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Item Open Access MapReduce Solutions Classification by Their Implementation(The International Journal of Engineering Pedagogy (iJEP), 2023) Orynbekova K.; Bogdanchikov A.; Cankurt S.; Adamov A.; Kadyrov Sh.Distributed Systems are widely used in industrial projects and scientific research. The Apache Hadoop environment, which works on the MapReduce paradigm, lost popularity because new, modern tools were developed. For example, Apache Spark is preferred in some cases since it uses RAM resources to hold intermediate calculations; therefore, it works faster and is easier to use. In order to take full advantage of it, users must think about the MapReduce concept. In this paper, a usual solution and MapReduce solution of ten problems were compared by their pseudocodes and categorized into five groups. According to these groups’ descriptions and pseudocodes, readers can get a concept of MapReduce without taking specific courses. This paper proposes a five-category classification methodology to help distributed-system users learn the MapReduce paradigm fast. The proposed methodology is illustrated with ten tasks. Furthermore, statistical analysis is carried out to test if the proposed classification methodology affects learner performance. The results of this study indicate that the proposed model outperforms the traditional approach with statistical significance, as evidenced by a p-value of less than 0.05. The policy implication is that educational institutions and organizations could adopt the proposed classification methodology to help learners and employees acquire the necessary knowledge and skills to use distributed systems effectively.Item Open Access 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 Open Access ENTROPY AND ESCAPE OF MASS FOR HILBERT MODULAR SPACES(arXivLabs, 2011) Kadyrov Sh.We study the relation between metric entropy and escape of mass for the Hilbert modular spaces with the action of a diagonal element.Item Open Access 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 Open Access Purely data-driven exploration of COVID-19 pandemic after three months of the outbreak(medRxiv, 2020) Saydaliev H.B.; Kadyrov Sh.It has been three months since the novel coronavirus (COVID-19) pandemic outbreak. Many research studies were carried to understand its epidemiological characteristics in the early phase of the disease outbreak. The current study is yet another contribution to better understand the disease properties by parameter estimation of mathematical SIR epidemic modeling. The authors use Johns Hopkins University’s dataset to estimate the basic reproduction number of COVID-19 for representative countries (Japan, Germany, Italy, France, and Netherlands) selected using cluster analysis. As a by-product, the authors estimate transmission, recovery, and death rates for each selected country and carry statistical tests to see if there are any significant differencesItem 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.Item Open Access 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 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 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 models