不变

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。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

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。

Also the relationship between the Lipschitz ergodicity and the domain of influence of an invariant set is discussed.

讨论了Lipschitz各态历经性与不变集的影响域之间的关系。

College of Mechanical Engineering and Applied ET,Beijing University of Technology,Beijing 100022,China

提出了一种基于BP神经网络与图像不变矩的页面识别方法。

Both agree that, in the Eucharist, the accidents of the bread and wine remain unchanged.

双方均同意，在圣体中，意外的面包和葡萄酒保持不变。

When the width of the channel is unchangeable, the more are the numbers of the channels, the narrower the channel becomes, the evener the oxygen on the surface of diffusion layer becomes.

当流道宽度不变时，流道数目越多，流道间隔越窄，越有利于氧气在扩散层表面上的均匀化分布。

There is only one belief in my mind that you are the only one everlast ing in my heart.

心底唯一的声音，只想告诉你，无论沧海桑田，你仍是我生命中不变的在乎。

Otherwise he can also check out those which remain the same everlastingly .

否则，他也可以检查出那些维持不变，永远。

Whereas the Ex Libris corporate structure will remain unaltered, this change in ownership will provide Ex Libris with additional resources for accelerating our current and future product strategies and our plans for international expansion.

这项所有权调整在Ex Libris公司的结构将维持不变，实质的意义则为Ex Libris目前和未来的产品策略和计划等的扩张提供更多的资源。

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。