direct sum

1. The Direct Sum Decomposition of(?)_ ( r, s)( sl_2) about Principal Indecomposable Modules
   （？）（r，s）（sl2）关于主不可分解模的直和分解式
2. Symplectic Geometry Characterization of Self-Adjoint Domains for Symmetric Differential Operators in Direct Sum Spaces(ⅱ)
   直和空间上对称微分算子自共轭域的辛几何刻画（Ⅱ）
3. The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given, and it was used in the proof of some equality about the rank of idempotent matrix.
   给出了两两互素多项式下线性变换的核的直和分解，并应用于幂等矩阵（对合矩阵）的秩的等式证明中。
4. In this paper we investigate the characterization of self-adjoint domains of symmetric differential operators with interior singular points in the direct sum spaces.
   本文研究了具有内部奇异点的，即直和空间上的对称微分算子自共轭域的辛几何刻划问题。
5. Introduces the concept of completion functor and discusses its relations with finite direct sum and matrix rings and its simplicity.
   引入完备化函子的定义，讨论其与有限直和、矩阵环的关系及单性。
6. Some Properties Keeped by Direct Sum of Rings
   环的直和保持的一些性质
7. Study on structure of subgroup of direct sum group
   直和群的子群结构的研究
8. A Sufficient Condition That Linear Space Is Decomposed to The Direct Sum of Linear Transformation Kernel And Image
   线性空间分解为线性变换的核与象的直和的一个充分条件
9. The Direct Sum of Fuzzy Rings
   Fuzzy环的直和
10. If a divisible unitary D-module is torsion-free, then it is isomorphic to a direct sum of copies of K.
    如果可除酉D模是挠自由的，则它同构于K的多重直和；
11. In this paper, we have established a sufficient condition that linear space V is decomposed to the direct sum of Linear transformation kernel Ker(σ) and image Im(σ).
    在本文中我们证明了线性空间V分解为它的线性变换的核ker（σ）与象Im（σ）的直和的一个充分条件。
12. This paper is on the basis of the research for the first question. With the structure of finite commutative ring, we know that a finite commutative ring can be expressed by direct sum of some finite commutative local rings.
    本文主要基于对问题一的研究，并由有限交换环的构造可以知道，有限交换环可以由一些有限交换局部环的直和表示，于是就将问题简化到对有限交换局部环上多项式的判定。
13. 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。
14. Decompositions of Module Homomorphisms on the direct sum of modules
    模同态在直和上的分解
15. The dimensional formulas and the equivalence conditions of direct sum of subspaces
    维数公式与子空间直和的等价条件
16. A new secret splitting scheme is proposed based on a n dimensional vector space be decomposed into direct sum of A-invariant subspaces under a linear transformation A of V, security and computational complexity of this scheme are also analyzed.
    基于n维向量空间V在它的一个线性变换A下分解成A-不变子空间的直和，提出了一种新的秘密分拆方案，并分析了这种方案的安全性及计算复杂度。
17. The outer direct product and the internal direct sum of BCI-algebras
    BCI&代数的外直积与外直和
18. This paper introduces the direct sum in BCI-algebras, and proved the direct sum and interior direct sam are equivalent in well BCI-algebras.
    本文在BCI-代数中引入直和的概念，在优BCI-代数中，证明了外直和与内直和是等价的。
19. Direct Sum of Pointwise Fuzzy Modules
    点态Fuzzy模的直和
20. Similar Quasi-direct Sum of Matrix and Group Inverse
    矩阵的相似准直和与群逆
21. On the Meta Direct Sum of BCI-Algebra
    关于BCI&代数的亚直和
22. The module category of quantum GL_n is a direct sum of the ones of infinitely many q-Schur algebras.
    量子GLn的模范畴等价于无穷多个q-Schur代数的模范畴的直和。
23. Some discussion on the properties of the direct sum of matrices
    关于矩阵直接和的性质的进一步讨论
24. Introduce the new concepts of weak domain, weak principal ideal ring and weak Euclidean ring. Investigate some properties keeped by direct sum of rings.
    引进了弱整环、弱主理想环、弱欧氏环等概念，研究了环的直和保持的一些性质。
25. Programming and Application of Direct Sum Method
    直和法的电算编程及其应用
26. In this paper, the interior structure of the subgroup of every group consisting of direct sum group is discussed, The structure of subgroup of direct sum group is obtained.
    研究了构成直和群的子群的每个群的内部结构，得到了直和群的子群的结构。
27. A Discussion on the Direct Sum of Two Closed Subspaces for Hilbert Space
    关于Hilbert空间中两闭子空间直和的一点讨论
28. Spectral Decomposition of Operators in Direct Sum Spaces
    关于直和空间上算子的谱分解问题
29. On the properties of direct sum and hereditary of weak CS modules
    关于弱CS模的直和性与遗传性
30. In the framework of matrix theory, the concepts of transition matrix, transformation matrix semigroup, matrix direct sum, matrix sum, as well as covering for fuzzy finite state machines are introduced.
    本文主要工作有如下两个方面：1.在矩阵理论框架下，引进了模糊有限自动机转移矩阵、变换矩阵半群、矩阵直和、矩阵和以及覆盖概念。

noun

1. a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets