Vol. 2 No. 6 (2024)

This issue will present several cutting-edge studies, covering water wave scattering, gravitational wave calculations, dynamical systems, fractional differential equations, and the transmission dynamics of tuberculosis. These studies not only demonstrate the profound connection between mathematics and physics but also enrich relevant theories. Readers will learn from this issue how to use innovative mathematical thinking to understand and deal with complex problems in the real world. It is hoped that these findings would encourage more researchers to continue researching and developing in their respective professions.

Open Access

Article

Article ID: 2043

A water wave scattering problem: Revisited
by Gour Das, Sudeshna Banerjea, B. N. Mandal

Journal of AppliedMath, Vol.2, No.6, 2024; 136 Views, 61 PDF Downloads

DOI: https://doi.org/10.59400/jam2043

The problem of water wave scattering by a thin vertical wall with a gap submerged in deep water is studied using singular integral equation formulation. The corresponding boundary value problem is reduced to a Cauchy type singular integral equation of first kind in two disjoint intervals where the unknown function satisfying the integral equation has square root zero at the end points of the two intervals. In this case the solution exists if the forcing function satisfies two solvability conditions. The reflection coefficient is determined here using the solvability conditions without solving the integral equation and also the boundary value problem.

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Open Access

Article

Article ID: 1949

From computer algebra to gravitational waves
by J.-F. Pommaret

Journal of AppliedMath, Vol.2, No.6, 2024; 168 Views, 69 PDF Downloads

DOI: https://doi.org/10.59400/jam1949

The first finite length differential sequence has been introduced by Janet (1920). Thanks to the first book of Pommaret (1978), the Janet algorithm has been extended by Blinkov, Gerdt, Quadrat, Robertz, Seiler and others who introduced Janet and Pommaret bases in computer algebra. Also, new intrinsic tools have been developed by Spencer in the study of Lie pseudogroups or by Kashiwara in differential homological algebra. The achievement has been to define differential extension modules through the systematic use of differential double duality. Roughly, if D = K[d] is the non-commutative ring of differential operators with coefficients in a differential field K, let D be a linear differential operator with coefficients in K. A direct problem is to find the generating compatibility conditions (CC) in the form of a differential operator D₁ such that Dξ = η implies D₁η = 0 and so on. Taking the adjoint operators, we have ad(D) ◦ ad(D₁) = ad(D₁ ◦ D) = 0 but ad(D) may not generate all the CC of ad(D₁). If M is the D-module defined by D and N is the D-module defined by ad(D) with torsion submodule t(N), then t(N) = ext ¹ (M) “measures” this gap that only depends on M and not on the way to define it. Also, R = homK(M, K) is a differential module for the Spencer operator d : R → T ^∗ ⊗ R, first introduced by Macaulay with his inverse systems (1916). When D : T → S₂T ^∗ : ξ → L(ξ)ω = Ω is the Killing operator for the Minkowski metric ω with perturbation Ω, then N is the differential module defined by the Cauchy = ad(Killing) operator and t(N) = ext ¹ (M) = 0 because the Spencer sequence is isomorphic to the tensor product of the Poincaré sequence by a Lie algebra. The Cauchy operator can be thus parametrized by stress functions having nothing to do with Ω, like the Airy function for plane elasticity. This result is thus pointing out the terrible confusion done by Einstein (1915) while ”adapting” to space-time the work done by Beltrami (1892) for space only. both of them using the same Einstein operator but ignoring it was self-adjoint in the framework of differential double duality (1995). Though unpleasant it is, we shall prove that the mathematical foundations of General Relativity are not coherent with these new results which are also illustrated by many other explicit examples.

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Open Access

Article

Article ID: 1977

On the qualitative analysis of the boundary value problem of the Ψ-Caputo implicit fractional pantograph differential equation
by Rahman Ullah Khan, Maria Samreen, Gohar Ali, Ioannis Argyros

Journal of AppliedMath, Vol.2, No.6, 2024; 184 Views, 46 PDF Downloads

DOI: https://doi.org/10.59400/jam1977

In this manuscript, the primary objective is to analyze a Ψ-Caputo fractional pantograph implicit differential equation using the Ψ-Caputo fractional derivative. We employ a newly developed method based on fixed-point theorems to explore the existence and uniqueness of the solution to our proposed problem. Furthermore, we investigate the stability of the proposed problem. Finally, we provide an example that illustrates the application of our newly obtained results, confirming their practical significance.

