查询词典 implicit function theorem

Furthermore, when the system is a periodic system, sufficient conditions are obtained that guarantee the existence, uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Liapunov function.

利用比较原理给出了系统一致持久性的充分条件；当系统是周期系统时，应用Brouwer不动点原理和构造Liapunov函数的方法给出其存在惟一且全局吸引的ω-周期正解的充分条件，并通过实例验证了文中定理条件的可实现性。

By Lasalle invariant theorem and Liapunov function, the global asymptotical stability of disease free equilibrium and the endemic equilibrium is proved.

利用La-salle不变原理和Liapunov函数得到了无病平衡点和地方病平衡点全局渐近稳定。

Theorem 1 (Uniqueness of Limit of Function) If exists, then its limit is unique.

定理 1 如果存在，那么这极限唯一。

Some methods for dealing with the stability problem has presented and these methods include: Lyapunov function, differential inequality, matrix norm and measure, Razumikhin theorem method etc. The results of stability for these systems are derived by using these methods. This paper may be summarized as follows.

本文考察了区间Lurie型控制系统与不确定时滞系统的稳定性问题，给出了判定系统稳定的一些处理方法，这些方法包括：Lyapunov函数法、微分不等式法、矩阵范数与测度法、Razumikhin定理等方法，并且应用这些方法得到了系统稳定的判别条件。

In Chapter 5, some knowledge about large-scale system and methods for investigating them are introduced, Lyapunov function, differential inequality, Razumikhin theorem, matrix norm and measure methods have been used to discuss the stability of uncertain large-scale system with delays and decay estimates for uncertain time-varying large-scale system with delays, the criteria of stability and decay estimates for uncertain large-scale system with delays are given.

第五章首先介绍了大系统的有关知识以及时滞大系统研究的方法，然后利用Lyapunov函数法、微分不等式法、Razumikhin定理法、矩阵范数与测度法研究了不确定定常时滞大系统的稳定性以及不确定时变时滞大系统的稳定性与系统衰减率的估计问题，得到了系统稳定的判别条件以及系统衰减率的估计。

Mean Value Theorem is to examine the function of the characteristics of a powerful tool, it is also an important means of research.

中值定理是研究函数特性的一个有力工具，它也是研究问题的重要手段。

In 2005 Zhou Houqing proved a theorem about the uniqueness of meromorphic function, we consider if we can weak the condition CM to weight using the idea of sharing value with weight so as to get a better conclusion.

权分担是亚纯函数唯一性理论中的重要内容。2005年周后卿证明了一个关于亚纯函数唯一性的定理，考虑能否运用权分担的思想将CM分担减弱为权分担，从而得到更好的结论。

In chapter 4 , with S-KKM mapping , a new Ky Fan\'s minimax inequality is proved , the locally convex H-space with uniform structure is introduced , s-HKKM mapping is defined as the generalization of KKM mapping, with the H-convexity of Hausdorff locally convex H-space , a new fixed point theorem for the compact andclosed mapping belonging to the class s-HKKM is established ;with local intersection property of muti-function ,K-H-quasi-convexity of mapping , connectedness of set and condensing correspondences, some new vector quasi-variational inequalities are established , respectively .

第四章利用S-KKM映射，建立了新的Ky Fan极小极大不等式；定义了带有一致结构的局部凸H-空间，利用Hausdorff局部凸H-空间的H-凸性，对于属于s-HKKM中紧的闭映射建立了新的不动点定理，利用对应的局部交性质、映射的K-拟-凸性、集合的连通性以及φ-condensing对应分别建立了相应的拟向量变分不等式。

Then we prove a nonsmooth minimax theorem by usingsome relative results about multi-valued maximal monotone mappings. Finally, we construct a nonsmooth minimax network to search for thesaddle points of the saddle functional. We have also proved that thetrajectory of the network is asymptotically convergent to thesaddle point of the saddle functional by usying Lyapunov function.

我们先介绍有关Clarke的广义梯度，次梯度及鞍泛函的有关结论；然后利用多值极大单调映象的满射性结果证明了一个非光滑的minimax定理；最后建立了一个非光滑的minimax神经网络来求解泛函的鞍点，并在一定的条件下构造出LYAPUNOV函数来证明网络的轨道渐近收敛于鞍泛函的鞍点。

A strong limit theorem on gambling strategy for Bernoulli sequences is extended to the sequences of arbitrary dependent random variables which take numberable values by using the conditional moment generating function .

利用条件矩母函数将关于Bernoulli序列赌博策略的一个强极限定理推广到取可列值的任意相依随机变量序列的情况，并且通过允许选择函数在一个区间中取值，推广了随机选择的概念。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。