| 摘要: |
| 本文研究了一类可数点集的盒维数的计算问题.通过构造双Lipschitz映射,把原可数点集的盒维数的求解问题转化为求解一类相对简单的可数点集的盒维数.获得了两个单调的可数点集在具有同阶间隔时具有相同的上盒维数和下盒维数的结论.该结论为计算一类可数点集的盒维数提供了方便. |
| 关键词: 盒维数 可数点集 单调 |
| DOI： |
| 分类号:O174.11 |
| 基金项目:国家社会科学青年基金资助(12CJY006);教育部人文社科规划基金资助(10YJA630131);中央高校基本科研业务费专项资金(x2jimD2118850). |
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| ON THE BOX-COUNTING OF COUNTABLE SETS |
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WU Xu
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School of Business Administration, South China University of Technology, Guangzhou 510640, China
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| Abstract: |
| In this paper, we investigate a class of countable sets' Box-counting computation. By constructing double Lipschitz map, we transform the solution of the original countable sets' Box-counting problem into the solution of a class of simpler countable sets' Box-counting problem. Finally, it is obtianed that a couple of monotonous countable sets have identical up Box-counting and down Box-counting when their interval orders are the same. The conclusion provides great convenience for computing a class of countable sets' Box-counting. |
| Key words: box-counting countable set monotone |
