查询词典 implicit function 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。

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。

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。

Based on this thought, in this thesis, the alternation theorem is first extended to the Chebyshev approximation problems with inequality constraints, and then two algorithms are devised for designing linear phase FIR filters with inequality constraints in Chebyshev sense according to the extended theorem.

L.J.Karam和McClellan在文献[20]中把交错点组定理扩展到复数域，并提出了求解复系数FIR滤波器的复Remez算法，但由于此扩展定理只是一个充分条件，所以此算法不能保证得到最优解。在文献[23]中，他们对复Remez算法进行了完善，使其收敛到最优解。

In this paper, infinitesimal classification is given and theorem condition of equivalent infinitesimal replacement is simplified,thus,this theorem is easy to operate.

对无穷小提出了新的分类法，并对等价无穷小替换定理的条件进行了简化，从而使得该定理应用更加方便。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样