Academic Journal of Applied Mathematical Sciences

Online ISSN: 2415-2188
Print ISSN: 2415-5225

Quarterly Published (4 Issues Per Year)





Archives

Volume 2 Number 7 July 2016

Pure Moving Average Vector Bilinear Time Series Model and Its Application


Authors: I. A. Iwok ; G. M. Udoh
Pages: 70-76
Abstract
Most time series assume both linear and non linear components because of their random nature. Thus, the classical linear models are not appropriate for modeling series with such behaviour. This work was motivated by the need to propose a vector moving average (MA) bilinear concept that caters for the linear and non linear components of a series on the basis of the ‘orders’ of the linear MA process. To achieve this, a matrix that preserved the ‘orders’ of the linear processes was formulated with given conditions. With the introduction of diagonal matrix of lagged white noise processes, some special bilinear models  emerged and the ‘orders’ of the pure linear MA processes were maintained in both the linear and non linear parts. The derived vector bilinear models were applied to revenue series, and the result showed that the models gave a good fit which depicted its validity.

Spectra of Graphs with End Vertices Appended to All Vertices of the Base Graph: The Golden Ratio and Energy


Authors: Paul August Winter ; Carol Lynne Jessop
Pages: 56-69
Abstract
In this paper, we determine the spectra of graphs obtained by appending h  end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations satisfying the characteristic equation, and the solutions to the eigenvalues of the base graph arise. We determine the relationship between the eigenvalues of the base graph and the eigenvalues of the new graph as constructed above, and determine that if  a  is an eigenvalue of the base .........