homogeneous Markov

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.

给出了用递归关系方法求任意 n 阶行列式的值的一般方法:首先,把已知的 n 阶行列式看作为阶数 n 的一个函数,记为 D(n);其次,按行或按列展开这个行列式,并仔细观察存在于余子式及 D(n)里的关系,建立关于 D(n)的某一递归关系,此关系总为一个齐次的或非齐次的递归关系;最后,借助于 D(0)、D(1)和D(2)等求出递归关系的通解的系数。

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

一类二阶齐次微分方程解的振动性

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.

讨论了在正交曲面坐标系中齐次标量Ｈｅｌｍｈｏｌｔｚ 方程变量分离的充要条件是Ｓｔａｃｋｅｌ行列式存在且ｈ１ｈ２ｈ３Ｓ ＝ ｆ１（μ１）ｆ２（μ２）ｆ３（μ３） 成立。

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.

获得Rd上齐次椭圆型Cardinal样条插值的存在唯一性，并获得Sobolev类上的函数在Lp（Rd）（1≤p≤∞）尺度下的插值误差估计，以及Sobolev类在L2（Rd）尺度下的一些极值问题的解；拓广了Laplace型的结果。

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

利用齐次变换对数控车床两轴联动系统的几何误差进行了系统分析,根据小溜板坐标系的不同建立方法分两种情况分析了整个建模过程,论述了两轴间的正交误差对空间误差的影响,建立了两轴联动系统空间误差的数学模型,并利用该数学模型计算出某台数控车床两轴联动系统的空间误差。

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.

对于有两个柔性杆的操作臂，用基于空间齐次变换和有限元的方法，推演出拉氏动力学闭式显方程。