代数

In section 1.3, taking the advantage of the classification by the index arrays ,pointed out the space spanned by class A,B,C respect!vivety are subalgebras of NQ. We also show that the subspace spanned by the elements of length 2 in C is an abelian subalgebras of NQ,denoted by H.we find H is contained in the center of subalgebra P of the subspace spanned by the elements in class C.

在1.3节中，应用指标数组我们讨论了各类元素的性质，指出其第A，B，C类元各自张成的子空间均是N_Q的子代数，特别是C类中所有长度为2的元素张成了N_Q的Abel子代数H，且含于C生成的子代数P的中心Z中。

We study the Dirac structures on protobialgebroid, give the integrable conditions for maximally isotropic subbundle being Dirac structure for protobialgebroid by the notion of characteristic pair. From the integrable conditions, we found out that Dirac structure has closed relations with twisting of protobialgebroid. Further, the closed relations are explained, the fact that twisting of protobialgebroids is a equivalence relation is verified.

详细研究了proto双代数胚匕的Dirac结构，给出了极大迷向子丛可积的充要条件，发现在这些充要条件中蕴含了proto双代数胚的扭关系，进一步阐明了扭与Dirac结构之间的内在联系，证明了扭在proto双代数胚范围内是等价关系。

Prof. Hsio-Fu Tuan,a member of Academia Sinica and eminent mathematician in China, has made outstanding contributions in the theory of modular representations of finite groups, algebraic Lie algebras and the study of p-groups,especially their "Anzanl" theorems.

从30年代末开始，他在有限P群、有限群模表示论和代数李代数方面做出了一系列重要贡献，得到了被冠以布饶尔－段－斯坦顿原则，布饶尔－段指标块分离原则，布饶尔－段定理等名称的突出成就，在中国开辟了代数群论等研究领域并形成了富有特色的研究群体。

First of all, the dissertation proves that the three structures are pairwisely isomorphic—the Boolean Algebra formed by the value range topological space, the Boolean Algebra by knowledge nodes, and the Boolean Algebra by data sub-classes. Thus the essential relations between the three Boolean Algebras are constructed. Furthermore, The three structures have the same multiplying mechanism.

首先，论文从理论上证明了由数值域拓扑空间形成的布尔代数、由知识结点集形成的布尔代数、和由数据子类结构集形成的布尔代数在结构上有两两同构的关系，从而建立了了这三者在本质上的联系，并且论证了它们具有相同的"繁衍"机制。

Moreover, the ultraproduct lattice implication algebras and the fuzzy ultraproduct of fuzzy subsets of lattice implication algebras are proposed by using the concept of ultrafilters, with the corresponding properties of fuzzy filters, fuzzy associative filters and fuzzy lattice implication subalgebras being discussed.

另外，文中借助于超滤概念提出了格蕴涵代数簇的超积及格蕴涵代数中模糊子集的模糊超积，并进而研究了模糊滤子、模糊关联滤子及模糊子格蕴涵代数的相应性质。

On the fuzzy ideals and the ultraproduct of BCK-algebras;2. On the Fuzzy Ideals and Their Ultraproduct of MV-Algebras;3. Moreover, the ultraproduct lattice implication algebras and the fuzzy ultrapr.

另外 ，文中借助于超滤概念提出了格蕴涵代数簇的超积及格蕴涵代数中模糊子集的模糊超积，并进而研究了模糊滤子、模糊关联滤子及模糊子格蕴涵代数的相应性质。

Keywords: Groebner basis; regular point; two-point algebra; radical square zero algebra; wild algebra

中文关键词： Groebner基；正则点；两点代数；根方零代数；野代数

The global dimension of a connected graded algebra equals to the global dimension of it viewed as a DG algebra with zero differential.

任意一个连通分次代数，如果将它视为微分为0的连通DG代数，其左整体维数与其作为连通分次代数的整体维数是一致的。

APSO and DES framework can both find a better solution, fewer minimum iterant times and average iterant times.

在物品较多的背包问题中，透过加速度粒子群演算法与双演化策略架构均能找到相较於以往文献的更好最佳解并且在较小代数与平均代数上，也均能得到相较以往文献的较少代数。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

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我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。