Open Access Original Research Article

On the Generalization of Factoriangular Numbers

Romer C. Castillo

Asian Research Journal of Mathematics, Page 1-21
DOI: 10.9734/arjom/2022/v18i530374

A factoriangular number is a sum of a factorial and its corresponding triangular number. This paper presents some forms of the generalization of factoriangular numbers. One generalization is the \(n^{(m)}\) -factoriangular number which is of the form \((n!)^{m}\) + \(S_m(n)\), where \((n!)^{m}\) is the \(m\)th power of the factorial of \(n\) and \(S_m(n)\) is the sum of the \(m\)-powers of \(n\).  This generalized form is explored for the different values of the natural number \(m\). The investigation results to some interesting proofs of theorems related thereto. Two important formulas were generated for \((n)^{m}\) -factoriangular number: \(Ft_{n^{(m)}}\) = \(Ft_{n^{(2k)}}\) = \((n!)^{2k}\) + \(2n+1\over2k+1\)\([n^{2k-2}+P(n^{2k-3})]T_n\) for even \(m=2k\), and \(Ft_{n^{(m)}}\) = \(Ft_{n^{(2k+1)}}\) = \((n!)^{2k+1}\) + \(n(n+1)\over k+1\)\([n^{2k-2}+P(n^{2k-3})]T_n\) for odd \(m=2k+1\)

Open Access Original Research Article

A numerical Approximation for the One-dimensional Burger–Fisher Equation

Haniye Hajinezhad

Asian Research Journal of Mathematics, Page 22-30
DOI: 10.9734/arjom/2022/v18i530375

In this paper, an implicit finite difference method based on the Crank–Nicolson method is proposed for the numerical solution of the one-dimensional Burger–Fisher equation. The Crank–Nicolson scheme provides a system of nonlinear difference equations, which is solved by an integration of the Jacobian-Free-Newton-Krylov (JFNK) and GMRES methods. Various numerical examples are given to demonstrate the efficiency of the proposed scheme. Comparison of the computed solutions with the analytical ones demonstrates the accuracy of this proposed method.

Open Access Original Research Article

Calibration Estimators of Finite Population Total for Cluster Sample - (I)

A. A. El-Sheikh, H. A. El-Kossaly

Asian Research Journal of Mathematics, Page 31-41
DOI: 10.9734/arjom/2022/v18i530376

In survey sampling, the use of auxiliary information can greatly improve the precision of estimates of population total and/or means. Calibration estimation has developed into an important field of research in survey sampling where the auxiliary information plays an important role. In this paper, calibration estimator for cluster sampling with equal clusters have been introduced to improve variance estimator with the aid of auxiliary information and proposed the estimator of variance of calibration estimator. Six distances measures, presented the estimator of the variance of calibration approach estimators are introduced and a simulation study has been conducted to compare between the performance of calibration estimators against Horvitz-Thompson estimator using R  statistical package.

Open Access Original Research Article

Harmonic Centrality and Centralization of Some Graph Products

Jose Mari E. Ortega, Rolito G. Eballe

Asian Research Journal of Mathematics, Page 42-51
DOI: 10.9734/arjom/2022/v18i530377

Harmonic centrality calculates the importance of a node in a network by adding the inverse of the geodesic distances of this node to all the other nodes. Harmonic centralization, on the other hand, is the graph-level centrality score based on the node-level harmonic centrality. In this paper, we present some results on both the harmonic centrality and harmonic centralization of graphs resulting from some graph products such as Cartesian and direct products of the path P2 with any of the path Pm, cycle Cm, and fan Fm graphs.

Open Access Original Research Article

An Improved Two-states Cyclical Dynamic Model for Plastic Waste Management

John Awuah Addor, Eric Neebo Wiah, Felix Illesanmi Alao

Asian Research Journal of Mathematics, Page 52-68
DOI: 10.9734/arjom/2022/v18i530378

The panacea to the global challenge of plastic waste management is the transition towards plastic circular economy, which can be sustained through tailor-made management strategies. However, cutting-edge strategic solutions are constrained by inadequate data due to inadequate plastic-based predictive models. This paper presents an improved version of an existing two-state cyclical dynamic closed (CDC) model. The CDC model was formulated using a homogeneous linear system of ordinary differential equations (ODEs) and was modified by introducing a separation target which plays an essential role in determining both quantity and quality of recycled plastics. The Laplace transforms technique was the main analytic solution technique used. Values of the parameters were computed using the global plastic data applied for the existing CDC model, and with a technique termed the nth-order product derivative proximity, alternating pairs of initial values were selected each for the global annual plastic production and the global annual plastic waste generation. The validation process of the new CDC model was accomplished using the root mean squared error (RMSE) and the mean average percentage error (MAPE), which are measures of the model’s predictive power. Comparatively, RMSEs of the new CDC model were smaller than the RMSEs of the existing CDC model. MAPEs for the new CDC model were 6.5%  and 7% (as against 13% and 18% in the existing model) respectively for the global annual plastic: production and waste generation, indicating that the new model predicts with 93.5% and 93% degrees of accuracy respectively for the global annual plastic: production and waste generation. Therefore, the new CDC model has outperformed the existing CDC model in terms of predictive power, and thus, establishing the new CDC model as an improved version of the existing one. The model can therefore make impactful policy decisions for sustainable plastic waste management thereby aiding to achieve the transition towards circular economy in plastic waste management.

Open Access Original Research Article

Mathematics in the Classroom: A Survey of Teachers' Opinions on the Use of Information and Communication Technologies (ICTs) in Teaching and Learning

Alfred Kofi Adams

Asian Research Journal of Mathematics, Page 69-78
DOI: 10.9734/arjom/2022/v18i530379

 

Aim: The purpose of this study was to look into how school mathematics teachers use ICT in their classrooms, as well as the perceived barriers and challenges to ICT integration in mathematics classrooms.

Study Design: The research was conducted using a descriptive cross-sectional survey research approach.

Methodology: A cluster sampling strategy was utilized to pick 120 teachers from public schools in the keta municipality of the Volta region for this study. The questionnaire was returned by 105 teachers, with an 87.5 percent response rate, and descriptive statistics were utilized to analyze the data. 72 percent of the 105 teachers were males and 28 percent were females.

Results: According to the findings, mathematics teachers use ICT in their classrooms to a very limited extent. Some mathematics teachers, on the other hand, frequently utilise ICT for common computer applications, including obtaining information on the internet for teaching, networking with colleagues and students, sending emails, and producing lesson notes etc. Respondents lacked proper training and access to instructional technologies, according to the findings.

The lack of printers and presentation equipment in schools, according to respondents, may hinder their ability to integrate ICT into the teaching and learning process.

Conclusions: Because of a lack of technical know-how and inadequate ICT tools, most mathematics teachers do not use ICT in their classroom. Teachers who have minimal experience with ICT, on the other hand, prefer to utilise it for non-teaching purposes.