罗安娜.一类分形集合及有关性质[J].南华大学学报(自然科学版),2005,(2):90~92.[.A Fractal Set and Its Properties[J].Journal of University of South China(Science and Technology),2005,(2):90~92.] |
一类分形集合及有关性质 |
A Fractal Set and Its Properties |
修订日期:2005-05-11 |
DOI: |
中文关键词: 2n-1分形集 自相似集 Hausdorff维数 Hausdorff测度 |
英文关键词:2n-1 fractal Set,Self-similar sets,Hausdorff dimension,Hausdorff measure, |
基金项目: |
罗安娜 |
衡阳师范学院数学系,湖南衡阳421008 |
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中文摘要: |
考虑闭区间[0,1],根据Cantor三分集的结构和性质,推广了三分集的形式,构造了2n-1分形集C2n-1,获得了它的一些实变性质,同时,利用分形几何知识,计算了C2n-1的Hausdofff维数。 |
英文摘要: |
Thinking close interval [0,1] and according to properties of Third middle Cantor Set, we generated Third middle Set, and constructed 2n-1 fractal Set C_2n-1, and obtained its real variable properties. In the meantime, we computed its Hausdorff dimension by knowledge of fractal geometry. |
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