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In fifth chapter,as applications of the existence theorem of〓-optimalcoupling operator for the jump processes,the estimate of the varied expontialconvergence rate for the jump processes and the existence of an order-preservingMarkov coupling for the jump processes are investigated,where,the obtained theexistence theorem of an order-preserving Markov coupling is a general theorem onPolish space endowed with semiorder,it includes the results that existence theoremon countable state apace endowed with total order or finite state space endow withsemiorder have been obtained by the internal and external mathematicians in recentten years.

第五章作为跳过程〓最优耦合算子存在性定理的应用，讨论了跳过程各种指数收敛速度的估计和保序Markov耦合的存在性。其中保序Markov耦合存在定理是具有偏序关系波兰空间上的跳过程最一般的定理，它包括了近10年来国内外对具有全序关系可数状态空间或具有偏序关系有限状态空间上的跳过程关于保序Markov耦合存在定理的研究成果。

This book, composed of material prepared for the Silliman Lectures by john von Neumann before his death, represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines adn the living human brain.

这本书是自动机理论研究中的重要材料之一。原书是冯·诺意曼在1955—1956年准备讲演用的未完成稿。

In the last thirty years, singular boundary value problem in Banach space has become one of the most important problems that attract the attention of more and more mathematicians and other technicians see.

近年来，由于Banach空间中的奇异边值问题在气体动力学、流体力学、边界层理论、非线性光学等应用学科的研究中具有较高的实用价值，该问题逐渐成为国内外数学工作者和其他科技工作者所关心的重要问题之一(见[9]-[11]、[15])。

Naturally,we confront with such a problem:can we generalizethe systematic work on the classical boundary value problem for analytic func-tions and singular integral equation to Clifford analysis?And so this problemhas especially theoretical and practical meaning,and naturally this problem hasbecome a common hot topic for mathematicians at home or abroad.

其结果在一定程度上推广了一些经典文献的结果，取消了这些在经典文献结果中对s=0或s=n的条件限制，需要指出的是，据作者所知，到目前为止，本文也是第一次系统而又比较深入地研究了取值在泛Clifford代数〓上的超复函数的性质，并获得了比较系统而又深入的结果；另外，本文还对Clifford分析中的某些比较特殊的Riemann边值问题与奇异积分方程做了一定程度的研究，由于文中所用的方法较曾经出现的文献而言有着根本的改进，因此，本文去掉了从前在这一问题的研究过程中所做出的一些不必要的条件限制，从而使得在比以往条件更弱的情况下，获得了比以前文献中更多的结果。

A simple example of the first type is the slide rule, which mathematicians and scientists have been using for generations.

好几代数学家和科学家沿用的计算尺就是第一类中的简单例子。

Massachusetts Institute of Technology mathematicians have created a model to describe how these frustrating snarls form.

麻省理工的数学家创造了一个数学模型，解释交通堵塞是怎么形成的。

He is the son of two mathematicians who worked on the team that developed the world's first commercial, stored-program computer, the Manchester University Mark 1, which was commercialised by Ferranti, a British company, in the1950s.

迪姆阁下的父母都是数学家，他们所工作的项目组开发出了世界上第一台商业性且具有存储应用程序的计算机，取名为曼彻斯特大学马克1号，并在上世纪五十年代由名为菲兰提的英国公司进行了商业化并投入市场。

Nevertheless, he continued to work on elliptic functions and at the same time earned his living as a supply teacher. Finally, some famous mathematicians were aware of his works.

虽然如此，但他仍然一方面做代课教师维生，一方面致力研究椭圆函数，并不断发表他的成果，这些成果受到当时著名的数学家重视。

Foreign mathematicians and philosophers have begun to explore the issues related to the origin of probability theory.

国外的数学家和哲学家们已经开始探讨与概率论起源有关的问题。

I stressed in my talks with her the role Stony Brook played, yet she focusses on the talk Grisha gave at Princeton, listing a collection of eminent mathematicians, none of whom is a geometer/topologist.

我向Nasar强调石溪分校在其中所起的作用，可是她只把注意力放在Grisha在普林斯顿所给的唯一一个报告上面，她给出了一个著名数学家的名单，没有一个几何或拓扑学家。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。