平衡点

This text utilizes the stability theory of differential equation, establishes the mathematical model of praying on the relation among the living beings, then according to the characteristic of differential equation group set up, through analyze to its equalization point,discuss the rail line distribution situation and overall stability, studies the dynamic change situation of every species during sufficient long time slot.

摘要本文利用微分方程稳定性理论，建立生物间捕食关系的数学模型，然后根据建立的微分方程组的特性，通过对其平衡点分析，轨线分布情况以及全局稳定性的讨论，研究出各物种在充分长时间段中的动态变化情况。

Routh-Hurwitz is used to determine that the characteristic equation has negative real root, and Center-Manifold theorem is used to study the stability of autonomous differential system in the case of hyperbolic and non-hyperbolic at the equilibrium point.

利用Routh-Hurwitz判定特征方程有负实部根，并利用中心流形定理研究了自治微分系统在平衡点处双曲和非双曲情况下的稳定性，由此产生系统趋于不同稳定点时病毒分裂的临界值，同时利用数值模拟验证了分析的合理性。

But many democrats voiced strong opposition ,among them California Congress woman Barble LeeIt does not strike the proper balance between protecting National security and preserving our chari's civil liberty.

不过很多民主党元发表他们的反对意见，美国国会女议员中的Barbara Lee说"保护国家安全和保存我们珍贵的民主权之间的平衡点兵不因为这一点儿被打破。"

And I think right now, I have a nice balance, she told CNN's Talk Asia.

而且我认为现在我已经找到了一个漂亮的平衡点。她告诉CNN 谈话亚洲。

At first,the cobweb model in a differential equation's form is established under the condition of continuous time.

首先，在连续时间的条件下，建立了蛛网模型的微分方程形式；其次，通过分析微分方程模型平衡点的稳定性，得到了蛛网模型稳定的条件；最后给出与微分方程模型相应的经济解释和具体应用。

At last, in order to searching the best consilience and balance between keeping the stability and the continuity of law and keeping up with the change of the social and economical development and its effects, we put forward our points of view of reforming mediation system of civil procedure in China in the view of practice, thus helping to build the authority of law and pushing the process of rule by law forward smoothly.

最后从实践的角度出发，提出自己的改革观点，以期在保持法律的稳定性和连续性与适应社会和经济的迅速发展变化所产生的影响之间寻求最佳契合点和平衡点，从而树立了法律的极大权威，推动我国依法治国进程的顺利进行。

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。

To confirm and expand the mass transit scale of a city is a complex nonlinear convex programming problem.

运用电力系统分析中的负荷持续时间曲线和盈亏平衡点理论对公交车辆规模和静态扩张问题进行了分析，建立了数学模型，并给出了相应的算法。

On the basis of the conclusion above, the nonlinear weak controllable vectors can be obtained, which compose the second class of weak controllable matrix, by means of matrix transfermations of the first class of weak controllable matrix. Furthmore the second criterion of weak controllability, accessibility and strong accessibility, which is more standard, more succinct and more practical, is obtained. On the basis of the first criterion and the second criterion, several important problems about nonlinear controllability are discussed, which include 1 local controllability; 2 three classes of local controllable decomposition, separately by means of local coordinate changes in the neighborhood of a nonsingular point, a point on a singular surface or a designated point x〓 with a designated input u〓; 3 the character of controllability of the ith state variable x〓 in different controllable areas and their boundaries.

在第一判别定理和第二判别定理的基础上，我们分析了非线性系统受控性质中的几个重要问题，所得到的结论包括i得到了非线性系统在可平衡点附近的能控性判别定理；ii分别给出了非线性系统在非奇异点、s阶奇面以及在状态空间内给定的一点x〓和输入u〓上的三种状态分解形式以及相应的求解方法；利用系统的Ⅰ型弱能控矩阵与Ⅱ型弱能控矩阵秩相等的条件，得到了只用系统的前n个弱能控向量来判断系统的弱能控性的判别定理；iii通过引入系统状态分量的三类受控区域边界的定义及相应的求解方法，初步探讨了非线性系统各个状态分量在不同的受控区域及其边界上的受控性质。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。