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The analytic technique which is first invented by professor Liu Wen is skillfully introduced to the study of strong limit theorems for Markov chain fields on trees by professor Liu Wen and his copartners. In this paper, the martingale technique is applied to continue the study in this respect.

刘文教授及其合作者把刘老师首创的分析方法巧妙的引入了树上马尔可夫链场的强极限定理的研究工作中,本论文应用鞅方法继续了这方面的研究工作。

If '' H '' is a subgroup of ''G'', the following useful theorems, stated without proof, hold for all cosets

如果 ''H''是''G''的子群,则下面陈述而不带证明的有用定理对所有陪集都成立

The sine, law of cosines's several sine law and the law of cosines are three angular corner relations and three jiao functions plants using abstract the is most common, the most important two theorems.

帮我把这段文字翻译为英文,谢谢,非常感谢摘要正弦定理和余弦定理是三角形边角关系及三角函数种最常见、最重要的两个定理。

We give all of these properties by means of theorems, and also give detail proofs. In the most important theorem, we give the relation between singularity and jumps and sharp cusps neighborhood. and the threshold detection of jumps and sharp cusps, and the relation between threshold and scales, where we partly resolve an open problem put forward by some researcher.

在最关键的定理中,给出了奇异性与突变点和尖点的领域的关系,以及突变点和尖点的阀值检测法,以及阀值和尺度的关系,这部分的解决了以前研究者提出的一个公开问题,同时研究了逼近程度和逼近理论,这在已有的基础上又向前进了一步。

Hence, when taking the equivalent duals of all former statements, one ends up with a number of theorems that equally apply to Boolean algebras, but where every occurrence of '' ideal '' is replaced by '' filter ''.

因此,当采用所有前者陈述的等价对偶的时候,你可能终结于同等的适用于布尔代数的定理,但是这里所有''理想''的出现都被替代为''滤子''。

In chapter 3, as a application of fixed point theorems in gauge spaces, by using the results in chapter 2 we study the existence and uniqueness of solution for integral equation of Voletrra type in C.

第三章,作为度规空间中的不动点定理的应用,我们利用第二章中的结果,在C空间中研究了Voletrra型积分方程解的存在性与唯一性。

Then I shall argue that in the vein of the incompleteness theorems there is no answer with mathematical certitude to the mind-machine debate and that much of the philosophical burden of proof will lie with mechanists in this debate.

笔者将指出:限制在不完备性定理的脉络下,心灵是否为机器这个问题不可能有数学上或逻辑上的明确答案,然而就哲学的观点而言,机器论者必须承担较大的举证责任。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究,揭示了差分、差商与导数之间的联系;将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中,简明地推导出Lagrange差分中值定理等4个定理,并在此基础上对&中间点&的渐近性进行了研究,得出了一系列&中间点&的渐近性的结果,概括了有关文献对微分中值公式的&中间点&的渐近性的讨论;给出的引理改进了函数逼近论的证明方法,精简了函数逼近论中的一些内容。

More than his monetarist theorems, this equation of "capitalism and freedom" was his greatest contribution to the rehabilitation of conservatism in the 1970s.

但是,成千上万的人被杀害、大规模的饥荒、折磨和非法的监禁恰巧是在他的门徒皮诺切特统治时发生的。

B. Those theorems that relate the sj/vj=si/vi dual accounting system to the pre-Marxian primal accounting system of Sj/=Si/ much in the way that a bi-lingual dictionary relates, say, my children's private nursery language to standard English.

B。 与sj/vj=si/vi二重的帐目清算体系相关的那些定理。它们与前马克思主义的最初的帐目清算系统sj/=si的大部分联系是一种双语字典的方式,就像我孩子们的私人托儿所语言与标准英语一样。

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在对危险的南部地区访问时,他斥责什叶派民兵领导人对中央集权的挑衅行为。

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