|
|||||
|
|
| 自相似集的质量分布原理与Hausdorff测度及其应用 | |
| 引用本文： | 许绍元,周作领,苏维宜. 自相似集的质量分布原理与Hausdorff测度及其应用[J]. 数学学报, 2010, 53(1): 117-124 |
| 作者姓名： | 许绍元 周作领 苏维宜 |
| 作者单位： | 赣南师范学院数学与计算机科学学院;中山大学岭南学院;南京大学数学系; |
| 基金项目： | 国家自然科学基金资助项目(10961003;10971236) |
| 摘 要： | 本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法,并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的. |
| 关 键 词： | Hausdorff测度与Hausdorff测度维数 自相似集 开集条件 |
| 收稿时间： | 2008-03-17 |
| 修稿时间： | 2009-06-10 |
On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications |
|
| Shao Yuan XU School of Mathematics , Computer Scienc,Gannan Normal University,Ganzhou ,P.R.China Zuo Ling ZHOU Lingnan School,Zhongshan University,Guangzhou ,P.R.China Wei Yi SU. On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications[J]. Acta Mathematica Sinica, 2010, 53(1): 117-124 | |
| Authors: | Shao Yuan XU School of Mathematics Computer Scienc Gannan Normal University Ganzhou P.R.China Zuo Ling ZHOU Lingnan School Zhongshan University Guangzhou P.R.China Wei Yi SU |
| Affiliation: | 1. School of Mathematics and Computer Scienc, Gannan Normal University, Ganzhou 341000, P. R. China; 2. Lingnan School, Zhongshan University, Guangzhou 510275, P. R. China; 3. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China |
| Abstract: | In this paper,the mass distribution principle for the self-similar sets satisfying the open set condition(OSC) is set up.As an application,we obtain a new method for computing the exact value of the Hausdorff measure for a class of self-similar sets satisfying OSC.In addition,we give two examples to show that the new method is effective and workable to compute the exact values of the Hausdorff measures of a class of self-similar sets satisfying OSC. |
| Keywords: | Hausdorff measure and Hausdorff dimension self-similar sets open set condition |
| 本文献已被 CNKI 等数据库收录！ | |
| 点击此处可从《数学学报》浏览原始摘要信息 | |
| 点击此处可从《数学学报》下载全文 | |