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Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

By using theories of almost type functions,the theorem about relation of asymptotically periodic functions and asymptotically periodic sequences ,as well as the equipollence of vector-valued asymptotically periodic functions and almost periodic functions on R+ are obtained.

利用概周期型函数的理论，得出了渐近周期函数和渐近周期序列二者的关系定理，以及R+上的向量值渐近周期函数与概周期函数的等价关系。研究了渐近强周期函数空间、渐近周期序列空间的可分性质

Toward an asymptote","* it grew asymptotically * By the corollary to Theorem 4.3, the origin is asymptotically stable.

根据定理4.3的推论，原点是渐近稳定的

They also show that the DSUR estimators have asymptotically mixed normal distribution and the tests of parametric restrictions can be constructed by the Wald statistic which is asymptotically distributed as a chi-square variate.

如Mark et al(2005)等提出了似无关动态协整模型的思想及其估计方法，以此来消除解释变量的内生性影响，并获得了一个标准的渐近分布。

In this paper, we discuss asymptotically stable sets of graph maps and give a necessary and sufficient condition for a fixed point of f to be asymptotically stable.

在本文中，我们讨论了图映射的渐近稳定集，并给出了f的不动点为渐近稳定的一个充分必要条件。

When the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulac function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.

选取适当的Dulac函数，利用Bendixson-Dulac判别法证明了极限环的不存在性，说明局部渐近稳定的病虫害平衡点也全局渐近稳定。

The separability of asymptotically strongly periodic function space and asymptotically periodic sequence space are also discussed.

研究了渐近强周期函数空间、渐近周期序列空间的可分性质。

Last we obtain globally asymptotically stability of boundary equilibrium by applying locally asymptotically stability and attractiveness and persistence by using uniform repeller theorem.

在第二章中研究了一类具有时滞的捕食与被捕食系统，分析了系统的正不变集，运用了特征值理论得到了边界平衡点性质，当时滞很小时，得到了系统在正平衡点局部渐近稳定的充分条件，以及当T增加到T_0时，系统在正平衡点附近产生Hopf分支的充分条件；利用局部渐近稳定性加吸引性得到了边界平衡点全局渐近稳定性的充分条件，且应用一致排斥定理得到了种群持久生存的条件。

First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem.

首先，利用广义系统的概念给出了系数矩阵为能控标准型的滑模面方程，并利用极点配置定理给出了能使系统稳定的滑模面；其次，构造了含有自适应律的离散趋近律，设计了能够使系统达到同步的变结构控制器，并利用Lyapunov稳定性定理，证明了系统的趋近运动的稳定性。

The design of output feedback H(subscript ∞) controllers is discussed for nonlinear discrete singular systems. First of all, by means of generalized Lyapunov function and linear matrix inequalities, zero solution E-asymptotically stable is studied for the system, a sufficient condition is given such that the system is zero solution E-asymptotically stable and a H(subscript ∞) norm constraint. And the output feedback H(subscript ∞) controller is designed to guarantee the performance of the resulting closed-loop system.

主要对非线性离散广义系统的输出反馈H控制器的设计问题进行讨论，首先利用广义Lyapunov函数和线性矩阵不等式，对系统的零解E-渐近稳定性问题进行分析，在此条件基础上给出系统零解E-渐近稳定且具有H范数约束的充分条件，然后设计系统的输出反馈H控制器，使得闭环系统具有同样的性能。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。