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Item 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 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 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 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 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 CORRELATION BETWEEN OIL PRICES AND CURRENCY EXCHANGE RATES.(СДУ хабаршысы - 2018, 2018) Abdimanapov D. ; Kadyrov Sh. ; Rozakhunova E.Abstract. In this article, we study how oil prices affect the USD vs. KZT exchange rates. Our methods base on elementary statistical data analysis. For this purpose, we collect Brent oil prices and US dollar exchange rates in Kazakh tenge for entire year of 2016, in a weekly basis. Our findings suggest that there is a strong correlation between two variables. Besides, we use simple linear regression analysis to provide a formula that predicts the USD rate given the oil price. To make the paper accessible to High school students, we keep most of the analysis as elementary as possible and self-contained.Item Open Access EFFECTIVE EQUIDISTRIBUTION OF PERIODIC ORBITS FOR SUBSHIFTS OF FINITE TYPE(arXivLabs, 2016) Kadyrov Sh.We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic diffeomorphisms and expanding maps on compact manifolds.Item Open Access LAGRANGE’S THEOREM AND 2- CONTINUED FRACTION EXPANSION(СДУ хабаршысы - 2019, 2019) Kadyrov Sh. ; Mashurov F.Abstract. The simple continued fraction theory is a sub-branch of number theory that is well developed. One of the classical results is due to Lagrange which states that the simple continued fraction expansion of a real number has eventually periodic expansion if and only if it is quadratic irrational. Similar results are not available when one considers N-continued fraction expansion which is not so well developed theory. In this article, authors aim to provide computational evidence when a quadratic irrational may not necessarily have eventually periodic 2-continued fraction expansion. Moreover, a proof is provided for a special type of real numbers for which Lagrange’s theorem does hold.