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Item Open Access PRINCIPAL COMPONENT ANALYSIS AND A MULTILINGUAL CONSTRUCT TO DETERMINE THE UNDERGRADUATE MAJOR SELECTION FACTORS(СДУ хабаршысы - 2020, 2020) Assanbayeva G. ; Kadyrov Sh.Abstract. In this article, we review mathematics behind well-known Principal Component Analysis from Linear Algebra implemented in various applied fields. As an application, we develop a construct to measure factors that affect college students in their major selection. This is a multilingual construct given in three languages, namely Kazakh, Russian, and English. To this end, we prepare a survey consisting of 27 Likert scale items in three languages and it is conducted among 314 undergraduate students in Kazakhstan. For dimensionality reduction, Principal Component Analysis is carried in python programming language which resulted in 9 major scales with only 22 elements. The overall reliability of the test is calculated to be 0,856. The nine scales are the effect of Uniform National Testing, state grant affect, personal interest affect, skills affect, occupation salary affect, teacher affect, external affect, university cost affect, parent’s affect.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 Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device(Applied and Computational Mechanics, 2017) Wei D.; Kadyrov Sh.; Kazbek Z.Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.Item Open Access DIOPHANTINE APPROXIMATION WITH RESTRICTED NUMERATORS AND DENOMINATORS ON SEMISIMPLE GROUPS(arXivLabs, 2014) Gorodnik A.; Kadyrov Sh.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 Automated Reading Detection in an Online Exam(International Journal of Emerging Technologies in Learning (iJET), 2022) Bakhitzhan K.; Kadyrov Sh.; Makhmutova A.In this article we study a deep learning-based reading detection problem in an online exam proctoring. Pandemia-related restrictions and lockdowns lead many educational institutions to go online learning environment. It brought the exam integrity challenge to an online test-taking process. While various commercial exam proctoring solutions were developed, the online proctoring challenge is far from being fully addressed. This article is devoted to making a contribution to the exam proctoring system by proposing an automated test-taker reading detection method. To this end, we obtain our own dataset of short video clips that resemble a real online examination environment and different video augmentation methods utilized to increase the training dataset. Two different deep learning techniques are adapted for training. The experiments show quite satisfactory results with model accuracy varying from 98.46% to 100%. The findings of the article can help educational institutions to improve their online exam proctoring solutions, especially in language speaking tests.Item Open Access Mathematical modeling of infectious diseases and the impact of vaccination strategies(Mathematical Biosciences and Engineering, 2024) Bolatova D.; Kadyrov Sh.; Kashkynbayev A.Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number R0 compared to pulse vaccination. By analyzing key parameters such as R0 , pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaksItem Open Access ENTROPY AND ESCAPE OF MASS FOR SL3(Z)\ SL3(R)(arXivLabs, 2010) Einsiedler M.; Kadyrov Sh.We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices.Item Open Access 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 Open Access 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 Open Access PRINCIPAL COMPONENT ANALYSIS AND A MULTILINGUAL CONSTRUCT TO DETERMINE THE UNDERGRADUATE MAJOR SELECTION FACTORS(SDU Bulletin: Natural and Technical Sciences, 2020) Assanbayeva G.; Kadyrov Sh.In this article, we review mathematics behind well-known Principal Component Analysis from Linear Algebra implemented in various applied fields. As an application, we develop a construct to measure factors that affect college students in their major selection. This is a multilingual construct given in three languages, namely Kazakh, Russian, and English. To this end, we prepare a survey consisting of 27 Likert scale items in three languages and it is conducted among 314 undergraduate students in Kazakhstan. For dimensionality reduction, Principal Component Analysis is carried in python programming language which resulted in 9 major scales with only 22 elements. The overall reliability of the test is calculated to be 0,856. The nine scales are the effect of Uniform National Testing, state grant affect, personal interest affect, skills affect, occupation salary affect, teacher affect, external affect, university cost affect, parent’s affect.