The concepts of superlinearspace and homogeneous basis are given in this paper.

n this paper it is gave that the definition of n-mean normalized block basic sequence,and it is obtained that the equivalent connditions of perfectly homogeneous basis

First,the determinant is regarded as a function of or- der n and denoted by D(n);Second,the determinant is expanded by row or by column,then the relation in both of D(n)and subdeterminants will be examined in details to set up certain a recursion,generally speaking,it must be a homogenous or a nonhomogenous recursion;fi- nally the coefficients of the general solution are found out with the aid.

Oscillatory behavior of solutions of a class of second order nonlinear homogeneous differential equation;

The necessary and sufficient condition of separation for homogeneous Scalar Helmholtz equation is both the existence of Stackel determinant and h 1h 2h 3S=f 1(μ 1)f 2(μ 2)f 3(μ 3)in orthogonal curvilinear coordinates system.

The existence and uniqueness of homogeneous elliptic polyharmonic cardinal spline interpolation are proved, the remainder formula and order of approximation in LP(Rd) (1≤p≤∞)spaces are given, and the extremal problem of sobolev dass in L2(Rd) is considered.