Open Access Original Research Article

On Generalized Third-Order Jacobsthal Numbers

Evren Eyican Polatlı, Yüksel Soykan

Asian Research Journal of Mathematics, Page 1-19
DOI: 10.9734/arjom/2021/v17i230270

In this paper, we investigate the generalized third order Jacobsthal sequences and we deal with, in detail, four special cases, namely, third order Jacobsthal, third order Jacobsthal-Lucas, modified third order Jacobsthal, third order Jacobsthal Perrin sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Open Access Original Research Article

Open Access Original Research Article

Investigating the Level of the Tenth-grade Students’ Self-Efficacy in Mathematics and its Impact on their Performance: A Study in Pemagatshel District

Pema Norbu, Pema Dukpa

Asian Research Journal of Mathematics, Page 34-46
DOI: 10.9734/arjom/2021/v17i230272

The study aimed at finding out the level of Mathematics self-efficacy and its relationship with the Mathematics performance of tenth-grade students. The study used a quantitative method.  The data was collected from one middle secondary school and three central schools under the Pemagatshel district from 3rd March to 16th March 2020.  A total of 300 students comprising 150 males and females each were included for the study. The data was collected using Mathematics Self-Efficacy Scales and analyzed using SPSS. The overall finding indicated that students had an average level of Mathematics self-efficacy (M=3.25; SD= 0.60). Among the four sources of self-efficacy, the study revealed that the students had high Mathematics self-efficacy in vicarious experience (M= 3.67; SD= 0.62). The Pearson correlation indicated a moderate positive correlation (r= .467, P=.05) between Mathematics self-efficacy and Mathematics performance. Higher the Mathematics self-efficacy, better the Mathematics performance, and lower the Mathematics self-efficacy, poorer the Mathematics performance. Therefore, it is imperative to strengthen the skills and strategies that enhance the Mathematics self-efficacy of the students.

Open Access Original Research Article

Bank Distress Prediction Model for Botswana

Hassan Kablay, Victor Gumbo

Asian Research Journal of Mathematics, Page 47-59
DOI: 10.9734/arjom/2021/v17i230273

"Financial distress" has many dierent meanings but generally it is said to be a state of unhealthy condition. Botswana's banking system comprises of commercial, development and savings banks. None of these types of banks has actually failed but rather some of them have experienced some form of distress. The Bank of Botswana uses the CAMELS ratings to measure distress. The CAMELS ratings is based on a score between 1 and 5, with 1 being the best score and indicates strong performance, while 5 is the poorest rating and it indicates a high probability of bank failure and the need for immediate action to rectify the situation. For this study, we consider 1-3 to be good scores (non-distressed) and a bank to be distressed if it has a score of 4-5. Utilising secondary data sources for the period 2015 to 2019, inclusive, the study evaluated the drivers of bank distress in Botswana. The data was sourced from the audited nancial statements and annual reports of the 11 banks involved in the study. Panel data logistic regression was used for analysis. The results of the study showed that Non-Performing Loans (NPL) ratio and Return on Equity (ROE) were the best predictors of bank distress.

Open Access Original Research Article

Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation

Bashiru Omeiza Sule, Taiwo Mobolaji Adegoke, Kafayat Tolani Uthman

Asian Research Journal of Mathematics, Page 60-71
DOI: 10.9734/arjom/2021/v17i230274

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

Open Access Original Research Article

Analyzing a New Third Order Iterative Method for Solving Nonlinear Problems

M. S. Ndayawo, B. Sani

Asian Research Journal of Mathematics, Page 72-90
DOI: 10.9734/arjom/2021/v17i230275

In this paper, we propose and analyse a new iterative method for solving nonlinear equations. The method is constructed by applying Adomian method to Taylor’s series expansion. Using one-way analysis of variance (ANOVA), the method is being compared with other existing methods in terms of the number of iterations and solution to convergence between the individual methods used. Numerical examples are used in the comparison to justify the efficiency of the new iterative method.

