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This study aimed to investigate Kyrgyz learners' engagement in online courses. In this respect, the Student Engagement Scale and appropriate open-ended questions were employed in order to obtain data from learners. The sample covers 400 undergraduate learners studying at Kyrgyz-Turkish Manas University. The study has a mixed research design, hence both quantitative and qualitative approaches were employed. The results of the study revealed that behavioral engagement has a significant effect on learner achievement. The study also demonstrated that the engagement of Kyrgyz learners in online cou ...Более
Asymptotic study of singularly perturbed differential equations of hyperbolic type has received relatively little attention from researchers. In this paper, the asymptotic solution of the singularly perturbed Cauchy problem for a hyperbolic system is constructed. In addition, the regularization method for singularly perturbed problems of S. A. Lomov is used for the first time for the asymptotic solution of a hyperbolic system. It is shown that this approach greatly simplifies the construction of the asymptotics of the solution for singularly perturbed differential equations of hyperbolic type.
In this study, we consider an optimal control problem for an Euler-Bernoulli beam equation. The initial velocity of the system is given by the control function. We give sufficient conditions for the existence of a unique solution of the hyperbolic system and prove that the optimal solution for the considered optimal control problem is exists and unique. After obtaining the Frechet derivative of the cost functional via an adjoint problem, we also give an iteration algorithm for the numerical solution of the problem by using the Gradient method. Finally, we furnish some numerical examples to dem ...Более
In this paper, we compute H.-norm of a transfer matrix, via bisection algorithm. The algorithm is given and applied some problems. The problems are choosen from various areas of control theory such as aircraft models and decentralized interconnected systems.
A numerical solution of the system of linear Volterra–Stieltjes integral equations of the second kind has been found and analyzed using the so-called generalized trapezoid rule. Conditions for estimating the error have also been determined and justified. A solution of an example obtained using the proposed method is given.
The problem of integrability of ordinary differential equations to find their exact solutions is a celebrated problem in the theory of differential equations which attracted attention of several workers in the area. This is due to the fact that: (a) differential equations are the most widely used continuous models of dynamic systems in physics, medicine, economics, biology and other sciences that study the surrounding reality, for which the explicit trajectory of the dynamic system's behavior is important as the explicit solution contains in itself the maximum information about the behavior of ...Более
In this paper, we define a subclass of analytic functions by denote (Formula Presented) satisfying the following subordinate condition (Formula Presented) where (Formula Presented). We give coefficient estimates and Fekete-Szegö inequality for functions belonging to this subclass.
One of the biggest problems of modern mathematics is, to a large extent, its isolation from the world around it. Extensive use of linear difference equations can make a great contribution to solving this problem. In the language of these equations, the problems of financial mathematics are beautifully presented. And as can be understood from the study of difference equations, this is by no means their only advantage. In particular, there is a direct connection between the theory of linear difference equations and the theory of linear ordinary differential equations. Therefore, we are convinced ...Более
In this paper we construct the asymptotics of the solution of the Cauchy problem for a singularly perturbed hyperbolic system by using the regularization method for singularly perturbed problems of S.A. Lomov. The regularization method for singularly perturbed problems of S.A. Lomov is used for the first time to construct the asymptotic solution of a hyperbolic system.
It is becoming necessary to examine learners’ use of and experiences with virtual laboratories. Learners’ interest and motivation to use virtual laboratories are important factors for the success of these platforms. This study was conducted to analyze Kyrgyz learners’ use of virtual laboratories in a physics course at the university level. The study was performed in the 2019–2020 spring term at a state university in Kyrgyzstan. The study took a quantitative approach, with 376 Kyrgyz learner participants studying at the undergraduate level. The participants were divided into three groups: the f ...Более
The solvability of synthesis problem of external and boundary controls is investigated for optimization of oscillation process, described by partial differential equations with Fredholm integral operator. Functions of the external and boundary actions are nonlinearly with respect to control. An integro-differential equation is obtained in the specific type for Bellman functional. An algorithm is developed for constructing solutions to synthesis problem of external and boundary controls.
Keywords: Generalized solution, Bellman functional, Frechet differential, Integro-differential equation, Fre ...Более