Open Access Original Research Article

Students Mathematics Interest in Senior High Schools: Empirical Evidence from Ashanti Region of Ghana

Yarhands Dissou Arthur

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/arjom/2019/v15i330147

The relevance of students’ academic interest in mathematics is of great concern to stakeholders in education. The present study models students’ interest in mathematics (SIM) using mathematics facility (MF), mathematics connection (MC), teacher motivation (TM) as well as instructor quality and availability (IQA). The study randomly selected 1500 students from 10 senior high schools from the Ashanti region of Ghana; however, 1,263 of the participants fully participated in the study. These participants were made to respond to validated self-administered questionnaires with alpha-reliability of 0.74, 0.69, 0.70, 0.699 and 0.68 for SIM, MC, MF, IQA and TM respectively. Findings from the study showed that MC, MF, IQA and TM explain 71.6% of the variance in students’ interest in mathematics. The study further found that approximately 15% of variability in teachers’ ability to connect mathematics to real life problems is attributable to availability of mathematics facility as well as instructor quality and availability. The study finally found that availability of mathematics facilities for teaching and learning explains 12.4% of instructor quality in teaching mathematics. The study concluded that students’ interest in mathematics is influenced significantly by the teachers’ ability to connect mathematics to real life and the immediate environment, availability of mathematics facility, teacher motivation as well as instructor quality and availability. The study recommended for mathematics educators to take into account the influence of these factors and integrate them in the delivery of mathematics in high schools.

Open Access Original Research Article

Portfolio Selection Strategies with Return Clause in a DC Pension Fund

Edikan E. Akpanibah, Udeme O. Ini

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/arjom/2019/v15i330149

This paper solves the problem faced by a pension fund manager in determining the optimal selection strategies involving four different assets comprising of one risk free asset and three risky assets whose prices are modelled by geometric Brownian motion. Also, a clause mandating the fund managers to return the accumulations with predetermined interest to members who lost their life during the accumulation period is considered. A stochastic optimal control model is formulated comprising of member’s monthly contributions, invested funds and the returned contributions. Also, an optimization problem from the extended Hamilton Jacobi Bellman (HJB) equation is established using the game theoretic approach. The explicit solutions of the optimal selection strategies and the efficient frontier are obtained by solving the extended HJB equation using the mean variance utility and separation of variable technique. Furthermore, a sensitivity analysis of the effect of some parameters on the optimal selection strategies is carried out numerically.

Open Access Original Research Article

Open Access Original Research Article

Hyers-Ulam-Rassias Instability for Linear and Nonlinear Systems of Differential Equations

Maher Nazmi Qarawani

Asian Research Journal of Mathematics, Page 1-16
DOI: 10.9734/arjom/2019/v15i330151

This paper considers Hyers-Ulam-Rassias instability for linear and nonlinear systems of differential equations. Integral sufficient conditions of Hyers-Ulam-Rassias instability and Hyers-Ulam instability for linear and nonlinear systems of differential equations are established. Illustrative examples will be given.

Open Access Review Article

Density Dependent Delayed Migration for Rosenzweig-Macaurther Model with Holling Type II Predator Functional Response

Samuel B. Apima, George O. Lawi, Nthiiri J. Kagendo

Asian Research Journal of Mathematics, Page 1-12
DOI: 10.9734/arjom/2019/v15i330148

The model describing the interaction between the predator and prey species is referred to as a predator-prey model. The migration of these species from one patch to another may not be instantaneous. This may be due to barriers such as a swollen river or a busy infrastructure through the natural habitat. Recent predator-prey models have either incorporated a logistic growth for the prey population or a time delay in migration of the two species. Predator-prey models with logistic growth that integrate time delays in density-dependent migration of both species have been given little attention. A Rosenzweig-MacAurther model with density-dependent migration and time delay in the migration of both species is developed and analyzed in this study. The Analysis of the model when the prey migration rate is greater than or equal to the prey growth rate, the two species will coexist, otherwise, at least one species will become extinct. A longer delay slows down the rate at which the predator and prey population increase or decrease, thus aecting the population density of these species. The prey migration due to the predator density does not greatly affect the prey density and existence compared to the other factors that cause the prey to migrate. These factors include human activities in the natural habitats like logging and natural causes like bad climatic conditions, limited food resources and overpopulation of the prey species in a patch among others.