In this paper, we introduce the concepts of stochastic transition matrices, random harmonic functions, extremely random harmonic functions and inevitable exit sets.

In order to solve this problem more effectively, we propose a definition for the urban traffic congestion in this paper, and study the cause and process of the congestion according to the definition, propose a vehicle flow assignment model according to the double random transforming matrix, and analyze the propagation of congestion phenomenon based on the cascade theory.

Wishart random matrix based Bayesian estimation for time-varying channel in the color noise

Based on the fundamental theory of damage mechanics of rock mass and the 3-D network simulation technique, the probability distributions of random matrix of the damage tensor on joint rock mass were studied.

An expression for the mean and covariance matrix of normal random matrix polynomial is derived by applying the method of matrix differentiation to generating function.

Finally, the fact is proved using mathematical induction and the character of stochastic matrix.

In this paper, some majorization inequalities of vector kronecker products are established by stochastic matrix, which are used to obtain other majorization inequalities about eigenvalue and singular of matrix kronecker products.

In this paper we obtained the following main results:Theorem 1 If A= (aij) is irreducible generalized stochastic matrix for which the sum ofevery equals s, and a then =s is unique eigenvalue of A, whose module equals s.