Vol. 2 No. 1 (2024)

The interdisciplinary nature of mathematical research and its association with diverse fields is a topic of great interest in the field. In this issue, we aim to provide valuable insights into the innovative intersections of mathematics with real-world applications, showcasing the versatility and impactful nature of mathematical research. Spanning domains such as quantum mechanics, music theory, pattern recognition, data analysis, and nonlinear equations, this issue seeks to explore the diverse applications of mathematical principles. We trust that this collection of papers will offer readers a deeper appreciation of the interdisciplinary nature of mathematical research and its potential to drive meaningful advancements across a variety of fields.

Open Access

Article

Article ID: 382

Random vector representation of continuous functions and its applications in quantum mechanics
by Hong-Xing Li, Wei Zhou, Hong-Hai Mi

Journal of AppliedMath, Vol.2, No.1, 2024; 118 Views, 115 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.382

The relation between continuous functions and random vectors is revealed in the paper. The main meaning is described as: for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors where every random vector is defined on one of these probability spaces, such that the sequence of conditional mathematical expectations formed by the random vectors uniformly converges to the continuous function. This is a random vector representation of continuous functions, which is regarded as a bridge to be set up between real function theory and probability theory. By means of this conclusion, an interesting result about function approximation theory can be obtained. The random vector representation of continuous functions has important applications in physics. Based on the conclusion, if a large proportion of certainty phenomena can be described by continuous functions and random phenomena can also be described by random variables or vectors, then any certainty phenomenon must be the limit state of a sequence of random phenomena. Then, in the approximation from a sequence of random vectors to a continuous function, the base functions are appropriately selected by us, and an important conclusion for quantum mechanics is deduced: classical mechanics and quantum mechanics are unified. Particularly, an interesting and very important conclusion is introduced as the fact that the mass point motion of a macroscopical object possesses a kind of wave characteristic curve, which is called wave-mass-point duality.

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Open Access

Article

Article ID: 281

Hindustani classical music revisited statistically: Does the order of Markov chain in the note dependence depend on the raga or the composition?
by Soubhik Chakraborty, Aiman Habib, Prerna Singh

Journal of AppliedMath, Vol.2, No.1, 2024; 116 Views, 74 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.281

Rendering musical notes randomly does not create music. To generate music, there has to be a pattern that makes the musical notes dependent. It is therefore of interest to know whether the probability of the next note depends on the current note only or whether it depends on the note(s) prior to the current note. In other words, it is important to explore the order of the Markov chain in the musical piece. In the context of Hindustani classical music, does this order depend on the raga or the composition? The present work addresses this fascinating question and attempts to answer it through Akaike’s information criterion (AIC). It appears, interestingly, that the order of the Markov chain is dependent on the raga, which has a well-defined melodic structure with fixed notes and a set of rules characterizing a particular mood that is conveyed by performance. As long as these rules are maintained, as in a raga bandish, the order of the Markov chain is invariant over the raga compositions.

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Open Access

Article

Article ID: 373

Enhancing handwritten numeric string recognition through incremental support vector machines
by Rani Kurnia Putri, Muhammad Athoillah

Journal of AppliedMath, Vol.2, No.1, 2024; 118 Views, 128 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.373

Handwritten digit recognition systems are integral to diverse applications such as postal services, banking, and document processing in our digitally-driven society. This research addresses the challenges posed by evolving datasets and dynamic scenarios in handwritten digit recognition by proposing an approach based on incremental support vector machines (ISVM). ISVM is an extension of traditional support vector machines (SVM) designed to handle scenarios where new data points become available over time. The dataset includes handwritten images (numbers “0” to “6”) and trials introducing new classes (“7”, “8”, and “9”). Evaluation utilizes k-fold cross-validation for robustness. Digital image processing involves converting images into numeric data using the histogram method. The result showed the positive outcomes of using ISVM in handwritten digit recognition, emphasizing its adaptability to incremental learning and its ability to maintain robust performance in the face of evolving datasets, which is crucial for real-world applications.

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Open Access

Article

Article ID: 424

Topological analysis of multiple tables
by Rafik Abdesselam

Journal of AppliedMath, Vol.2, No.1, 2024; 122 Views, 76 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.424

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 the quantitative, qualitative, or mixed variables considered. Like 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 different homogeneous themes. Its results are compared to those from the MFA method.

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Open Access

Article

Article ID: 477

A new optimal iterative algorithm for solving nonlinear equations
by Dhyan R. Gorashiya, Rajesh C. Shah

Journal of AppliedMath, Vol.2, No.1, 2024; 107 Views, 80 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.477

The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations, considering a fixed point and an initial guess value on the x -axis. The concepts of the slope of a line and the Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with a computational efficiency index of 1.414 and an informational efficiency of 1. The validity of the algorithm is examined by solving some examples and their comparisons with Newton’s method.

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Open Access

Article

Article ID: 465

Conformal theory of central surface density for galactic dark halos
by R. K. Nesbet

Journal of AppliedMath, Vol.2, No.1, 2024; 77 Views, 43 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i1.465

Numerous dark matter studies of galactic halo gravitation depend on models with a core radius of r 0 and a central density of ρ 0 . The central surface density product ρ 0 r 0 is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration , for a = a N + , where Newtonian acceleration a N is due to observable baryonic matter. Neglecting a halo cutoff at a very large galactic radius, conformal is constant over the entire halo, and a = a N + is a universal function, consistent with a recent study of galaxies with independently measured mass, that constrains acceleration due to dark matter or to an alternative theory. An equivalent dark matter source would be a pure cusp distribution with a cutoff parameter determined by a halo boundary radius. This is shown to imply a universal central surface density for any dark matter core model.

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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.