##### A Logistic Differential Equation Model Rendition of Customers’ Consumption of Electrical Energy

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/ARJOM/2016/29618

This paper presents a logistic differential equation model of customers’ consumption of electrical energy in Ghana. The objective is to model the industrial and commercial consumption of electrical energy of customers of the Electricity Company of Ghana in the Sekondi-Takoradi Metropolis of the Western Region. The paper applies a model based on the Logistic Differential Equation. The consumption data of customers were obtained through an Automatic Meter Reading System which enables a remote reading from customer’s energy meter.

The rate of change of energy consumption has been expressed in the form of the Logistic Differential Equation. Analytical solution has been obtained and constants estimated by fitting a historical energy consumption data to a linear regression equation. The carrying capacity of the Logistic equation referred to as the Optimal Asymptote in this paper has been obtained using the Fibonacci Search Technique. All computations were done based on algorithms which were implemented using the C# Programming Language.

A forecast of a customer’s electricity consumption has been done. The forecast consumption was compared with the actual historical consumption in order to ascertain the level of disparity of the forecast from the actual. The Mean Absolute Percentage Error, which measures the forecasting accuracy or predictive power of the model, has been estimated to be ±6.77%. Practically, the model has predicted correctly to the precision of a maximum of 10% above and a minimum of 2% below the historical energy consumption data.

##### Sheffer Polynomials and their Delta Operators

A. Maheswaran, C. Elango

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2016/29899

Aims/objectives: In this paper, we study the Sheffer polynomials through the sequential representation of delta operator in Finite Operator Calculus. The major objective is to investigate the characterization of the delta operator for the Simple Laguerre, the Boole and Mittag-Leffer polynomials. From our investigation, we derive many interesting Propositions for the above polynomials.

##### Common Fixed Point Results in Ordered S-metric Spaces for Rational Type Expressions

Arvind Bohre, Suresh Nagle, Rashmi Jain, Manoj Ughade

Asian Research Journal of Mathematics, Page 1-16
DOI: 10.9734/ARJOM/2016/28960

The aim of this paper is to present some common fixed point theorems for g-monotone maps involving rational expression in the framework of S-metric spaces endowed with a partial order using a class of pairs of functions satisfying certain assumptions.

##### Vacuum Energy of the Laplacian on the Spheres

Louis Omenyi

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2016/30523

Let Δg be the Laplacian on smooth functions on a compact Riemannian manifold (M, g)  and ζg the associated spectral zeta function. Some special values of the spectral zeta function and their generalisations such as the spectral height and spectral determinant usually defined in terms of the spectral zeta function to be ζ'g (0) and exp(ζ'g(0)) respectively, have been computed explicitly, see e.g [1,2] and . Another special value of the spectral zeta function which has been a fundamental issue in quantum field theory is  the Vacuum (Casimir) energy. Casimir energy is defined, mathematically, via the spectral zeta function as a function on the set of metrics on the manifold by ζg (-1/2) [4,5] and . In this paper, a general technique for computing the Casimir energy of the Laplacian on the unit n -dimensional sphere, Sn by factoring the spectral zeta function through the Riemann zeta function ζR is presented.

##### Mathematical Analysis of Effect of Isolation on the Transmission of Ebola Virus Disease in a Population

F. O. Akinpelu, M. M. Ojo

Asian Research Journal of Mathematics, Page 1-12
DOI: 10.9734/ARJOM/2016/30297

Outbreak of Ebola virus disease in early 2014 in West Africa is a major highlight for many researchers throughout the world because of the high mortality rate. Ebola disease is caused by a virus called the Ebola virus which can be transmitted from infected humans to uninfected humans through direct contact with the body fluids. Research has placed evidence that Ebola virus can be transmitted through the bodies of humans who recently died of the disease. Because of that, an epidemic model of (S, E, Iu, Id, Is, R, D) is presented to study the dynamical spread of Ebola in the population. The existences of the disease free and unique endemic equilibrium were determined under certain conditions. Furthermore, the Local Stability analysis of the disease – free equilibrium (DFE) was investigated via the threshold parameter (Reproduction number R0 ) obtained using the next generation matrix technique. The result shows that the DFE is asymptotically stable at Reproduction number less than unity (R0 <1) and Unstable whenever Reproduction number is greater than unity (R0 >1). Numerical simulations are carried out to confirm the analytical results and explore the possible behaviour of the formulated model. Numerical simulation shows that if the detection rate of infected undetected is sufficiently large, then the isolation techniques can lead to the eradication of the disease in the population.