Classification of Markov chains describing the evolution of random strings

Abstract

We have calculated the residual resistivity of an AI-Zn alloy in the first stages of aging at 20 "C, determining the influence of numerous basic parameters (shape, density and concentration of Guinier-Preston (GP) zones, pseudopotentials and decomposition kinetics) on the resistivity anomaly. By considering the GP zones to be truly spherical and evolving temporally with a diameter proportional to the one-third power of the aging time we achieved agreement between experiment and theory. 0305-4608/84/112601 + 12%02.25 0 1984 The Institute of Physics

Random walks on regular languages and algebraic systems of generating functions

“…Malyshev's Theorem. Random walks on regular language have previously been studied by Malyshev and co-authors in [18] and [9], in which they are called "random strings". Malyshev proves the following basic theorem:…”

The classification of matrix GI/M/1-type Markov chains with a tree structure and its applications to queueing

“…It is also well known that the derivative of A at y = 1 determines where the minimal fixed point X min is located. Let A (1) (1) be the derivative of A at y = 1. If A (1) (1) > 1, then X min < 1; otherwise, X min = 1.…”

“…Let A (1) (1) be the derivative of A at y = 1. If A (1) (1) > 1, then X min < 1; otherwise, X min = 1. In this section, these results are generalized to cases with m ≥ 1 and K ≥ 1.…”

“…If A has a fixed point Y in N K m (1) (defined in Section 4), Y can play a role similar to that of y = 1 for the m = K = 1 case. Instead of the derivative A (1) (y) at y = 1, we consider the Jacobian matrix A (1) (Y , Y ) at Y . Then we look at the Perron-Frobenius eigenvalue sp(A (1) (Y , Y )) to locate the minimal nonnegative fixed point of A.…”

“…The matrix M/G/1-type Markov chain with a tree structure was introduced in [13]. The classification conditions of this class of Markov chains were found in [1], [4] and [5]. In a recent paper, [6], the scalar M/G/1type, the scalar GI/M/1-type and the matrix M/G/1-type Markov chains with a tree structure were studied.…”