不动性

Since bounded closed sets in infinite dimensional space are notcompact generally,in order to employ Horn's fixed point theorem the compactness of operator Pis initially proved in section 3 in this chapter.

由于无限维空间的有界闭集一般不具备紧性，为了应用Horn不动点定理，我们先证明了Poincare算子P的紧性。

In this paper,the existence and stability of fixed points are studied to a Nonlinear Evolution Equation and the nonexistence of limit cycles is proved by the Bendixon-Dulax.

研究了一个非线性发展方程不动点的存在性及其稳定性，并运用Bendixon-Dulax判别法证明了此方程极限环的不存在性

In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression.

在最后一部分讨论了带有特征值的非线性二阶差分方程正解存在性问题，利用锥压缩与拉伸不动点定理及逼近性理论，在一定的假设条件下，得到了差分方程正解存在性。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

Under certain donditions ,the existence of generalized synchronization can be turned to the problem of compression fixed point in the family of Lipschitz functions.Theoretical proofs are proposed to the Lipschitz smooth,H lder continuity and exponential attractive property of generalized synchronization manifold.

若满足一定条件，广义同步流形的存在性问题可转化为Lipschitz函数族压缩不动点问题，并且理论上证明了两类广义同步流形的Lipschitz光滑性、H lder连续性和指数吸引性。

In chapter 2, by virtue of the properties of partially ordered F-type topological space, we establish some fixed point theorems of increasing mappings in this kind of space. At the same time, we investigate the existence of maximum fixed point and minimum fixed point of increasing mappings on an order interval.

第二章，利用半序F-型拓扑空间的基本性质，建立这类空间上单调增映射的不动点定理，研究其序区间上单调增映射的最大、最小不动点的存在性。

In this project,we primarily investigated the growth of solutions of some types of differential equations,and the hyper order,the exponents of convergence of zeros and fixed points of solutions with infinite order, especially, expononts of convergence of fixed points of first, second order derivatives and differential polynomials of solutions.

中文摘要：在本项目中，重点研究了几种类型的微分方程解的增长性，及无穷级解的超级，零点收敛指数，不动点收敛指数，特别是解的一阶，二阶导数及微分多项式的不动点收敛指数。

By using the cone and partail ordering theory, and mixed monotone operator theory in nonlinear funtional analysis, the existence and uniqueness of the common fixed point for two non-monotone binary operator are discussed in partial ordering Banach space.

利用锥与半序理论和混合单调算子理论，讨论了半序Banach空间中两个非单调二元算子的公共不动点的存在性和唯一性，并给出了迭代序列收敛于公共不动点的误差枯计，所得结果是某些已知结果本质改进和推广。

This paper discusses convergence of Ishikawa iteration sequence and existence of fixed points for set-valued nonexpansive mapping in uniformly covex Banach space, and the conditions are shown which guarantee the convergence of the iteration sequence to a fixed point.

讨论了δ集值非扩张映象在一致凸Banach空间中不动点非空的充分必要条件与Ishikawa迭代序列的收敛性及确保迭代程序收敛到不动点的条件，所得结果是单值非扩张映象的推广和发展。

YAA at amino acid level.

从实验室保存的一株能高效降解苯胺的不动杆菌中克隆到完整的苯胺双加氧酶基因簇，序列分析表明该基因簇包含6个完整的ORF，全序列与已报道的不动杆菌YAA的苯胺双加氧酶基因簇在氨基酸水平上有较高的同源性。

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。