 2 grades of 164 undergraduate students majoring in mathematics at a private university in Kazakhstan. The results showed that while the currently used practice of setting prerequisite grade requirements is accurately identifying successful completions of Calculus 2, the ROC method is more accurate in identifying possible failures in Calculus 2. The findings also indicate that prior completion of Calculus 1 is positively associated with success in a Calculus 2 course. Thus, this study contributes to the field of mathematics education by providing a new data-driven methodology for determining the optimal threshold grade for mathematics prerequisite courses.Item Open Access SINGULAR SYSTEMS OF LINEAR FORMS AND NON-ESCAPE OF MASS IN THE SPACE OF LATTICES(JOURNAL D’ANALYSE MATHEMATIQUE, Vol. 133, 2017) Kadyrov S.; Kleinbock D.; Lindenstrauss E.; Margulis G.A.Singular systems of linear forms were introduced by Khintchine in the 1920s, and it was shown by Dani in the 1980s that they are in one-to-one correspondence with certain divergent orbits of one-parameter diagonal groups on the space of lattices. We give a (conjecturally sharp) upper bound on the Hausdorff dimension of the set of singular systems of linear forms (equivalently, the set of lattices with divergent trajectories) as well as the dimension of the set of lattices with trajectories “escaping on average” (a notion weaker than divergence). This extends work by Cheung, as well as by Chevallier and Cheung. Our method differs considerably from that of Cheung and Chevallier and is based on the technique of integral inequalities developed by Eskin, Margulis and Mozes.Item Open Access ESCAPE OF MASS AND ENTROPY FOR DIAGONAL FLOWS IN REAL RANK ONE SITUATIONS(ISRAEL JOURNAL OF MATHEMATICS, 2014) Einsiedler M.; Kadyrov S.; Pohl A.Let G be a connected semisimple Lie group of real rank 1 with finite center, let Γ be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space Γ\G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full.Item Open Access Modeling tuberculosis transmission dynamics in Kazakhstan using SARIMA and SIR models(Scientific Reports, 2024) Kalizhanova A.; Yerdessov S.; Sakko Y.; Kadyrov Sh.; Gaipov A.; Kashkynbayev A.Tuberculosis (TB) is a highly contagious disease that remains a global concern affecting numerous countries. Kazakhstan has been facing considerable challenges in TB prevention and treatment for decades. This study aims to understand TB transmission dynamics by developing and comparing statistical and deterministic models: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the basic Susceptible-Infected-Recovered (SIR). TB data from 2014 to 2019 were collected from the Unified National Electronic Health System (UNEHS) using retrospective quantitative analysis. SARIMA models were able to capture seasonal variations, with Model 2 exhibiting superior predictive accuracy. Both models showed declining TB incidence and revealed a notable predictive performance evaluated by statistical metrics. In addition, the SIR model calculated the basic reproduction number (R0) below 1, indicating a receding epidemic. Models proved the capability of each to accurately capture trends (SARIMA) and provide mathematical insights (SIR) into TB transmission dynamics. This study contributes to the general knowledge of TB transmission dynamics in Kazakhstan thus laying the foundation for more comprehensive studies on TB and control strategies.Item Open Access Fractal Dimension of Exceptional Sets in Semi-Regular Continued Fractions(faculty of engineering and natural sciences, 2025) Kadyrov Sh.; Kazin A.; Duisen S.This paper examines how the average value of the sequence bn in the Lehner expansion of a real number x influences its box dimension. Our primary objective is to analyze how variations in the average of bn impact the box dimension, which serves as a measure of the complexity of the sequence. Using the box-counting method, we numerically estimate the box dimension and explore its relationship with the fractal nature of Lehner expansions.Item Open Access Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems(Mathematical Methods in the Applied Sciences, 2020) Kadyrov Sh.; Kashkynbayev A.; Skrzypacz P.; Kaloudis K.; Bountis A.We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n>1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS models.