In this paper, we study the asymptotic equipartition property (AEP) for m order nonhomogeneous Markov information source.

The purpose of this paper is to study the strong law of large numbers for asymptotic circular Markov chains and the asymptotic equipartition property for asymptotic circular Markov chains, which is a more common case of nonhomogeneous Markov chains in real life.

A class of asymptotic equipartition property theorems for arbitrary discrete information source

By applying formal asymptotic analysis, we obtain two-dimensional model system of linearly dynamic elastic “membrane” and “flexural” shells from three-dimensional equations.

On certain conditions of assumption, we build the mathematical model in imitation of distribution of population in two spaces, and according to the mathematical model we make a study of the asymptotic distribution of population in two spaces, obtain several important results, announce .

According to the hypothesis of parameters in random effect model with equilibrium design and one-way classification H0:μ=μ0,σ2α=σ2α0,σ2=σ20H1:μ≠μ0,or σ2α≠σ2α0 or σ2≠σ20,a statistical estimator to test H0 is presented by using maximum likelihood ratio method,and then the asymptotic distribution of test statistics and its rule are given.