张俊雅,孔德荣,李文侠.自仿Sierpinski地毯中集合的维数[J].数学年刊A辑,2010,31(2):189~202 |
自仿Sierpinski地毯中集合的维数 |
Dimensions of Sets Related to Self-affine Sierpinski Carpets |
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DOI: |
中文关键词: 数字频率 水平纤维频率 Hausdorff维数 |
英文关键词:Digit frequency Frequency of horizontal fiber Hausdorff dimension |
基金项目:国家自然科学基金,上海市重点学科基金 |
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中文摘要: |
研究广义Sierpinski地毯的两类子集,它们的编码分别具有线性制约的部分数字频率和水平纤维频率.计算这两类集合的Hausdorff维数,并给出相应的Hausdorff测度为正无穷的充分条件. |
英文摘要: |
The authors consider two classes of subsets of the general Sierpinski carpets for which the location codes of the points have digit frequencies or frequencies of horizontal fibers linearly constrained. They calculate the Hausdorff dimensions of these subsets and give sufficient conditions for the corresponding Hausdorff measure to be infinite. |
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