Open Access Original Research Article

Boundary Value Method for Direct Solution of Sixth-Order Boundary Value Problems

Olaiya Olumide O., Azeez Rasaq A., Modebei Mark I.

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/arjom/2020/v16i830203

In this work, 7th order continuous block methods called the Boundary Value Method (BVM) for the numerical approximation of sixth-order boundary Value Problem (BVPs) is proposed. These methods are derived using the Chebyshev polynomial as basis functions. The BVM comprises the main methods and additional methods, put together to form a block method and thus solved simultaneously to obtain an approximate solution for sixth-order BVPs. This method do not require a starting value as it is self-starting. The BVM is found to be consistent and its convergence was discussed. Numerical examples are shown to illustrate the applicability of the method. To show the efficiency of this method, the approximated solution derived from the methods is compared to the exact solutions of the problem and thus maximum errors are recorded and compared to those in other method from literature.

Open Access Original Research Article

Chemostat Model with Periodic Nutrient Input Described by Fourier Series

Jane Ireri, Ganesh Pokhariyal, Stephene Moindi

Asian Research Journal of Mathematics, Page 16-27
DOI: 10.9734/arjom/2020/v16i830205

In this paper we present a periodic Chemostat model of two species competing for a single nutrient available in limiting supply. The nutrient input is varied periodically using a Fourier series function to take into account the changing patterns as seasons vary. We show both analytically and numerically that varying the nutrient input using a Fourier Series function results in a better model to describe coexistence of species in natural environments.

Open Access Original Research Article

The Inverse Sushila Distribution: Properties and Application

A. A. Adetunji, J. A. Ademuyiwa, O. A. Adejumo

Asian Research Journal of Mathematics, Page 28-39
DOI: 10.9734/arjom/2020/v16i830206

In this paper, a new lifetime distribution called the Inverse Sushila Distribution (ISD) is proposed. Its fundamental properties like the density function, distribution function, hazard rate function, survival function, cumulative hazard rate function, order statistics, moments, moments generating function, maximum likelihood estimation, quantiles function, Rényi entropy and stochastic ordering are obtained. The distribution offers more flexibility in modelling upside-down bathtub lifetime data. The proposed model is applied to a lifetime data and its performance is compared with some other related distributions.

Open Access Original Research Article

On Hyperoctahedral Enumeration System, Application to Signed Permutations

Iharantsoa Vero Raharinirina

Asian Research Journal of Mathematics, Page 40-49
DOI: 10.9734/arjom/2020/v16i830207

In this paper, we give the definition and basic facts about hyperoctahedral number system. There is a natural correspondence between the integers expressed in the latter and the elements of the hyperoctahedral group when we use the inversion statistic on this group to code the signed permutations. We show that this correspondence provides a way with which the signed permutations group can be ordered. With this classication scheme, we can find the r-th signed permutation from a given number r and vice versa without consulting the list in lexicographical order of the elements of the signed permutations group.

Open Access Original Research Article

Alpha Power Transformed Extended Bur II Distribution: Properties and Applications

A. A. Ogunde, B. Ajayi, D. O. Omosigho

Asian Research Journal of Mathematics, Page 50-63
DOI: 10.9734/arjom/2020/v16i830209

This paper presents a new generalization of the extended Bur II distribution. We redefined the Bur II distribution using the Alpha Power Transformation (APT) to obtain a new distribution called the Alpha Power Transformed Extended Bur II distribution. We derived several mathematical properties for the new model which includes moments, moment generating function, order statistics, entropy etc. and used a maximum likelihood estimation method to obtain the parameters of the distribution. Two real-world data sets were used for applications in order to illustrate the usefulness of the new distribution.

Open Access Original Research Article

Behaviour under Moving Distributed Masses of Simply Supported Orthotropic Rectangular Plate Resting on a Constant Elastic Bi-Parametric Foundation

T. O. Awodola, S. Adeoye

Asian Research Journal of Mathematics, Page 64-92
DOI: 10.9734/arjom/2020/v16i830211

This work investigates the behavior under Moving distributed masses of orthotropic rectangular plates resting on bi-parametric elastic foundation. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. The solutions to the problem are obtained by transforming the fourth order partial differential equation for the problem to a set of coupled second order ordinary differential equations using the technique of Shadnam et al[1]. This is then simplified using modified asymptotic method of Struble. The closed form solution is analyzed, resonance conditions are obtained and the results are presented in plotted curves for both cases of moving distributed mass and moving distributed force.

Open Access Original Research Article

Extinction Growth Model

Daniel Ochieng Achola

Asian Research Journal of Mathematics, Page 93-107
DOI: 10.9734/arjom/2020/v16i830212

Objectives: To develop a mathematical model that incorporates genetic defect in estimating the growth rate of roan antelopes in Ruma National Park,Kenya.
Methodology: This study has developed an improved Oksendal and Lungu’s stochastic logistic model to estimates population growth rate of roans by incorporating genetic defect that were not considered by Magin and Cock. Appropriate adjustments were made to Vortex version 9.99 a computer simulation programme to simulate the extinction process.
Results: There is a high-level impact between inbreeding and population growth(survival) in small populations. Supplementation of both juvenile and adult roans ensured population survival for longer period.
Conclusion: Due to unpredictable consequences to the ecosystem and conflict with wildlife management policies in protected areas, this paper recommends supplementation instead of predator control to curb inbreeding which is a major threat to small populations. Supplementation should be done in phases without causing disruption to social groups.

Open Access Original Research Article

Open Access Original Research Article

Open Access Original Research Article

Mechanism of Instrumental Game Theory in the Legal Process via Stochastic Options Pricing Induction

Kwadwo Osei Bonsu, Shoucan Chen

Asian Research Journal of Mathematics, Page 152-173
DOI: 10.9734/arjom/2020/v16i830215

Economic theory has provided an estimable intuition in understanding the perplexing ideologies in law, in the areas of economic law, tort law, contract law, procedural law and many others. Most legal systems require the parties involved in a legal dispute to exchange information through a process called discovery. The purpose is to reduce the relative optimisms developed by asymmetric information between the parties. Like a head or tail phenomenon in stochastic processes, uncertainty in the adjudication affects the decisions of the parties in a legal negotiation. This paper therefore applies the principles of aleatory analysis to determine how negotiations fail in the legal process, introduce the axiological concept of optimal transaction cost and formulates a numerical methodology based on backwards induction and stochastic options pricing economics in estimating the reasonable and fair bargain in order to induce settlements thereby increasing efficiency and reducing social costs.