By introducing the weight function and multi-parameters and using the way and the technioue of real analysis,we give a Hilbert-type integral inequality with the homogeneous kernel of 0-order.

By using the way of real analysis and estimating the weight coefficient,this paper introduces a parameter α≥-3/4+(((21)~(1/2))/12) and gives a more accurate extension of a Hilbert-type inequality with the homogeneous kernel of positive-degree with a best constant factor.

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.

The homogeneous transformations were made use of to analyze systematically the geometric errors of the two-axis system in an NC lathe.

The explicit, closedform dynamic model of flexible two-link robotic manipulators is developed based on homogeneous transformation matrices, finite element model and the Lagrangian formulation of dynamics.