Vol. 1 No. 4 (2023)

The field of mathematical research is characterized by its diverse and extensive scope, encompassing pure mathematical conjectures and applied models in data science and ecology, thereby highlighting the interdisciplinary nature of applied mathematics research. In this issue, we aim to provide a captivating exploration of applied mathematics from multiple perspectives. By advancing earlier mathematical theories, confirming classical mathematical conjectures, and developing mathematical models to address common real-world scenarios, this issue promises to offer readers valuable insights and information, contributing to the ongoing discourse in applied mathematics.

Open Access

Editorial

Article ID: 1237

Editorial for Journal of AppliedMath (Volume 1, Issue 4)
by Sara I. Abdelsalam

Journal of AppliedMath, Vol.1, No.4, 2023; 47 Views, 32 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.1237

N/A

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Open Access

Article

Article ID: 192

A logical approach to validate the Goldbach conjecture: Paper 1/3
by Manish Khare, Kalyanlakshmi Chitta

Journal of AppliedMath, Vol.1, No.4, 2023; 121 Views, 110 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.192

This paper is a first of the series of three papers which provide a general proof to validate the Goldbach conjecture. This conjecture states that every even number can be expressed as a summation of two prime numbers. At the onset, concept of successive-addition of‐digits‐of‐an‐integer‐number (SADN) and its properties in terms of basic algebraic functions like addition, multiplication and subtraction are discussed. SADN classifies odd numbers into 3 sequences—the S1, S3 and S5 sequences—which comprise of odd numbers having SADN 7 or 4 or 1; SADN 3 or 9 or 6 and SADN 5 or 2 or 8 respectively. The S1 and S5 sequences are of interest in the analysis. Furthermore, composites on the S1 sequence are derived as products of intra-sequence elements of the S1 and S5 sequences while composites on the S5 sequence are derived as products of inter-sequence elements of the S1 and S5 sequences. SADN also shows why such combinations for even numbers of SADN (1, 4, 7) will be found on the S5 sequence while those for even numbers of SADN (2, 5, 8) will lie on the S1 sequence and both the sequences have a role to play in identifying the prime number combinations for even numbers with SADN (3, 6, 9). Thereafter, analysis moves to calculating the total number of combinations for a given even number that would include combinations in the nature of two composites (c1 + c 2); prime & composite ( p + c ) and two primes ( p 1 + p 2). Identifying the total number of c 1 + c 2 and p + c combinations yield the number of p 1 + p 2 combinations. The logic employed in present discussion shows that at least one such p 1 + p 2 combination exists for the even numbers having SADN digit within 1 to 9. This encompasses all even numbers and hence generalizes this method for all even numbers.

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Open Access

Article

Article ID: 232

On the Halin Turán number of short cycles
by Addisu Paulos

Journal of AppliedMath, Vol.1, No.4, 2023; 78 Views, 76 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.232

A Halin graph is a graph constructed by embedding a tree with no vertex of degree two in the plane and then adding a cycle to join the tree’s leaves. The Halin Turán number of a graph F , denoted as exH(n, F ), is the maximum number of edges in an n-vertex Halin graph. In this paper, we give the exact value of exH(n, C4), where C4 is a cycle of length 4. We also pose a conjecture for the Halin Turán number of longer cycles.

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Open Access

Article

Article ID: 202

Some important notes on an almost α-cosymplectic (k, µ, ν)-manifolds
by Pakize Uygun

Journal of AppliedMath, Vol.1, No.4, 2023; 82 Views, 87 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.202

The current work looks at certain geometric requirements that must be satisfied for an invariant submanifold of an almost α- cosymplectic (k, µ, ν)-manifolds to be totally geodesic. Consequently, we obtain some interesting results invariant submanifolds of an almost cosymplectic (k, µ, ν)-manifolds. Additionally, we give an example on 5-dimensional case.

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Open Access

Article

Article ID: 271

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset
by Edosa Osa, Patience Orukpe, Iruansi Usiholo

Journal of AppliedMath, Vol.1, No.4, 2023; 35 Views, 33 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.271

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.

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Open Access

Article

Article ID: 325

Applications of intuitionistic fuzzy sets to assessment, decision making and to topological spaces
by Michael Gr. Voskoglou

Journal of AppliedMath, Vol.1, No.4, 2023; 88 Views, 8 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.325

The intuitionistic fuzzy sets, in which the elements of the universe have their membership and non-membership degrees in [0, 1], is a generalization of Zadeh’s fuzzy set. In this paper intuitionistic fuzzy sets are used as tools for assessment and decision making. This is useful in cases where one is not sure about the suitability of the linguistic characterizations assigned to each element of the universal set. Further, it is described how the notions of convergence, continuity, compactness, and of Hausdorff topological space are extended to intuitionistic fuzzy topological spaces. Applications illustrating our results are also presented.

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Open Access

Review

Article ID: 236

A comprehensive review article on fractional models involving ecology and eco-epidemiology
by Sanjukta Pramanik, Krishna Pada Das, Partha Karmakar, Seema Sarkar Mondal

Journal of AppliedMath, Vol.1, No.4, 2023; 109 Views, 124 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i4.236

This paper deals with the various definitions involved in the very old yet novel topic called fractional calculus. This survey intends to report some of the major works carried out in the arena of fractional calculus that took place since 2010. Fractional calculus is a prominent topic for research within the discipline of applied mathematics doe to its usefulness in solving problems in several different branches of science, engineering, medicine, finance, economics and the likes. With the various definitions involved in this field, we explore the various models taken into consideration to study the effect and impact of fractional calculus to understand how the dynamics of such models change.

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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

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.

The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

Optimization imposition upon drone gimbal control electronics

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.