渐近的

The objective of Chapter 2 is to give the weak convergence theorem of S ={T1 :t E G of asymptotically nonexpansive mappings in a uniformly convex Banach space without assuming that X has a Frechet differentiable norm.

本文第二章在G仅要求是一个定向网，X为不具有范数Frechet可微条件的一致凸Banach空间的情况下，给出了一族渐近非扩张映射的弱收敛定理。

For instance, we obtained the existence and uniqueness theorem and several judgement theorems on stability and instability for several types of nonlinear singular systems. Using Z-transformation, we estabilished the response formula of discrete singular systems with delay, and obtained the sufficient and necessary condition of rearchability.

如我们得到了某些非线性广义系统解的存在唯一性定理，及稳定与渐近稳定的判据；利用Z变换方法，得到了滞后离散广义系统的一般响应公式，进而得到了局部可达与局部能控的充要条件等。

For the model with exponent input, the endemic equilibrium is locally asymptotically stable when the period of latency is small enough; the endemic equilibrium is unstable when the period of latency is large enough.

对于带有指数输入的情形，发现地方病平衡点当潜伏期充分小时是局部渐近稳定的，当潜伏期充分大时是不稳定的。

When the parameters are unknown, based on the Lyapunov theory, corresponding controller and the adaptive law of parameters are designed to suppress chaos to any unstable equilibrium by the adaptive control strategy. The asymptotical stability of chaos control is guaranteed in theory by lemma of Barbalat.

当该混沌系统的参数未知时，基于Lyapunov稳定性理论，利用自适应控制策略，设计了相应的非线性控制器和参数自适应律将混沌系统的轨道控制到其任意一个平衡点，并借助Barbalat引理，从理论上证明保证了混沌控制的渐近稳定性。

Compared to state-of-the-art methods based on Kohonen's adaptive-subspace self-organizing map, our method avoids confusion of data in the manifold representation. Each neuron in the network approximately learns the mean vector and principal subspace of the data in its local region. The data representation is therefore more discernable.

与现有的基于Kohonen的自适应子空间自组织映射网络(Adaptive-subspace self-organizing map， ASSOM)方法相比较，本文方法有效地克服了流形表达中出现的数据混淆现象，网络中各神经元渐近学习各自区域内样本数据的平均向量和主元子空间，数据表达更加清晰可辨。

But the rigid body limit equilibrium method can not reflect the process of progressive instability and mechanical mechanism on failure for rock mass while the nonlinear finite element method is difficult to solve the displacement discontinuity of weak structural plane.

重力坝的深层抗滑稳定分析多采用刚体极限平衡分析方法和非线性有限元法，但通常的刚体极限平衡法不能反映坝基岩体渐近失稳过程和破坏的力学机制，非线性有限元法则难以解决坝基中软弱结构面位移不连续问题。

If the initial state of the system is zero and the input is one-sided white noise, the input and output of the system are approximately stationary. This is a special case for non-stationary processes.

对零初始条件下的渐近平稳过程这一非平稳特例做了较详细的研究给出了若干有意义的结果。

Moreover, if a method is algebraically stable, then the numerical solutions of this method can preserve the stability property of the analytic ones.

并且证明了如果一个方法是代数稳定的，则该方法的数值解保持解析解的渐近稳定性。

Using asymptotic analysis and numerical optimization, approximative yield equations are obtained for the extended Gurson model, accounting for the void size effect.

通过渐近分析、数值优化的方法对参变式屈服曲线作进一步的近似，得到了考虑尺寸效应的修正的Gurson屈服形式。

This research is theoretically important for studying the stabilization and asymptotical stability of the coupled generalized control systems.

这对耦合广义控制系统的镇定及渐近稳定性的研究具有重要的理论价值。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。