Vol. 2 No. 3 (2024)

This issue mainly focuses on analyzing and solving prevalent societal problems using mathematical models. The spread of dengue illness, syphilis infection, and electricity availability are all urgent social problems that affect people's lives. Mathematical modeling can explain these social phenomena and provide useful information, consequently solving connected problems and contributing to the progress and development of human society.

Open Access

Article

Article ID: 532

Fundamental properties of the gyroscope oscillation
by Ryspek Usubamatov

Journal of AppliedMath, Vol.2, No.3, 2024; 882 Views, 137 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.532

Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century, when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of the oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and the kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.

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Open Access

Article

Article ID: 179

Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies
by Elvis Kobina Donkor, Bismark Ansu, Shaibu Osman, Dominic Otoo, Winnie Mokeira Onsongo, Ernest Yeboah Boateng

Journal of AppliedMath, Vol.2, No.3, 2024; 156 Views, 145 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.179

Syphilis is a sexually transmitted infection which when left untreated would lead to major health problems. Syphilis can easily be contracted by direct contact with Syphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on from an infected mother to her unborn child. In this paper, a nonlinear deterministic model of Syphilis disease was constructed to determine the dynamics of Syphilis infections. The study deduced model’s equilibria and analyzed the local and global stability of these equilibria. The model was extended to optimal control problem by adding time-dependent controls that helped characterize a range of possible controls that minimized the disease. The control system was solved qualitatively and numerically to evaluate the effectiveness of the considered controls using Pontryagin’s Maximum Principle. The analysis indicated that strategies B and C are considered most effective as they substantially minimized the exposed, asymptomatic and symptomatic infectious. We recommend that stakeholders should consider strategy B and C in their effort to miti-gate the disease from the population as they all have the same effect of substantially minimizing the exposed, symptomatic and asymptomatic populations.

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Open Access

Article

Article ID: 563

Computation of topological indices of linear chains of perylene and coronene using M-polynomial
by Ashwini Shivappa Yalnaik, Mookanahallipatna Shivanna Ranganath, Veerabhadraiah Lokesha, Raju Basavaraju Jummannaver

Journal of AppliedMath, Vol.2, No.3, 2024; 1267 Views, 1211 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.563

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.

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Open Access

Article

Article ID: 1437

Parameter estimation for photovoltaic systems: An enhanced Broyden-like approach
by Isaac Azure, Stephen B. Twum, Baba Seidu

Journal of AppliedMath, Vol.2, No.3, 2024; 1302 Views, 50 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.1437

Solar energy, specifically photovoltaic systems, has emerged as a prevalent source of electrical power worldwide, gaining acceptance on many continents. While numerous African countries are gradually embracing this alternative energy due to abundant sunlight, the high cost of solar panels and accessories remains a barrier to widespread adoption. This study focuses on refining recently developed iterative methods, leveraging quadrature rules of integration, to accurately estimate parameters in the design of photovoltaic (PV) systems for predetermined power outputs under diverse environmental conditions. The research compares these methods, particularly the authors’ MS-3/8 and TS-3/8 approaches, with the commonly used Newton-Raphson method. In the examination, a 10 W PV system with a single diode PV module is considered. Results indicate that the MS-3/8 method demonstrates greater efficiency and requires fewer iterations to converge to the estimated power output of the PV system compared to the Newton-Raphson method and other approaches by different authors. Ultimately, the research introduces a suggested mathematical model for a Four-Diode PV system, offering an alternative method for determining the parameters of the photovoltaic system.

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Open Access

Article

Article ID: 160

Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants
by Elvis Kobina Donkoh, Dominic Otoo, Shaibu Osman, Maxwell Baafi, Martin Anokye, Ernest Yeboah Boateng

Journal of AppliedMath, Vol.2, No.3, 2024; 554 Views, 220 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.160

Dengue fever is one of the neglected tropical diseases around the globe and its ravaging effect over the period has been enormous in the affected areas. Globalisation, immigration and urbanization and poor urban planning have become the contributory factors in the spread of infectious diseases. In this paper, a model describing the dynamics of dengue fever incorporated with infection immigrants is formulated and analysed using ordinary differential equations with a constant immigration recruitment rate. The model was qualitatively and quantitatively analysed for its local stability, basic reproductive number and sensitivity of the model parameters values to the basic reproductive number to understand the impact of the parameters on the disease spread. In the analysis, it was found that in the presence of infectious immigrants, there cannot be a disease free state demonstrated by ∅ ≥ 0 where the model demonstrates a unique endemic equilibrium state if the fraction of infectious immigrants ∅ is positive. The unique endemic equilibrium for which there is a fraction of infectious immigrants is globally asymptotically stable. Numerical simulation was performed and the results displayed graphically and discussed. It was revealed that immigration of infected immigrants contributes significantly in the spread of dengue fever and that it can be controlled by preventing the influx of infected immigrants and reducing the mosquitoes and human contact rate.

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Open Access

Article

Article ID: 1711

Gravitational redshift explained as a Doppler Effect in uniformly accelerated frames
by A. Sfarti

Journal of AppliedMath, Vol.2, No.3, 2024; 450 Views, 420 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.1711

Einstein predicted a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional with the distance from the gravitational source. In the following, we will present an approach to the experiment relying on the Einstein Equivalence Principle and on the recently derived expressions of the Doppler Effect for uniformly accelerated motion of the source and the receiver. We will conclude with a chapter on the numerical limits of applicability of the described method.

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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.