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First, the method for constructing linear stego-codes is proposed by using the direct sum of vector subspaces.

利用线性空间的直和分解得到了一种线性隐写码的构造方法。

Ii Decompose F/f(x into direct sum of local rings and prove your conclusion.

将F/f(x 分解成局部环的直和，并证明你的结论。

Rains proved that, in the split linear case, is the direct sum of and , where and are the associated codes of in, and is some element of .

Rains 证明了当是分裂型线性码的时候，是与的直和，这里与是它的两个相伴码，。

This paper have also explored the nonwandering property of sum of operator, direct sum of operator,tensor products of operators and differentiation operators which can be viewed as weighted shifts on some space.

本文也研究了和算子，直和算子，张量积算子以及在某种意义下可看成加权移位的微分算子在一定空间上的非游荡性。

Then we study that quadratic Lie colour algebra also can be decomposed to direct sum of ideas who contains no nontrivial non-degenerate idea of L . And the decomposition is unique except the order of the ideas .

然后给出了二次李color代数也可以分解为不包含非平凡的非退化的color理想的直和，而且分解除理想次序外是唯一的。

In this paper,from the six-term exact sequence,it is proved that the direct sum of Z and K1 -group of a Toeplitz algebra is always isomorphic to the topological K1 -group of the boundary of the relative domain.

本文通过六项正合列计算出，在强拟凸域上，它的拓扑边界上连续函数代数的K_(1-)群同构于区域上Toeplitz代数的K_1-群与Z的直和。

By using the tensor product of matrix, stride permutation matrix and matrix power series under the meaning of matrix direct sum, the parallel algorithm, including the scrambling algorithm, can be expressed integrally. This description provides a convenient tool for the study and application of parallel FFT algorithm.

本文提出了矩阵直和意义下幂级数的矩阵运算，同时利用迭代形式的矩阵方程将混合基FFT的并行算法及其数码倒置算法完整地表示出来，为并行FFT算法的研究和应用提供了方便的表示手段。

At last we introduce the most important theory in this thesis which is the uniqueness of decomposition . Complete Lie colour algebra of any finite dimension can be decomposed to direct sum of simply complete ideas .And the decomposition is unique except the order of the ideas .

最后给出了本文最重要的一个定理——完备李color代数的分解唯一性定理，指出有限维完备李color代数可以分解为单完备理想的直和，而且除这些单完备理想的次序外，这种分解是唯一的。

Exponential dichotomy describes a kind of hyperbolicity of the system. That is, the state space can be decomposed into a direct sum of two subspaces, which are continuous and invariant. And with the time evolving forward, the system is exponentially attracting in one subspace and exponentially expanding in the other subspace.

指数二分性描述了系统的一种双曲性现象：状态空间可以分解成两个连续不变的子空间的直和，随着时间的正向变化，系统在其中一个子空间上表现出指数压缩行为，而在另一个上面表现出指数扩张行为。

In this paper, we mainly use complex semisimple algebras knowledge. First, we give the structure formula of C. Second, we show that any n x n symmetric matrix A is congruent under the symplectic group to the direct sum of a identity matrix and a tridiagonal matrix.

记正交代数和辛代数的交集构成的李代数为L，本文主要是运用复半单李代数的知识，首先给出了L的结构公式，然后给出了任一n×n对称矩阵A辛合同于一个单位矩阵和一个三对角矩阵的直和。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。