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In this paper, the convergent conditions in sequence or parallel update mode and the sufficient condition with only one global stable state for Hopfield network model with discrete time and continuous states when its neurons' activation function is non-decreasing (not being strictly monotone increasing) are discussed.

主要讨论离散时间连续状态的Hopfield网络模型中当神经元的激活函数为单调增函数时，并行和串行收敛的充分条件以及具有全局惟一稳定点的充分条件。

A fixed point of a discrete-time neural network with generalized input-output function and by using the converse theorem of Lyapunov function we study the uniformly asymptotical stability of equilibrium in this discrete-time neural network with variable weight and give some sufficient conditions that guarantee the stability of it.

本文首先介绍了几类离散神经网络模型的由来及其研究概况，利用Schauder不动点原理证明了一类具有广义输入输出函数的离散神经网络模型平衡点的存在性，利用Lyapunov函数逆定理给出了这类离散神经网络模型在时变权值下的一致渐近稳定性的充分条件。

In this thesis, we firstly introduce several class of discrete-time neural network models and the research progress of the neural networks. By Schauder fixed-point principle we prove the existence of an equilibrium (i.e. a fixed point) of a discrete-time neural network with generalized input-output function and by using the converse theorem of Lyapunov function we study the uniformly asymptotical stability of equilibrium in this discrete-time neural network with variable weight and give some sufficient conditions that guarantee the stability of it.

本文首先介绍了几类离散神经网络模型的由来及其研究概况，利用Schauder不动点原理证明了一类具有广义输入输出函数的离散神经网络模型平衡点的存在性，利用Lyapunov函数逆定理给出了这类离散神经网络模型在时变权值下的一致渐近稳定性的充分条件。

Is it sufficient to have a single currency with free and guaranteed convertibility?

是否有足够的单一货币自由兑换，并保证？

For solving problem (1), this dissertation first presents a sufficient and necessary condition by dealing with inequalities using projection operator in convex analysis, and then proposes a kind of new neural network model based on the constraint domain:〓(2) Where P is a projection operator on Q.

本文利用凸分析中的投影算子处理不等式约束，首先给出二次规划问题(1)解存在的充分和必要条件，据于此提出一种新的基于约束区域神经网络模型〓(2)来进行求解，其中P为Q上的投影算子。

For a finite-security and finite- state financial market with three forms of friction: ask-bid spread, transaction costs and tax, by using the theory of convex analysis and some optimization techniques, a series of necessary and sufficient conditions are established to characterize weak and strong no-arbitrage respectively.

对存在买进卖出价差、交易费和税收三种摩擦和有限个可能的自然状态的金融市场，利用凸分析理论和最优化技术刻划出了强无套利和弱无套利的一系列充要条件，以往许多这方面的结果均是我们的特例。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

The sufficient conditions enabling a singular system with observer-based guaranteed cost controller to stabilize its linear state feedback is obtained by use of a new method in combination with the convex optimization theory.

通过基于状态观测器的线性状态反馈控制并采用一种新方法，结合凸优化理论得到了不确定广义时滞系统的最优保成本控制器的设计方法。

A sufficient condition of quadratic stability for the impulsive and switched systems is given with a switching law by way of convex combination and single Lyapunov function.

在有限个备选状态反馈控制器的条件下，利用凸组合技术和李雅普诺夫函数等方法，给出脉冲切换线性广义系统二次稳定的充分条件及切换律的设计。

The switching law is given out according to convex combination condition and the sufficient condition of the stabilization is obtained by switching among a finite number of controllers under the assumption that a single controller cannot make the systems stable and has H-infinity disturbance attenuation.

在假定每个单一的控制器均不能使系统稳定且具有H扰动衰减度的条件下，利用凸组合条件给出了切换律的设计方案，通过在有限个控制器间的切换得到了镇定的充分条件。

I can not negligent, he should do what?

我不能不在意了，他要做什么呢？

It is very dangerous to swim in the river alone.

一个人到河里游泳是很危险的。