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We showthat End〓is an algebra in 〓,and then we construct a derived Lie algebra〓 in 〓 and prove existenceness of its enveloping algebra under the condi-tion that the"braiding"in the category 〓 is symmetric on 〓.

Radford的双积定理给出了在Yetter-Drinfel'd范畴〓中构造辫子群[48-50]的一种方法。因为，冲积已被发展为交叉积，许多冲积的相应结果被搬到了交叉积上。

The research of differential structure on the algebra system, has opened up a new field for the research of algebra, and offered a new method and thinking, greatly expanded the scope of application of algebra.

代数系统上的微分结构的研究，为代数学的研究开辟了新的领域，提供了新的方法和思路，极大的扩展了代数学应用的范围。

150 Chapter 1 The History and Future of Computers 3.2 Boolean Algebra Table 3-2 Distributivity Idempotency Absorption laws 分配律同一律吸收律 a=ab+ac a+= a+a=a aa=a a+ab=a a=a'=a'b''=a'+b' DeMorgan's laws德摩根定理计算机专业英语 1-151 Chapter 1 The History and Future of Computers 3.2 Boolean Algebra Since a finite set of n elements has exactly 2n subsets, and it can be shown that the finite Boolean algebras are precisely the finite set algebras, each finite Boolean algebra consists of exactly 2n elements for some integer n.

由于n个元素的有限集有且只有个子集由于个元素的有限集有且只有2n个子集，而且很显然有限布个元素的有限集有且只有个子集，尔代数一定是有限集合代数，所以对某个整数n而言而言，尔代数一定是有限集合代数，所以对某个整数而言，每个有限布尔代数也有且只有2n个元素。例如，上文定义的集合T的限布尔代数也有且只有个元素。

Semilattice graded weak Hopf algebra is a special case of weak Hopf algebra and a generalization of Hopf algebras, in Section 1.3, we will give results and applications to the Maschke's and Dual Maschke's Theorem of semilattice graded weak Hopf algebra.

尽管有限Clifford幺半群的量子偶确实是有限群量子偶的一个推广，但是[L2]中的量子偶一般情况下是不能够看作是Hopf代数量子偶的一个推广，这是因为我们在[L2]中要求所有讨论的弱Hopf代数都是交换的。

The elementary transformation matrix throughout the linear algebra theory has, it makes some of the problems of linear algebra, become more simple, makes it easier to understand, so elementary transformation in the role of linear algebra is very important.

标签：论文摘要，翻译，论文矩阵的初等变换贯穿于整个线性代数理论的始终，它使线性代数里的一些问题变的更加简单，使人更容易理解，所以初等变换在线性代数中作用十分重要。

Based on the Lie algebra that describes the symmetries, it is proved in this dissertation that a sufficiently large class of control Hamiltonians can be provided by the universal enveloping algebra of the Lie algebra, on which the quantum mechanical control systems can be modelled.

基于描述量子力学系统对称性的李代数结构，本文证明该李代数的泛包络代数提供了足够大的一类控制哈密顿量，因而可以在其上建立量子力学控制系统的模型。

It is easy to see that the bialgebra H we find,canbe regarded as the enveloping algebra of a Lie algebra,whose generators are thoseof the Lie algebra of type A and n-1 other elements which commute with genera-tors above.

可以看出，我们找到的H作为代数，恰为在An-1型李代数上增加与之可换的n-1个生成元后得到的包络代数，其自然表示的矩阵元恰好生成代数AR。

We use algebra to describe the semantics. Algebra provides a common base for function, class and algebra specification.

它以代数作为数学基础，这使得函数、类和代数规范等具有统一的合成基础。

Now the university to open higher algebra, general consists of two parts: a preliminary linear algebra, algebra polynomials.

现在大学里开设的高等代数，一般包括两部分：线性代数初步、多项式代数。

This paper takes advantage of interval algebra and rectangle algebra theories. and brings forward a new reasoning method based on combination of the MBR model's cardinal direction relation and rectangle algebra relation; And provides the composing method based on the direction relation matrix by using the direction relation matrix to denote the direction relations between the objects'MBRs.

本文以物体的MBR为模型，利用区间代数及矩形代数理论，提出了一种基于MBR的主方向关系与矩形代数关系相结合的推理方法；同时利用方向关系矩阵表示物体MBR之间的方向关系，得到了基于方向关系矩阵的组合推理方法。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。