群代数

However, despite such categorical pronouncements as "…the above shows that the ring is not the fundamental system for associative algebra of double composition "found in [Vandiver,1939], semirings never became popular and the interest in them among algebraists gradually petered out, although it never died completely.

这些年来，半环被各类研究者所探究或者是在他们的本身及尝试从半群理论和环论中拓展研究方法，或者联系于各种应用。然而，尽管这种范畴的看法"…上面表明环不是最基本的系统对于双复合结合代数"（这句话出自[Vandiver ，1939]）。半环没有受到他们的欢迎和引起他们的兴趣进而逐渐淡化，尽管没有彻底的消亡。

We shall use algebraic methods to study graphs which are highly regular although this regularity is not expressed in terms of the automorphism group.

我们将用代数方法来研究高度正则的图，尽管这种正则性不是用自同构群来表达的。

Based on the new theories developed in biology,the basic theoreticalproblems of the genetic algorithm,which are the representation scheme,co-nvergence and convergence rates of the genetic algorithms,etc.,are discussedwith Boolean algebra,group theory,martingale theory and axiomatic method inthe framework of the Markov chain.

本文以生物学发展的新理论为背景，在遗传算法的Markov链框架下运用Boole代数、群、鞅及公理化方法研究遗传算法的表示、收敛性与收敛速度等基本理论问题。

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

Keywords: The quantitative property of groups; Table Algebras; Cayley graphs

中文关键词：群的数量性质；表代数；Cayley图

Chapter 1 is the introduction of this paper, which introduces the weak hopf algebra, hopf π coalgebra, and some properties of them.

另外，探讨了弱Hopf群弱余代数的一些基本性质和结论，为以后的章节奠定了一些理论基础。

In chapter 2, we introduce weak hopf π coalgebra and two kinds of special subalgebra over it.Some basic properties are studied to make a basis for the following chapter.

第三章主要是在弱Hopf群余代数上建立Yetter-Drinfeld模，探讨其性质并给出它的等价条件，从而对其结构有更本质的认识。

It proves that the first cohomology group of Block Lie algebraL with coefficients inL-module V is trivial.

证明了系数在模V上的Block型李代数的一阶上同调群是平凡的。

Using derivations and skewderivations,we get the dimension of the second cohomology groups of finite-dimensional Lie superalgebras of Cartan type with a non-degenerate associativeform.

利用导子与斜导子，我们又给出了具有非退化结合型的有限维Cartan型李超代数的第二上同调群〓的维数。

Although many results have been obtained, there are still a number of very interesting questions about composition operators unsolved. There is much more to be learned about the collective compactness and convergence of composition operator sequences, compactness of various product of composition operators, cyclicity, closed range and spectra of composition operators in various settings. Commutants of composition operators seem to be very difficult to characterize. Only a little is known about their reducing invariant subspaces. There has been no work on C〓 algebras generated by composition operators.

尽管已取得如此丰富的结果，但是关于复合算子仍然有大量非常有意义的问题值得研究，例如：复合算子序列的总体紧性及收敛性、复合算子的各种乘积的紧性、复合算子的闭值域问题、复合算子在各种解析函数空间上的谱的描述、换位复合算子的刻画、复合算子诱导的不变子空间问题、循环复合算子的研究、由复合算子生成的C〓-代数的研究、不同解析函数空间之间的加权复合算子及复合算子半群等等问题。

He knows that he's one of the mostdominant players in the NBA right now.

我知道他现在是联盟里最有统治力的球员之一了。

Using analysis method of BCG , the dissertation analyzed the management of voluntary service organizations .

利用BCG分析方法对我国的志愿服务组织管理进行了分析。