遍在

On the basis of analyzing the characteristic of the basic immune algorithm and utilizing the ergodic property of the chaotic sequence, an adaptive immune evolutionary algorithm combined with chaotic sequence is proposed and used at the training of the neural networks.

在分析基本免疫算法优化性能的基础上，利用混沌序列的遍历性，给出了一种嵌入混沌序列的自适应免疫进化算法，并将其应用于神经网络的训练中。

Firstly, we consider the problem of the representation formula for the transition probability density of a right process under Girsanov transform. Secondly,we consider the problem of the MEMMs (minimal entropy martingale measure)for Markov switching Levy processes, and justify that the minimal entropy martingale measure is obtained by some regime switching Esscher transform. At last,we consider the problem of the invariant measure and the ergodic property of recurrent right processes. This paper includes 5 chapters.

首先，我们考虑了满足一定条件的右过程在Girsanov变换下的转移概率密度的表达式问题；其次，我们考虑了由Markov调制的Lévy过程的最小相对熵鞅测度的问题，证明了其最小相对熵鞅测度是某个状态转换Esscher变换；最后，我们考虑了右过程的不变测度及其遍历性的问题。

In the third chapter,we will discuss the properties of Haar measure,and then wewill prove the Ergodic theorem;at last,we follow Dale,Baaj and Skandalis to give twoexistence theorems of Haar measure,which we proved in different language.

在第三章我们讨论了Haar测度的性质，证明了〓双代数中的平均遍历定理，并且用算子的观点叙述证明了Dale和Baaj、Skandalis分别给出的两个Haar测度存在定理。

Li 101 proved the nonlinear ergodic theorem for semitopological semigroups of Lipschitzian mappings in the uniformly convex Banach space with the Frechet differentiable norm without using the concept of invariant mean and submean. In Chapter 1, we extend the results in [23 [24] to the case of almost-orbit.

Li［10］避开了不变平均及不变子平均的概念，在具Frechet可微范数的一致凸Banach空间中，给出了一般拓扑半群上渐近非扩张半群的遍历压缩定理。

Moreover, when X is a Hilbert space, Miaxoguchi and Takahashi provided the ergodic retraction theorem for general semigroups of asymptotically nonexpansive mapping by using the concept of invariant submean.

进一步，当X是Hilbert空间时，Miaxoguchi及Takahashi引入了不变子平均的概念，在一般拓扑半群上给出了渐近非扩张半群的遍历压缩定理。

When G is not a commutative semitopological semigroup, Lau and Takahashi proved the ergodic theorem for right reversible semigroups of nonexpansive mappings by using the methods of invariant means.

而当G非交换时，Lau和Takahashi利用不变平均技巧，在假定G是右可逆，X具一致Frechet可微范数及RUC存在不变平均等条件下，给出了非扩张半群的遍历压缩定理。

In chapter 2, some preliminary kownledges in topologically dynamical system and ergodic theory, which will be used in this paper, are reviewed.

在第二章中，我们介绍了本文涉及到的一些拓扑动力系统和遍历理论的预备知识。

In the first chapter we introduce the basic notions and results of topological dynamics, including some basic knowledge of ergodic theory which will be used in context.

在第一章中，我们简要的介绍了本文涉及到的拓扑动力系统与遍历理论的一些基本概念与结论。

These sets are interesting subsets of natural number in combinatorial number theory, ergodic theory and topological group.

这些集合是人们在组合数论、遍历理论以及拓扑群中感兴趣的重要的自然数子集。

In this paper, we study the existence and ergodicity on invariant measures of set-valued mappings.

中文摘要：在这篇文章里，我们研究了集值映射不变测度的存在性和遍历性。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。