On asymptotic representation of numerical solutions of the nonlinear order differential equations and its application;

In this paper, asymptotic representation of solutions of linear functional differential equations in R n is investigated with an uniform stability and convergence theorem for a special type of functional differential equations, and the same asymptotic integration formula same as that in is obtained under weaker conditions.

In this paper, a robust mean absolute deviation M(α)(α∈S p-1 ) and its asymptotic expressions are obtained.

Two kinds of robust PP mean absolute deviations M_1(a),M_2(a),(a∈ S~(p-1))and their asymptotic expressions are obtained,furthemore,the asymptotic distributions of M_1(a) and M_2(a) uniform for a∈S~(p-1) are derived which are supremums of the Gauss processes on S~(p-1).

The expressive problem of higher order asymptotic representation for modified Szzsz operators is studied, and a equality formula of higher older asymptotic representation is obtained, and the direst, in verse theorems of simultaneous approximation are given.

In order to study critical behaviour of D vector model by using Ginzherg Landau theory based on cumulant expansion,both the free energy and moments of single site and their asymptotic expressions for D vector model up to 6th order are derived.