Vol. 2 No. 2 (2024)

This issue demonstrates the close connection between mathematics and computer technology. The combination of mathematical knowledge and computer technology has been shown to efficiently handle natural disasters. Furthermore, the application of computers in mathematics education can assist students in better understanding mathematics. These studies show that the perfect combination of mathematics and computer technology can accelerate the development of human society in a variety of sectors.

Open Access

Article

Article ID: 231

Pseudosymmetric normal paracontact metric space forms admitting (α, β)−type almost η−Ricci-Yamabe solitons
by Tuğba Mert, Mehmet Atçeken

Journal of AppliedMath, Vol.2, No.2, 2024; 1060 Views, 1008 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.231

In this paper, we have considered normal paracontact metric space forms admitting (α, β)−type almost η−Ricci-Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admitting (α, β)−type almost η−Ricci-Yamabe soliton have introduced according to choosing of some special curvature tensors such as Riemann, concircular, projective, W1 curvature tensor. After that, according to choosing of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting (α, β)−type almost η−Ricci-Yamabe soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications are made under the some conditions.

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Open Access

Article

Article ID: 451

H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake
by Michael Dowglas de Gois Silva, Fábio Roberto Chavarette

Journal of AppliedMath, Vol.2, No.2, 2024; 951 Views, 785 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.451

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.

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Open Access

Article

Article ID: 391

Computer visuality in mathematics teaching
by Laxmi Rathour, Dragan Obradovic, Lakshmi Narayan Mishra, Vishnu Narayan Mishra

Journal of AppliedMath, Vol.2, No.2, 2024; 920 Views, 341 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.391

The purpose of this study is to look at the changes that computers have made in mathematics itself and in the mathematics curriculum. The aim of the study is to investigate the various applications of computers in education in general, especially in mathematics education, and their application in the mathematics curriculum and in the teaching and learning of mathematics. The primary use of educational tools for mathematical purposes is the quality verification of results. There are various tools for developing student logic based on interactivity. Mathematics education tools are designed for innovative, interactive, and dynamic learning in different areas of mathematics. It is undeniable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by numerous researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is the development of students’ constructive thinking. This work aims to describe the application of educational tools with which it can develop interactivity and help pupils and students to better and more clearly understand mathematics and to understand that it is all around us, that it is our everyday life.

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Open Access

Article

Article ID: 405

Relativistic light clocks: Arbitrary orientation in uniform motion and hyperbolic motion analysis
by Adrian Sfarti

Journal of AppliedMath, Vol.2, No.2, 2024; 333 Views, 242 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.405

In this paper, we address the general case of a light clock in uniform translational motion parallel to itself and perpendicular to its uniform velocity v , as well as the case of the light clock in relativistic hyperbolic motion. Neither case has been previously addressed in the specialized literature, which typically restricts itself to canonical orientations where the light clock moves parallel to either the vertical or horizontal axis with uniform velocity, without acceleration. Therefore, it becomes interesting to study the more general case where the clock has an arbitrary orientation and/or is accelerated. Our paper is divided into two main sections. The first section deals with the light clock moving with constant velocity, oriented at an arbitrary angle with respect to the x-axis. We prove that the moving clock exhibits a standard time dilation, identical to that of a light clock moving in a canonical orientation. The second section deals with the light clock moving with constant acceleration, i.e., in hyperbolic motion. For the light clock in hyperbolic motion, we derive the period as measured from the perspective of an inertial frame and draw parallels with the case of uniform motion, outlining a term that is similar (but not identical) to the γ factor of uniform motion. We also point out that this factor depends not only on acceleration but also on the height of the light clock. This dependency on the dimension of the light clock distinguishes the accelerated case from the case of uniform motion. The first three sections deal with the theoretical aspects of light (optical) clocks, while the fourth section addresses the experimental implementations of optical clocks.

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Open Access

Article

Article ID: 79

A novel decision-making approach based on interval-valued T-spherical fuzzy information with applications
by Muhammad Safdar Nazeer, Kifayat Ullah, Amir Hussain

Journal of AppliedMath, Vol.2, No.2, 2024; 1496 Views, 1305 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.79

Multi-attribute group decision-making (MAGDM) is a very significant technique for selecting an alternative from the provided list. But the major problem is dealing with the information fusion during the information. Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN) are the most generalized and flexible t-norm (TN) and t-conorm (TCN), which are used for information processing. Moreover, the interval-valued T-spherical fuzzy set (IVTSFS) is the latest framework to cover the maximum information from the real-life scenarios. Hence, the major contribution of this paper is to deal with the information during the MAGDM process by introducing new aggregation operators (AOs). Consequently, the interval-valued T-spherical fuzzy (IVTSF), Aczel-Alsina weighted averaging (IVTSFAAWA), IVTSF Aczel-Alsina (IVTSFAA) ordered weighted averaging (IVTSFAAOWA), IVTSFAA weighted geometric (IVTSFAAWG), IVTSFAA ordered weighted geometric (IVTSFAAOWG), and IVTSFAA hybrid weighted geometric (IVTSFAAHWG) operators are developed. It is shown that the proposed operators are valid and the results obtained are reliable by discussing some basic properties. To justify the developed AOs, an example of the MAGDM is discussed. The sensitivity of these AOs is observed keeping in view of the variable parameter. To show the importance of the newly developed theory, a comparison of the proposed AOs is established with already existing operators.

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Open Access

Article

Article ID: 484

The Markov chain of Hidden Markov Model of interaction of the K-RAS4B proteins in catalytic environment with lipid membranes has a Hilbert measure
by Orchidea Maria Lecian

Journal of AppliedMath, Vol.2, No.2, 2024; 1685 Views, 376 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.484

A Hidden Markov Model containing both stationary Markov processes and time-varyingMarkovprocessesisconsidered: thecorrespondingMarkovchainisnewly proven to be one whose transition operators are on a space with Hilbert metric (whose measure exists and is unique). The Markov chain is therefore newly proven to be one with bounded moments. The further mathematical developments are envisaged. Applications are newly given for the analytical expressions of description of allosteric systems. The model of interaction of the K-RAS4B proteins with lipid membranes is newly considered accordingly; new drug design is explained

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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.