Vol. 1 No. 2.1 (2023): Special Issue – Mathematical Models and Applications

This special issue of Journal of AppliedMath focuses on mathematical models and applications. These topics are related to social focus and some classic physical problems. These mathematical models can not only explain specific phenomena, extract useful data from them, and assist individuals in solving related practical problems, but they can also promote the development of certain fields. 

  • Open Access

    Article

    Article ID: 69

    Optimization imposition upon drone gimbal control electronics

    by Erhe Zheng, Timothy Sands

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 313 Views, 42 PDF Downloads

    The goal of the manuscript is to design a relatively good control structure for the noise suppression of a drone’s camera gimbal action. The gimbal’s movement can be simplified as a rest-to-rest reorientation system that can achieve the boundary result of a dynamic system. Six different control architectures are proposed and evaluated based on their ability to control the trajectory of the dynamic-system position and speed, their running time, and their quadratic cost. The robustness of the control architecture to uncertainties in inertia and sensor noise is also analyzed. Monte Carlo figures are used to assess the performance of the six control systems. The conditions for applying different architectures are identified through this analysis. The analysis and experimental tests reveal the most suitable control of the drone’s camera gimbal rotation.

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  • Open Access

    Article

    Article ID: 109

    Impact analysis of correlated and non-normal errors in nonparametric regression estimation: A simulation study

    by Javaria Ahmad Khan, Atif Akbar, Nasir Saleem, Muhammad Junaid

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 180 Views, 33 PDF Downloads

    In nonparametric regression, the correlation of errors can have important consequences for the statistical properties of the estimators, but the focus is on the on the identification of the effect on Average Mean Squared Error (AMSE). This is performed by a Monte Carlo experiment where we use two types of correlation structures and examine them with different correlation points/levels and different error distributions with different sample sizes. We concluded that if errors are correlated, then the distribution of errors is important with correlation structures, but correlation points/levels have a less significant effect, comparatively. When errors are uniformly distributed, AMSE is the smallest, followed by any other distribution, and if errors follow the Laplace distribution, then AMSE is the largest, followed by other distributions. Laplace also has some alarming effects. More specifically, the kernel estimator is robust in the case of a simple correlation structure, and AMSEs attain their minimum when errors are uncorrelated.

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  • Open Access

    Article

    Article ID: 105

    Strategies for optimizing electronic tips service profit

    by Ekaterina Dmitrievna Lapina, Viacheslav Igorevich Gorikhovskii

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 115 Views, 21 PDF Downloads

    Electronic tip systems have become very popular in the era of cashless payments. With the widespread use of such services, the problem of maximizing profits has arisen, which concerns both establishments using electronic tip services and the services themselves that provide such services. Identifying factors that influence guests’ economic behavior when leaving tips will allow for the creation of an optimal strategy to increase the efficiency of the system. This study used data on the profits of the electronic tip service in public catering establishments. A simulation model was created to evaluate and compare the effectiveness of different strategies; a methodology for finding the optimal strategy was described; and a clustering of establishments was performed using analysis of variance to customize the optimal strategy.

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  • Open Access

    Article

    Article ID: 97

    Mathematical analysis of epidemic model to assess the impact of lockdown on COVID-19

    by Partha Karmakar, Krishna Pada Das, Satyajit Saha, Bhagabat Das, Rakesh Kumar

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 112 Views, 39 PDF Downloads

    Covid-19 and its variants, have been a worst pandemic, the entire world has witnessed. Tens of millions of cases have been recorded in over 210 countries and territories as part of the ongoing global pandemic that is still going on today. In this paper, we propose a SEI mathematical model to investigate the impact of lockdown to the controlling and spreading of infectious disease COVID-19. The epidemic model incorporates constant recruitment, experiencing infectious force in the latent period and the infected period. The equilibrium states are computed. Under some conditions, results for local asymptotic stability and global stability of disease-free and endemic equilibrium are established by using the stability theory of ordinary differential equations. It is seen that when the basic reproduction number , the dynamical system is stable and diseases die out from the system and when , the disease persists in the dynamical system. When , trans critical bifurcation is appeared. The numerical simulations are carried out to validate the analytical results.

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  • Open Access

    Review

    Article ID: 134

    Machine learning-based approaches for financial market prediction: A comprehensive review

    by Bhaskar Nandi, Subrata Jana, Krishna Pada Das

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 603 Views, 173 PDF Downloads

    This research paper investigates the use of machine learning techniques in financial markets. The paper provides a comprehensive literature review of recent research on machine learning applications in finance, including stock price prediction, financial time series forecasting, and portfolio optimization. Various machine learning techniques, such as regression analysis, decision trees, support vector machines, and deep learning, are discussed in detail, with a focus on their strengths, weaknesses, and potential applications. The paper also highlights the challenges associated with machine learning in finance, such as data quality, model interpretability, and ethical considerations. Overall, the paper demonstrates that machine learning has significant potential in finance but calls for further research to address these challenges and fully explore its potential in financial markets.

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  • Open Access

    Perspective

    Article ID: 101

    Theory of gyroscopic effects for rotating objects

    by Ryspek Usubamatov

    Journal of AppliedMath, Vol.1, No.2.1, 2023; 151 Views, 171 PDF Downloads

    Scientists began to study gyroscopic effects at the time of the Industrial Revolution. Famous mathematician L. Euler described only one gyroscopic effect, which is the precession torque that does not explain other ones. Since those times, scientists could not explain the physics of gyroscopic effects, Recent studies and the method of causal investigatory dependency demonstrated, that the nature of gyroscopic effects turned out that be more sophisticated than contemplated by researchers. The external torque acting on the spinning objects generates the system of the eight inertial torques and their interrelated motions around axes presented in the 3D coordinate system. The interrelated torques and motions of the spinning disc were described by mathematical models, and validated by practical tests that explain the physics of the gyroscopic effects based on the kinetic energy conservation law. The inertial torques generated by the centrifugal, and Coriolis forces, the change in the angular momentum, and the dependent motions of the spinning object around axes constitute the fundamental principles of the gyroscope theory. The derived gyroscopic theory opened a new chapter in the dynamics of rotating objects of classical mechanics that should be presented in all word encyclopedias.

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