Let mij be the mean first passage time from state i to state j in an n-state ergodic homogeneous Markov chain with transition matrix T . Let G be the weighted digraph without loops whose vertex set is the set of states of the Markov chain and arc weights are equal to the corresponding transition probabilities. We show that

In this paper we prove a general theorem on |A; δ|k -summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. c © 2007 Elsevier Ltd. All rights reserved.

∣ p . Hardy’s inequality thus asserts that the Cesáro matrix operator C = (cj,k), given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1). (The norm is in fact p/(p − 1).) Hardy’s inequality leads naturally to the study on lp norms of general matrices. For example, we say a matrix A = (aj,k) is a weighted mean matrix if its entries satisfy aj,k = 0, k > j and aj,k ...

In this paper we consider the problem of finding norms of certain matrix operators on sequence space bvp . In fact, we consider these problems for weighted mean, and generalized Cesaro matrices on sequence space bvp . Mathematics subject classification (2010): 26D15, 47A30, 40G05, 47D37, 46A45, 54D55.

OBJECTIVES To determine the adjunctive effect of grafting biomaterials/biological agents with open flap debridement (OFD) in the treatment of deep intraosseous defects. BACKGROUND No systematic review of treatment outcomes in patients who received graft biomaterials or biological agents have been published. METHODS A rigorous systematic review of randomized controlled trials of at least 6-m...

The choice of surface template plays an important role in cross-sectional subject analyses involving cortical brain surfaces because there is a tendency toward registration bias given variations in inter-individual and inter-group sulcal and gyral patterns. In order to account for the bias and spatial smoothing, we propose a feature-based unbiased average template surface. In contrast to prior ...

This paper analyses the weighted fair queueing (W F Q) system subject to two classes of network applications. The ar rival traffic flows follow Poisson processes.The service times is exponentially distr ibuted. The system is modelled as a two-dimensional M arkov chain and use matrix geomet r ic technique to solve its stationary probabilities. The determination of the steady state probabilities ...

By a generalized inverse of a given matrix, we mean a matrix that exists for a larger class of matrices than the nonsingular matrices, that has some of the properties of the usual inverse, and that agrees with inverse when given matrix happens to be nonsingular. In theory, there are many different generalized inverses that exist. We shall consider the Moore Penrose, weighted Moore-Penrose, Draz...