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; 343 Views, 50 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.69

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; 206 Views, 56 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.109

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; 132 Views, 30 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.105

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; 145 Views, 48 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.97

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; 929 Views, 253 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.134

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; 210 Views, 187 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i2.101

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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Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

eISSN

2972-4805

Publication Frequency

Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

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Volume Arrangement

2024

2023

Featured Articles

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana

Masting in GSM network design is one of the most challenging problems in cell planning. The effect of uniform design pattern has been proven geographically to be hexagonal using uniform cell range. In this paper, we present a new uniform greedy semi-regular tessellation model called the octagonal square tessellation model (OSTM) to address the problem of global minimum overlap difference and area. Data from MTN Kumasi-East Ghana was collected and analyzed using the developed model. The original layout for the 0.6 km cell range accounted for an overlap difference of 937.66 m and a total area of 21.41 km² for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km². This is a 59.87% reduction of the original total area. Our solution is shown to be optimal in overlap difference and area for non-uniform cell range.

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.