Abstract: A set D of vertices in a graph G(V,E) is called a total dominating set if every vertex v∈V is adjacent to an element of D. The domination subdivision number of a graph G is the minimum number of edges that must be subdivided in order to increase the domination number of a graph. In this paper, we determine the total domination number for strong product graph and establish bounds on the total domination subdivision number for strong product graph.

Abstract: This study examines the long run behaviour of the closing prices of the Nigerian bank stocks using Markov Chain. A total of eight (8) Nigerian bank stocks were randomly selected and data on their daily closing prices between 1st January, 2004 and 29th May, 2013 were collected secondarily through cashcrasft website. Then, variations in daily closing prices were classified into three states Markov Chain of drop, rise and stable. If the closing at day t+1 is greater than that of the day t, it was classified as rise, if that of the day t+1 is less than that of the day t, it was classified as drop but when the closing price for day t is same as that of the day t+1, it was classified as stable. Based on these classifications, transition probabilities, the limiting distribution of the transition matrix as well as the steady state transition probabilities were computed for each stock. Finding suggests that despite the current situation in the market, there is still hope for Nigerian bank stocks as some of these bank stocks tend to experience an increase in price in the long run as shown by the results of the steady state probability. Although, this finding is very informative and crucial to investors, stock brokers and other regulator in this sector, this finding is subject to unforeseen circumstances such as change in government policy, among many other factors. Despite these limitations, it is hope that the results of this study will very useful to investors, intending investors and other relevant stakeholders who are involve in stock trading.

Abstract: In this paper we prove a common fixed point theorem of compatible mappings of type (R). Our result modify the result of M. Koireng Meitei [4].

Abstract: In this Paper a multi item EOQ model with stock dependent demand for deteriorating items is considered in fuzzy environment. Inventory costs such as holding cost and setup cost have been represented by exponential membership function and profit, deteriorating rate and total investment constraint are represented by linear membership functions. The model has been solved by fuzzy non-linear programming (FNLP) method. Results have been presented along with those of corresponding crisp model and a sensitivity analysis.

Abstract: A generalized dual to a control problem containing support functions is formulated and various duality theorems are established under generalized convexity hypotheses. This dual model represents the combination of Wolfe and Mond-Weir type dual models to the control problem and hence it is described as a generalized dual. Some special cases are obtained. A close relationship of duality results with those of the nonlinear programming problems involving support functions is indicated.

Abstract: This paper examines the causal relationship between financial development and economic growth for 27 medium-income countries in the period 1970 to 2012. We develop a new proxy for financial development that refers to the input of real resources into the financial system and apply the panel bootstrapped approach to Granger causality. The results show, for three countries the findings support strong evidence on supply-leading hypothesis which implies that financial development induces economic growth and for six countries the findings support strong evidence on demand-following. Our results confirm for twenty one countries suggesting that their financial development does not depend on economic growth.

Abstract: The predictive performance of two EGARCH^{i} models for modeling daily changes in logarithmic exchange rates (log Rt^{ii}) are analyzed here. One is based on modeling the data on assumption of normal distribution and the other is based on the standardized student-t distribution. In particular, the (log Rt) of USDKES^{iii}, EUROKES^{iv} and GBPKES^{v} are considered. For each assumption EGARCH is fitted, with varying numbers of parameters, and attempt to replicate the empirical (log Rt) sequence via simulation. Assessing the fit of each model, it is concluded that the families of EGARCH models with t-innovations adequately reflect the empirical nature of the (log Rt) sequence and therefore provides a better prediction model.