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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.
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.
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 outbreaks
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.
A DECENTRALIZED, LOW COMPUTATIONAL COST STRATEGY FOR COORDINATION AND SEARCH WITH A ROBOT FLOCK
(Journal of Theoretical and Applied Information Technology, 2021) FREDY H.; MARTÍNEZ S.
The coordination of a flock of robots is a high demand application in applications such as motion planning, navigation, herding (tracking and/or tracing), area coverage (exploration, search and rescue, etc.), object transportation (surrounding and moving together), and compound tasks, all of which are currently heavily researched in robotics. Many approaches have been proposed to solve this problem, but they largely compromise system characteristics such as fault tolerance, capacity, efficiency, and in particular cost, since real implementations require special hardware. This paper proposes a coordination strategy for a system composed of small robots of minimalist design under the condition of minimum processing and sensing capacity. The communication requirements have been limited to a local communication strategy sufficient to achieve the relative orientation of each swarm member. The usefulness of the scheme is evaluated by simulation in specialized search tasks in an unknown region. The results show the high capability of the scheme and the ease of implementation on real prototypes.