查询词典 compactification theorem

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

Introduced in the third chapter with 区间套 theprinciple, the true principle, the fluxionary calculus proved threemethods have carried on the proof to a zero theorem; Then introduces azero theorem the promotion; Finally introduced the zero theorem twoapplications.

在第三章中介绍了用区间套原理、确界原理、微积分证明三种方法对零点定理进行了证明；接着介绍零点定理的推广；最后介绍了零点定理的两个应用。

Also: the renewal theorem, conditional probability and expectation, regular conditional distributions, stationary sequences aud the bergodic theorem, martingales, and the optimal stopping theorem.

更新理论，条件概率和期望，规则的条件分布，平稳序列和 bergodic 定理，鞅，最优停步理论。泊松过程，布朗运动，强马尔可夫性和不变原则。

Meanwhile, important random acute angle principle、theorem of random full mapping and theorem of random one-one mapping are proved.

同时我们证明了重要的随机锐角原理、随机满射定理和随机一一映射定理。

In addition also introduced the differential theorem of mean in the proof equality and the inequality, the certificate equation root existence, asks the limit, to ask the approximate value, as well as aspect and so on research function condition should thus deepen to the differential theorem of mean understanding.

此外还介绍了微分中值定理在证明等式和不等式、证明方程根的存在性、求极限、求近似值，以及研究函数性态等方面的应用，从而加深对微分中值定理的理解。

We prove the existence theorem of rationed with Borel points for meromorphic functions in the unit circle, discuss the operations of algebroid functions and the existence theorem of Nevanlinna direction of algebroid function dealing with mutiple values, and obtain some uniqueness theorems dealing with mutiple values of algebroid functions.

证明了单位圆内限定Borel点的亚纯函数的存在性定理，讨论了代数体函数的运算性质以及涉及重值的Nevanlinna方向的存在性定理，得到了一些涉及重值的代数体函数的唯一性定理； 2。

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

Since the structure self-organization and self-learning abilities of GFNN, it is different from the universal approximation theorem of FLS and BP theorem of NN.

由于GFNN的结构自组织和参数自学习能力，使得它与模糊逻辑系统中的万能逼近定理以及人工神经网络的BP逼近定理不同，GFNN不再只是一个存在性定理，它给出了GFNN的实现过程。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。