International Journal of Mathematics and Statistics Studies (IJMSS)

# Index

## A STATISTICAL MODEL OF PRICES OF ESSENTIAL COMMODITIES IN GHANA (Published)

The purpose of this study is to report an “index” that can be used as a measure of the standard of living of Ghanaians. To accomplish this objective, secondary data on prices of some selected commodities compiled by the Price Statistics section of the Ghana Statistical Service (G.S.S.) was used to conduct the study. The data covers the period from 2008 to 2013 and it was collected by month and for each Region (nine in all). The data was analyzed using Principal Component Analysis, a multivariate data analysis tool. At the end of the analysis, nine (9) indices were reported, one for each Region. These indices allowed for comparative study of the cost of living for the six years for all the Regions. The cost of living for instance, was highest in Eastern Region and Lowest in Ashanti Region for the period 2008; for 2009, it was highest in Eastern Region and lowest in Central Region; for 2010, it was highest in Volta Region and lowest in the Ashanti Region; for 2011, it was highest in Central Region and lowest in Ashanti Region; for 2012, it was highest in Central Region and lowest in Ashanti Region and lastly, for 2013, it was highest in Central Region and lowest in Ashanti Region

## THE STRUCTURE OF INDICES OF CONTROL SYSTEMS FOR CERTAIN SINGLE – DELAY AUTONOMOUS LINEAR SYSTEMS WITH PROBLEM INSTANCES (Published)

This paper investigated the structure of indices of control systems for single – delay autonomous linear systems on the interval [0, 4h] and on [0, ∞) for special coefficient matrix cases, as well as provided a note on Euclidean controllability and application instances of the determination of their controllability dispositions.

The development of the associated control index matrices exploited the continuity of these matrices for positive time periods, change of variables technique, the method of steps and backward continuation recursions to obtain these matrices on successive intervals of length equal to the delay h.

The indices were derived using the stage – wise algorithmic format, starting from the right – most interval of length h. The structure could be gleaned and deciphered from the emerged sign convention and recognizable exponential integral ordering.

Keywords: Controllability, Index, Matrices, Method, Recursive, Steps.

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