Open Access Original Research Article

Modified Adomian Decomposition Method for the Solution of Integro-Differential Equations

R. O. Ijaiya, O. A. Taiwo, K. A. Bello

Asian Research Journal of Mathematics, Page 111-124
DOI: 10.9734/arjom/2021/v17i230278

This paper is concerned with modification of the Adomian Decomposition Method for solving linear and non-linear Volterra and Volterra-Fredholm Integro-Differential equations. The Modified form of ADM was carried out by replacing the Adomian polynomials constructed in the conventional Adomian Decomposition Method with the constructed canonical polynomials. The modified Adomian Decomposition Method was applied to solve some existing example. The results obtained using the newly modified ADM proved superior when compared with the conventional ADM.

Open Access Original Research Article

A Bioeconomic Analysis of a Renewable Resource in the Presence of Illegal, Unreported and Unregulated Fishing

Mahmud Ibrahim

Asian Research Journal of Mathematics, Page 125-144
DOI: 10.9734/arjom/2021/v17i230279

The issue of illegal, unreported and unregulated (IUU) fishing is of prime concern to fisheries in developing countries where the regulatory regimes are often weak. This study proposes a Gordon-Schaefer bioeconomic model with non-constant catchability and nonlinear cost to study the impact of IUU fishing on the stock size of a marine fishery in Ghana. The static equilibrium reference points of the model are established and discussed. Bifurcation analysis on the modified Schaefer model shows the existence of a transcritical bifurcation point were the model is structurally unstable. Pontryagin’s maximum principle is employed to investigate the necessary conditions of the model, and also established are the sufficiency conditions that guarantee the existence and uniqueness of the optimality system. The characterization of the optimal control gives rise to both the boundary and interior solutions, with the former indicating that the resource should be harvested if and only if the marginal revenue of harvest exceeds the marginal revenue of stock. Numerical simulations with empirical data on the Ghana sardinella are carried out to validate the theoretical results. It is shown that IUU fishing leads to excessive exploitation of the resource biomass to levels below 50% of the carrying capacity. This has the tendency of making the fishery unsustainable, with its concomitant loss of revenue to fishers.

Open Access Review Article

H-PSO Routing Optimization Model for Zoomlion Ghana Limited

Justice Kangah, Emmanuel Ayitey, Frank B. K. Twenefour

Asian Research Journal of Mathematics, Page 91-101
DOI: 10.9734/arjom/2021/v17i230276

This research combines Particle Swarm Optimization (PSO) with Crossover and Mutation Operators of Genetic Algorithm (GA) to produce a hybrid optimization algorithm to solve a routing problem identified at Zoomlion Ghana Limited, Sekondi Takoradi branch. PSO is known to converge prematurely and can be trapped into a local minimum especially with complex problems. On the other hand, GA is a robust and works well with discrete and continuous problems. The Crossover and Mutation operations of GA makes the iterations converges faster and are reliable. The hybrid algorithm therefore merges these operators into PSO to produce a more reliable optimal solution. The hybrid algorithm was then used to solve the routing problem identified at Zoomlion Ghana Limited, Sekondi Takoradi branch. A total of 160 public waste bin centers scattered in the metropolis and the distance between them were considered. The main aim was to determine the best combination of the set of routes connecting all the bin centers in the municipality that will produce the shortest optimal route for the study. MATLAB simulation was run of the list of distances to determine the optimal route. After 10,000 iterations, PSO produced an optimal result of 81.6 km, GA produced an optimal result of 88.9 km and the proposed hybrid model produced an optimal result of 79.9 km

Open Access Review Article

On the Irrationality and Transcendence of Rational Powers of e

Sourangshu Ghosh

Asian Research Journal of Mathematics, Page 102-110
DOI: 10.9734/arjom/2021/v17i230277

A number that can’t be expressed as the ratio of two integers is called an irrational number. Euler and Lambert were the first mathematicians to prove the irrationality and transcendence of e. Since then there have been many other proofs of irrationality and transcendence of e and generalizations of that proof to rational powers of e. In this article we review various proofs of irrationality and transcendence of rational powers of e founded by mathematicians over the time.