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In chapter 4, we retroduce monoial category and center over it. moreover, we introduce weak center over weak hopf π coalgebra. After studying of the relationship between it and Yetter-Drinfeld moduels, we could found they are isomophic.

第五章主要讨论了弱Hopf群余代数上的弱相对Hop(来源：Ab9BC论文网www.abclunwen.com)f群余模，引入了迹运算，中心等，在此基础上对弱相对Hopf群余模的研究。

Varieties of drinks of the Coca Cola Company are available in over 200 countries and regions all over the world.

全世界共有200多个国家及地区的消费者可以在当地享用这个公司提供的各种饮料。

On the edge of collapsing, i begin to think about myself over and over.

在崩溃的边缘，我开始一遍又一遍地反思自己。

In this way, colouring of over two million tons of plastic products was achieved over the past year.

这样，我们在过去的一年里为超过2百万吨塑料产品进行着色。

But the customers come up with smiling faces over and over again to please the staff, want to buy scarce goods.

而是顾客拿出笑脸一遍又一遍讨好店员，想买点紧俏商品。

The relationship between the public interest and civil rights is: who has the greater priority? The neo-liberal advocates that civil rights should take a priority over the public interest; and communalism advocates that public interest should take precedence over civil rights.

公共利益和公民权利之间的关系表现在：两者谁更优先上，新自由主义主张公民权利优先于公共利益，而社群主义则主张公共利益优先于公民权利。

ABSTRACT Over the last few years much attention has been paid to the development of the technologies for Community Antenna Television networks. New technologies that can be used to support data communication service over CATV networks are developed. The new Hybrid Fiber Coaxial technology is spreading out rapidly in CATV networks. The usage of fiber provides large bandwidth and thus enables some new services to be delivered along with television broadcast. The CATV networks are expected to support diverse traffic with various service requirements.

随着新技术的不断发展，人们希望能够利用有线电视网络提供新的业务，HFC技术在有线电视网络中的广泛使用使得有线电视网络的带宽增加，也使得有线电视网络除电视广播外还能够提供其他的服务，这些服务的服务质量要求各不相同，如：数据服务要求低的丢失率，对延时的要求较低；而语音服务可容忍一定的丢失，但对延时、延时抖动有严格的要求，因此需要开发新的协议。

Secondly, some discussions are given to the two basic problems on polynomialfunctions over finite commutative ring R ―when does a function over R become apolynomial one?

然后，我们讨论一般有限交换环上关于多项式函数的两个基本问题：多项式函数的判别问题和多项式函数的个数问题。

We prove that the Jordan semi-triple derivable maps of the algebra of all n×n matrices over a 2-torsion free commutative ring with unity is the sum of an inner derivation and A_φ, where A_φis the image of A underφapplied entrywise andφis an additive derivation over R.

证明了作用在一个包含单位元的可交换的2-无挠环上的矩阵代数上的拟三重Jordan可导映射是一个内导子与A_φ的和(这里A_φ是A在φ下逐点作用的像)。

In this paper, we will investigate the matrix equation in composition over a complete Brouwerian lattice. First, we give an equivalent condition for the solvability of this equation, i.e. theorem 2.2.3 in this paper: The matrix equation in composition over a complete Brouwerian lattice is solvable iff is the minimal solution of this equation.

本文主要探讨完备Brouwer格上的型矩阵方程，首先给出该类矩阵方程可解的一个等价条件，即本文的定理2.2.3：完备Brouwer格上的型矩阵方程可解的充要条件是是它的解，且是最小解。

As of Tuesday, Google's results were still censored in China.

截至周二，谷歌的搜索结果仍受中国审查。

In order to make the positive action increase and negative one decrease, the sub-forces of the social factors must be adjusted to form a centripetal force.

在这一过程中，人的主体性发挥是社会有机体健康发展的灵魂。