查询词典 duality theorem

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

Theorem g is called binomial theorem.

定理g称为二项式定理。

The classical theorems of analytic function of one complex variable such as Morera theorem and Liouville theorem were generalized to the regular function, similarly to biregular function.

Clifford分析中，正则函数是单复分析中全纯函数在高维空间的推广，全纯函数的经典函数理论如Morera定理，刘维尔定理等都可推广到正则函数，同样也可推广到双正则函数。

By using the integral equation and the Schauder fixed point theorem, through considering the height of nonlinear term on some bounded set, a new existence theorem is established.

利用积分方程和Schauder不动点定理，通过考察非线性项在某些有界集合上的高度建立了一个新的存在定理。

Theorem and Burnside Theorem about p-nilpotence.

和Burnside关于p-幂零的定理。

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

The thesis consists of the followingmain results:the Cauchy's integral formula on certain distinguished boundaryfor LR regular functions with values in a universal Clifford algebra 〓,theCauchy's integral theorem,the mean value theorem,the maximum modulus the-orem.the Taylor's expansion,the Laurent's expansion and the residue theoremetc..

第一章叙述了泛Clifford代数基本理论，其中，我们首先准确而又富有创造性地给出了在泛Clifford代数〓上的一个对合运算表示，由此，我们给出了在泛Clifford代数〓上的一个内积，然后，我们借此给出了在泛Clifford代数〓上的相应的两个等价的范数，并证明了若在〓上赋予其中的一个范数，则〓是一个Banach代数。

At last, by martingale large number theorem and central limit theorem, we study the hypothesis testing of parameters.

最后， 利用鞅大数定律和中心极限定理对参数作了假设检验。

To solve this problem, an algorithm to analyze and research the multi-harmonic sources was proposed based on certain assumptions, and the calculation formulae of harmonic superposition were deduced based on Big Number Theorem and Central Limit Theorem of probability statistics.

针对这一问题，论文在一定假设条件下，提出了一种研究多谐波源谐波电流叠加的方法，利用概率统计学中的大数定理和中心极限定理，推导出了谐波叠加的计算公式。

A historical region of southwest France between the Pyrenees and the Garonne River. The duchy of Aquitaine was joined with France after the marriage of Eleanor of Aquitaine to King Louis VII in1137, but its possession was disputed after her subsequent marriage to Henry II of England.

阿基坦法国西南部一个历史地区，位于比利牛斯山和加隆河之间，在1137年阿基坦的埃莉诺与国王路易斯七世结婚之后阿基坦公国加入法国，但当她再嫁英国亨利二世后，其归属权便受到争议

There are moments when I look at the smiling , happy faces of my expectant staff and wonder how they will cope when confronted by an outraged housemaster along with an unrepentant and recalcitrant bleached blond teenager in 18 years ' time .

有时候，我看着那些满怀期待的员工微笑，幸福的脸，想着当他们遇到一位愤怒的宿舍管理员和一位不知悔改，叛逆，而且将头发染成白色的18岁少年时，他们会如何处理。