In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

SEMI-MARKOV DECISION INCLUDING AN UNKNOWN Masami Kurano Chiba University PROCESSES PARAMETER (Received February 27, 1984: Revised May 8,1985) We consider the problem of minimizing the long-run average (expected) cost per unit time in a semiMarkov decision process including an unknown parameter. In the case of general state and action spaces and compact parameter space we construct the adaptive ...

— The Economics of Happiness is one of the research areas of greatest growth in recent years. Throughout this work, a venture based model in which satisfaction of Spanish entrepreneurs with their professional life is performed. We analyze the responses of 9,989 entrepreneurs using data from the Global Entrepreneurship Monitor (GEM), and six hypothesis are discussed. The results show that, for t...

We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from below by exp(−nd), 0 < d < 1, where n is the sample size.

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

We discuss the notions of strong convergence and weak convergence in n-inner product spaces and study the relation between them. In particular, we show that the strong convergence implies the weak convergence and disprove the converse through a counter-example, by invoking an analogue of Parseval’s identity in n-inner product spaces.