Vol. 2 No. 4 (2024)

This issue focuses on geometry, including differential geometry and its practical applications. Symplectic manifolds and basis differences in Clifford geometric algebra are topics covered in differential geometry. The allure of geometry stems from its ability to solve problems and its deep linkages with other disciplines.

Open Access

Article

Article ID: 167

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana
by Elvis Kobina Donkoh, Francois Mahama, Shaibu Osman, Dominic Otoo, Joseph Ackora-Prah

Journal of AppliedMath, Vol.2, No.4, 2024; 596 Views, 173 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.167

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 km 2 for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km 2 . 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.

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Open Access

Article

Article ID: 553

GeoGebra—A great platform for experiential learning, explorations and creativity in mathematics
by Qamil Kllogjeri, Pellumb Kllogjeri

Journal of AppliedMath, Vol.2, No.4, 2024; 889 Views, 175 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.553

In this paper we are presenting some examples of how GeoGebra is used in: a) explaining concepts of the first derivative, monotony, extremums; b) studying the properties of the function (strictly increasing/decreasing); c) demonstrating the mean value theorem. The results and the conclusions are based on the experiment carried out in the teaching and learning process in the chapter of derivatives in a third-year class of a secondary school in Albania. Also, there are some encouraging facts got by the use of GeoGebra: the double representation and the dynamic features of GeoGebra allow the students to quickly grasp the mathematical concepts and properties and be actively involved in further explorations. The use of GeoGebra tools is similar to the use of the tools of virtual games, and this is a great advantage to stimulate the students to learn mathematics and master their mathematical performance the same way they play games. On the other side, using GeoGebra, it is easier for the teachers to explain mathematical concepts, the properties of algebraic objects, to discuss about different situations and aspects of the subject under study and to methodically reason the results got. GeoGebra provides a very commodious environment for the students to effectively interoperate with each other. Our results showed that GeoGebra is effective in teaching and learning mathematics. GeoGebra software contributed in enhancing students’ understanding of mathematical concepts and improved students’ interest to learn mathematics. Also, we admit that not all the stages of implementing GeoGebra software in the classroom are flowing smoothly. Based on our experience and the other researchers, it is observed that the effectiveness is dependent on the way GeoGebra is integrated in the teaching and learning process, implying that the research must continue with the commitment of many researchers of mathematics, physics and other sciences.

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Open Access

Article

Article ID: 1435

Predictive modeling for industrial productivity: Evaluating linear regression and decision tree regressor approaches
by Isaac Azure

Journal of AppliedMath, Vol.2, No.4, 2024; 777 Views, 182 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.1435

This research discusses the importance of predictive modeling in optimizing efficiency in various sectors, particularly in industrial settings. It compares the effectiveness of linear regression and decision tree regression models in predicting productivity. The study aims to provide insights into the strengths and limitations of each technique, assisting decision-makers in selecting the best model for their needs. It begins by explaining the theoretical foundations of both models and conducts a literature review to highlight their practical implementations. The methodology involves data collection, preprocessing, model training, evaluation, and comparison using real-world datasets. Performance metrics such as Mean Squared Error (MSE) are used for evaluation. The comparative analysis reveals that the linear regression model consistently outperforms the decision tree regressor model in terms of lower MSE values across all datasets. Overall, the study offers empirical evidence and practical insights into the predictive capabilities of both models, with potential implications for strategic decision-making in various industries.

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Open Access

Article

Article ID: 1700

Differentials of the basis in Clifford Geometric Algebra
by Yingqiu Gu

Journal of AppliedMath, Vol.2, No.4, 2024; 446 Views, 89 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.1700

In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformation is not the same in different contexts. In differential geometry, the linear transformation is the connection operator. While in quantum mechanics, the operator algebra corresponds to the differentials of matrices. Corresponding to the variation of the metric, the variation of the frame contains a unusual fourth-order tensor. We also derive the Lie differential of the frame corresponding to the Lorentz transformation group. The definition of differential of the frame is different, so the corresponding linear transformation is also different. In this paper, the unified point of view to deal with the variation of frame or basis vectors will bring great convenience to the research and application of Clifford algebras.

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Open Access

Article

Article ID: 1698

Regularity, synthesis, rigidity and analytic classification for linear ordinary differential equations of second order
by Víctor León, Bruno Scárdua

Journal of AppliedMath, Vol.2, No.4, 2024; 285 Views, 192 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.1698

We study second order linear homogeneous differential equations a(x)y'' + b(x)y' + c(x)y = 0 with analytic coefficients in a neighborhood of a regular singularity in the sense of Frobenius. These equations are model for a number of natural phenomena in sciences and applications in engineering. We address questions which can be divided in the following groups: (i) Regularity of solutions. (ii) Analytic classification of the differential equation. (iii) Formal and differentiable rigidity. (iv) Synthesis and uniqueness of ODEs with a prescribed solution. Our approach is inspired by elements from analytic theory of singularities and complex foliations, adapted to this framework. Our results also reinforce the connection between classical methods in second order analytic ODEs and (geometric) theory of singularities. Our results, though of a clear theoretical content, are important in justifying many procedures in the solution of such equations.

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Open Access

Commentary

Article ID: 206

Onthe geometry of an almost α-cosymplectic (k, µ, ν)-spaces
by Pakize Uygun, Mehmet Atçeken, Tugba Mert

Journal of AppliedMath, Vol.2, No.4, 2024; 1134 Views, 1107 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i4.206

The object of the paper is to investigate almost α-cosymplectic (k,µ,ν)-spaces. Some results on almost cosymplectic (k,µ,ν)-spaces with certain conditions are obtained.

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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.