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Open Access

Article

Article ID: 2209

Multistability and organization of chaos and quasiperiodicity in a memristor-based Shimizu-Morioka oscillator under two-frequency excitation
by Paulo C. Rech

Journal of AppliedMath, Vol.2, No.6, 2024; 110 Views, 53 PDF Downloads

DOI: https://doi.org/10.59400/jam2209

In this paper we investigate the organization of chaos and quasiperiodicity in a parameter plane of a continuous-time three-dimensional nonautonomous dynamical system. More specifically, we investigate a memristor-based Shimizu-Morioka oscillator, where the external excitation is represented by the sum of two different sinusoidal functions with angular frequencies ω1 and ω2. Through a scan carried out in the (ω1, ω2) parameter plane, with the dynamical behavior of each point in the phase-space being characterized by the Lyapunov exponents spectrum, we show that this system presents chaos and quasiperiodicity regions, without presenting, however, periodicity regions. Parameter regions for which the multistability phenomenon was detected, also are observed. Basins of attraction of coexisting chaotic and quasiperiodic attractors, as well as the attractors themselves, are reported.

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Open Access

Article

Article ID: 1870

Analysis and modelling of the transmission dynamics of tuberculosis in the presence of latent and active populations
by Aliyu Ibrahim, Mahdi Audu Janda, Stella Nyambura Kahianyu, Ass Gueye, Peter Chola Nkandu, Eugene Tettey Ayerkain

Journal of AppliedMath, Vol.2, No.6, 2024; 276 Views, 60 PDF Downloads

DOI: https://doi.org/10.59400/jam1870

Tuberculosis, a chronic infectious disease caused by Mycobacterium tuberculosis, remains a significant global health challenge, particularly in developing countries. This project investigates the dynamic transmission of tuberculosis, focusing on the interplay between latent and active populations. We develop and analyze an (Susceptible, Latent, Infectious, Recovered) compartmental mathematical model to examine key parameters affecting TB transmission dynamics. Our study employs stability and sensitivity analyses to provide critical insights into the basic reproduction number and equilibrium points of the TB transmission model. Through numerical simulations, we explore how various intervention strategies impact the spread of tuberculosis. The model yields an approximate reproduction number of 0.3, suggesting that under the current conditions represented in the model, TB would naturally decline in the population. Key findings emphasize the importance of maintaining a low transmission rate and improving the recovery rate to expedite the elimination of tuberculosis. The model demonstrates the complex interplay between susceptible, infected, latent, and recovered populations over time, highlighting the persistent nature of TB due to factors such as latent activation and loss of immunity in recovered individuals. This project provides a robust foundation for public health strategies aimed at controlling and ultimately eliminating tuberculosis. Our results underscore the need for targeted interventions focusing on reducing transmission, managing latent infections, and enhancing treatment efficacy. These insights can inform policy decisions and resource allocation in TB control programs, contributing to the global effort to combat this persistent disease.

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Open Access

Article

Article ID: 2152

Distribution of lattice points in the shifted balls
by Ilgar Jabbarov, Jeyhun Abdullayev

Journal of AppliedMath, Vol.2, No.6, 2024; 28 Views, 15 PDF Downloads

DOI: https://doi.org/10.59400/jam2152

In this work we study the mean value of the difference between the number of integer points and the volume of a ball as a function of the center of a ball in the unit cube [0, 1]³, applying new method. This mean value is estimated by its possible exact value. Using methods of Fourier analysis, we lead the question to the estimates of double trigonometric integrals. This method allows consider the question on lattice points in domains of arbitrary nature without any symmetry.

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Editors-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

Dr. Nehad Ali Shah

Sejong University, Korea

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

2025

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.