遍历理论

The stochastic property, ergodic property and regular property of the chaotic generator are studied, and three types combination of chaos and evolution computation are investigated.

论述了进化计算的理论基础，建立了进化计算的统一模型；研究了混沌发生器的随机性、遍历性和规律性以及混沌与进化计算相结合的三种方式。

Oseledec\'s Multiplicative Ergodic Theorem does not only solve the existence of Lyapunov exponents, but also show much more information of the dynamical structure.

Oseledec的乘法遍历定理解决了Lyapunov指数的存在性问题，并对动力系统的动力学结构给出了更多的信息，它现在已成为动力系统理论的最基本定理之一。

In the dissertation, we consider ergodic theory and its applications of discrete-time Markov chains and continuous- time Markov processes.

本学位论文研究了离散时间马氏链和连续时间马氏过程的遍历性的理论及其应用。

Furthermore, based on the ergodic theory of Markov process we analyze the stationary distribution of network residual series, and prove the efficient conditions under which the unique asymptotic stationary distribution exists.

同时，根据马氏过程的遍历理论，对网络输出残差的平稳条件进行了研究，证明了网络输出平稳残差的充分条件，给出了残差序列存在唯一的渐近平稳分布的条件。

Nowdays the idea and methods of ergodic theory are applied to studies of various phenomena in statistical physics and condensed matter physics, for example, the Monte-Carlo simulations, critical phenomena, phase transition and anomalous transport.

遍历理论的思想和方法现今正被应用于统计物理和凝聚态物理等的各种现象，如Monte-Carlo、临界现象、相变、反常输运的分析。

In chapter 3, on the basis of measure, integration and ergodic theory, it is proved that the statistcal properties and the general complexity of the binary sequences (CG-sequences){b〓} b〓∈{1,-1} generated by a kind of chaos systems and mapping η〓 are as good as white noise sequences. These results lay the foundation of further development.

第三章运用测度、积分以及遍历理论中的一些基本原理，证明了由一类混沌差分系统和映射η〓所产生的二元序列{b〓}，b〓∈{-1，1}，具有与白噪声类似的统计特性和广义复杂度。

After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.

首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius-Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

Ergodicity in the configuration space was also verified.

理论和数值符合表明在位形空间的遍历性。

On basis of recursion theory of deep optimization traversal, stimulated the logical graph of water project by visual programming technology, and applied it to the west water source project of Weihe valley.

运用图论中节点连接表法描述各水源之间的逻辑联系关系，探索了分析流域拓扑结构的基本思想；以深度优先遍历的递归理论为基础，采用可视化编程技术，用计算机模拟了与研究对象有水力联系的水源工程逻辑结构图，并以渭河流域西部水源工程为研究对象进行了实现。

Shannon's model can be modified to make practical provably secure cryptosystems possible.

假定敌手拥有无限的时间、设备和资金，对敌手的计算能力不做任何限制，那么即使敌手能在很短的时间内将所有的密钥都遍历一遍的话，基于信息理论安全模型的密码系统也不会被攻破。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新