Open Access Minireview Article

Generating Distribution Functions Based on Burr Differential Equation

Reinpeter Ondeyo Momanyi, J. A. M. Ottieno

Journal of Advances in Mathematics and Computer Science, Page 55-64
DOI: 10.9734/jamcs/2020/v35i830313

One of the most prominent families of statistical distributions is the Burr’s system. Recent renewed interest in developing more flexible statistical distributions led to the re-examination of Burr’s system. Solutions of Burr differential equation are expressed in terms of distribution functions. Burr [1] considered only 12 distribution functions known in literature as the Burr system of distributions, yet there are more than that in number. Studying the Burr system, it was realized that 9 of the Burr distributions are powers of cdf ′s, popularly now known as exponentiated distributions. The remaining 3 are direct solutions in terms of cdf′s. Detailed studies using generator approach techniques to generate Burr distributions has not been undertaken in literature. This motivated us to generalize solutions of Burr differential equation by generator approach. With this aim in mind, beta generator method, exponentiated generator method and beta-exponentiated generator method (a combination of beta and exponentiated generator methods) was proposed. However in this paper, we will focus on exponentiated generator technique as it generates cdf ′s. The other two generator approach techniques generate pdf′s and distributions of order statistics.

Open Access Original Research Article

Modelling and Prediction of Outpatients Department on Hospital Attendance at the Cape Coast Teaching Hospital Using the Box-Jerkins ARIMA Model

Bridget Sena Borbor

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/jamcs/2020/v35i830309

Aims: Outpatient department is one of the first points of contact for patients accessing health care and provide patients with their primary healthcare as they seek services at the facility. With the introduction of community-based health planning and services, there seems that the outpatient departments have witnessed corresponding progressive and significant increase in attendance at the various health facilities in Ghana of which the research seeks to investigate.

Materials and Methods: The data collected were outpatient hospital attendance of patients on a monthly basis from 2012 to 2019 obtained from the Cape Coast Teaching Hospital. Box Jenkins’s methodology of time series analysis was used to analyse the data. The modified Box Pierce (Ljumg-Box) Chi-square statistic criteria of the largest  and minimum Chi-square statistic value was in selecting the best fitted model for outpatient department attendance.

Results: The autocorrelation function (ACF) and partial autocorrelation function (PACF) plots suggested an autoregressive (AR) process with order 2 and moving average (MA) process with order 1 which was used in selecting the appropriate model. Candidate models were obtained using the lowest Chi-square value and highest value to select adequate models and the best model. The best non-seasonal model for the data was ARIMA (2, 2, 1) for the outpatient department attendance. Model diagnostics test was performed using Ljung-Box test.

Conclusion: The findings of the forecast showed that OPD visits will increase in the next five years. Specifically, continued use of the outpatient department in accessing health care at all levels will experience an increase in hospital visits across the months from June 2020 to December 2025.  Recommendations from this research included among others that, the health authorities should continue to expand the outpatient department services to increase access to healthcare by all as it services goes to the core people in the community.

Open Access Original Research Article

Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

Atokolo William, Akpa Johnson, Daniel Musa Alih, Olayemi Kehinde Samuel, C. E. Mbah Godwin

Journal of Advances in Mathematics and Computer Science, Page 13-33
DOI: 10.9734/jamcs/2020/v35i830310

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

Open Access Original Research Article

Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

Fadwa A. M. Madi, Fawzi Abdelwahid

Journal of Advances in Mathematics and Computer Science, Page 34-43
DOI: 10.9734/jamcs/2020/v35i830311

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

Open Access Original Research Article

Numerical Simulation of Extreme Temperature (Heat Wave) in Bangladesh Using WRF-ARW Model

Md. Abdul Aziz, M. A. Samad, M. R. Hasan, M. N. U. Bhuiyan, M. A. K. Mallik

Journal of Advances in Mathematics and Computer Science, Page 44-54
DOI: 10.9734/jamcs/2020/v35i830312

Every year Bangladesh experiences different types of natural hazards and heat wave is one of them. In the present study, an advanced high-resolution Weather Research and Forecasting (WRF-ARW) numerical mesoscale model is used to simulate a severe heat wave event occurred during April over Bangladesh and eastern part of India. The model is integrated for 6 days starting from UTC of 19 April to UTC of 24 April 2016, on a single domain of 10 km horizontal resolution. For validation of the model performance, the model simulated results of temperature at 2 m height, relative humidity (RH), mean sea level pressure (MSLP) at UTC of 6 days are compared with the BMD observed data. And the results indicate that the model is able to simulate the occurrence of the heat wave event with 6 days over Bangladesh.

Open Access Original Research Article

Generalized Hadamard Matrices and Generalized Hadamard Graphs

W. V. Nishadi, A. A. I. Perera

Journal of Advances in Mathematics and Computer Science, Page 65-75
DOI: 10.9734/jamcs/2020/v35i830314

Hadamard matrices and their applications have steadily and rapidly grown during the last 2 decades. Due to that many researchers have developed various concepts on Hadamard matrices. This paper concentrates on Generalized Hadamarad matrices. In the first part of this work, some new results on construction of generalized Hadamard matrices GH(p; pn) over Cp are introduced. In the second part, graphs obtained from generalized Hadamard matrices are introduced, namely generalized Hadamard graphs. In particular, we show that the generalized Hadamard graphs are pn- regular. Our results have been illustrated by constructing pn- regular graphs for different values of p and n.

Open Access Original Research Article

Open Access Original Research Article

Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings

Lao Hussein Mude, Owino Maurice Oduor, Ojiema Michael Onyango

Journal of Advances in Mathematics and Computer Science, Page 83-90
DOI: 10.9734/jamcs/2020/v35i830316

One of the most interesting areas of research that has attracted the attention of many scholars are theory of zero divisor graphs. Most recent research have focused on properties of zero divisor graphs with little attention given on the automorphsisms, despite the fact that automorphisms are useful in interpreting the symmetries of algebraic structure. Let R be a commutative unital finite rings and Z(R) be its set of zero divisors. In this study, the automorphisms zero divisor graphs of such rings in which the product of any three zero divisor is zero has been determined.

Open Access Original Research Article

On Almost Semi-Invariant Submanifold of A Normal Almost Paracontact Manifold

Gajendra Singh

Journal of Advances in Mathematics and Computer Science, Page 91-100
DOI: 10.9734/jamcs/2020/v35i830317

In the present paper we have obtained some properties of an almost semi-invariant of a normal almost paracontact manifold. The integrability condition of distributions  have also been discussed. According to these cases normal almost paracontact manifold is categorized and its used to demonstrate that the method presented in this paper is effective.

Open Access Original Research Article

Application of Navier – Stokes Equation to Solve Fluid Flow Problems

Ebiendele Ebosole Peter, Adamu Bala

Journal of Advances in Mathematics and Computer Science, Page 101-114
DOI: 10.9734/jamcs/2020/v35i830318

The Navier – Stokes equations were used to obtain the velocity profile for two different fluid flow problems, firstly to a laminar flow through a pipe and secondly to flow of incompressible fluid between two boundaries, one boundary is the air and the other boundary moving with a velocity, inclined at an angle . The velocity profiles were obtained and presented in a diagram of showing how the fluid flow through the channels.