极限点

In chapter 3,the bifurcation theory of topological current is established inthe neighborhoods of limit point,bifurcation point and higher degeneratedpoint respectively.

第三章讨论和建立了拓扑流在极限点，分岔点和高阶退化点的分歧理论。

LetJbe a continuous map of a unit square into itself and f can be descendent. This paperpresents slecific featrue for f with homochinic points.

设f是可降的二维自映射，本文给出了这类自映射有异状点的特征──存在f的链回归点，但不是周期点，并且f的队极限点集与周期点集的交非空。

We also call they as convergence in distribution, convergence in probability and almose sure convergence.

Fridy(1985，1993)运用自然密度的定义将实数序列的极限点的概念拓广到了统计极限点的概念。

The limit point is analysed by establishing the mathematic model of cyclinder and taper orthoyonal.

通过建立圆柱与圆锥正交时的数学模式，对极限点进行几何分析，用微积分的方法求出极限点的坐标及变化规

The main objective of this paper is to extend and complete the Sims limit-point, limit-circle classification on second order linear differential equations with a complex coefficient , and to study its Weyl function and Weyl solution , then we obtain some new results.

本文的主要目的是推广和完善Sims关于复系数二阶微分方程的极限点和极限圆理论，并且研究了它的Weyl函数和Weyl解，得到了一些新的结论。

As to the problem of divergency of conventional power flow method,By using an augment eqution this method can get the exact limit of voltage stability and the whole PV curve without encountering the numerical difficulty of ill-conditioning.

针对常规潮流法在鞍结分岔点附近不收敛，该方法通过增加一维潮流方程，消除了功率极限点附近的雅可比矩阵奇异的现象，获取精确的电压稳定极限和整支PV 曲线。

Deviate argument; Limit circle case; Limit point case; The boundedness of solutions; Integral inequality

基础科学，数学，数学分析偏差变元；极限圆型；极限点型；有界性；积分不等式

The joint effect of active and reactive power on the voltage stability of a typical power system was considered by analysing the two parameter bifurcation problem related to nonlinear oscillation phenomena. Numerically, as the active power P1 increases, the Hopf points get closer and eventually coincide at P1=1.455 43 the cyclic fold curve gets closer and closer to the Hopf curve and finally intersects the Hopf curve at a singular point the period-doubling points also get closer and finally coincide at P1≈0.65. The stability behaviour is pre-determined using the normal form approach near the limit point of the Hopf curve. Hence, in the power system attention should be paid to both the consumption of active power and the decrease in the reactive power to prevent nonlinear oscillations. A controller can be designed to absorb some active power and to avoid the nonlinear oscillations that damage the system components.

针对一个典型的单机无穷大电力系统，通过分析系统的双参数分岔的非线性振荡现象，综合考虑有功和无功功率对电压稳定性的影响数值分析表明，随着有功功率的增加，电力系统的Hopf点越来越靠近，最终合为一点在P1=1.455 43处同时圈折cyclic fold 曲线也越来越靠近Hopf曲线，并在Hopf曲线的稳定与不稳定临界点处与Hopf曲线相交倍周期分岔点也随着越来越靠近，最终在P1≈0.65 合为一点应用正规形理论方法，初步确定了Hopf曲线极限点附近的稳定性态因而，电力系统应注意让负荷利用有功功率，减少无功功率的产生以防止非线性振荡另外，可以设计一个稍微吸收网络的有功功率的控制器，以避免因周期振荡而造成电力系统仪器的损坏或电压崩溃

Then we can establish global convergence to a stationary point, that is, if {xk} is the sequence generated by the affine-scaling interior-point trust-region method, then every limit point of the sequence is a stationary point for the problem.

其次我们建立了收敛到一个稳定点的全局收敛结果，即若{x_k}是由仿射尺度内点信赖域法产生的序列，则序列的每个极限点都是问题的一个稳定点。

Are countable sets:Λ-Γ,〓-Γ are either empty or countably infinite, where Γ denotes the set of γ-limit points of f; tree map's depth of attracting center is finite and the attracting center is Γ provded all the branching points are periodic points. In chapter Ⅲ. we discuss certain relationship between isolated chain recurrent point and eventually periodic point of some continua.

主要利用树的特殊偏序关系证明了：不在周期点集闭包中的ω极限点都有无限轨迹；Ω-〓，Ω-Γ为可数集，Λ-Γ，〓-Γ或为空集或可数无限，其中Γ为f的γ极限点集；当分支点都是周期点时，连续树映射的吸引中心深度有限，且吸引中心就是Γ。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。