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In precise, we obtain the exact Hausdorff measure functions for level sets of N-parameter symmetric stable processes.

具体来说，我们得到了对称稳定过程的水平集的确切Hausdorff测度函数。

Another problem he did not answer is the Hausdorff dimension and the exact Hausdorff measure functions for level sets of this processes.

为比较起见，我们回顾了一些相关过程的水平集的Hausdorff测度函数的解决过程。

Hausdorff distance is a popular measure between two sets of points, and has been widely used in object matching, tracking and recognition.

Hausdorff距离(Hausdorff distance， HD)是一种点集与点集之间的距离测度，常用于目标物体的匹配、跟踪和识别等。

The Hausdorff distance was used to measure the similarity of sets, while the tolerance "box" was as a set.

将各故障在特征空间中的容错区间作为集合，用Hausdorff距离测定集合间的相似程度来决定类别。

By the partial estimate principle established in Ref. [46] and the special structure of the self-similar sets, we can get a better upper bound of the Hausdorff measure by means of a better covering set.

主要是利用文[46]中的部分估计原理，同时结合所考虑的自相似集的特殊结构，寻找一个较好的覆盖集合，得出其Hausdorff测度的一个上界。

By formulating the growth of the Local times, we thus obtain the lower bounds of the Hausdorff measure functions for the level sets of strictly stable processes.

进一步，我们考虑了该局部时的增量的变化率，从而获得了水平集的Hausdorff测度函数下界。

W. Ehm gave this stochastic processes in 1981, and he obtained most of the exact Hausdorff measure functions for the sets of the range and graph of the processes, excluding some special cases, i.

Ehm在1981年给出了这类过程的定义，并得到了除一些特殊情况（即当稳定过程所在的参数空间的维数与它的特征指标的乘积恰好与稳定过程所取值的空间的维数相等）外，该过程的像集和图集的确切Hausdorff测度函数。W。

On the other hand, when we are proving the upper bounds of the Hausdorff measure functions for the level sets, although we get the answer to the cases for the symmetric processes, we had to consider multi-integral of highly dimensional functions, the proof is quite complex. Therefore, we suggest that the proof for the corresponding problem needs some new ways.

另一方面，我们在证明严格稳定过程的水平集的Hausdorff测度函数的上界时，虽然我们得到了对称的多参数稳定过程的水平集的Hausdorff测度函数上界，但是我们的方法必须考虑多重的高维积分，其证明过程也已经相当复杂，因此，我们认为，为了得到一般的严格稳定过程的水平集的Hausdorff测度函数上界，还需要引入其它新的研究方法。

Keywords: multi-parameter stochastic process; Hausdorff measure; fractal sets; multifractal analysis; sample path

中文关键词：多指标随机过程； Hausdorff测度；分形集；重分形分析；样本轨道

In Chapter One,we find the relationship between strong open set condition , Hausdorff dimension,the positivity of the Hausdorff measure and β space of graph-directed self-similar sets in complete metric spaces.

在第一章中，我们讨论了在度量空间中，图定向自相似集的强开集条件、Hausdorff维数，正的Hausdorff测度和β空间之间的关系。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。