| Koch曲线的Hausdorff测度的估计值的改进 |
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| 引用本文： | 时金金,程值军.Koch曲线的Hausdorff测度的估计值的改进[J].南阳师范学院学报,2010,9(12):25-27. |
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| 作者姓名： | 时金金 程值军 |
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| 作者单位： | 延安大学西安创新学院理工系,陕西西安710100 |
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| 摘 要： | 研究了Koch曲线的Hausdorff测度的上、下界的估计,得到两个结论.其一,考虑了一种部分覆盖,利用这个覆盖计算出了Koch曲线的Hausdorff测度的一个新的上界估计值Hs（K）≤14099566×38476s≈0.587847293.其二,导出一个估计式μ（V）≤1.88｜V｜s,并结合质量分布原理得到了Koch曲线的Hausdorff测度的一个更好的下界估计值Hs（K）≥0.531914893.
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| 关 键 词： | Koch曲线 Hausdorff测度 估计 |
The improvement on the Hausdorff measure of Koch curve |
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| SHI Jin-jin,CHENG Zhi-jun.The improvement on the Hausdorff measure of Koch curve[J].Journal of Nanyang Teachers College,2010,9(12):25-27. |
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| Authors: | SHI Jin-jin CHENG Zhi-jun |
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| Institution: | (Department of Technology,Xi＇an Innovation College of Yan＇an University,Xi＇an 710100,China) |
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| Abstract: | In this paper,the lower bound and upper estimation of the Hausdorff measure about the Koch curve is investigated.Some new conclusions are obtained as follows.The first,some part-coverage was considered.Using this coverage,a new upper bound estimation value of the Koch curve Hs（K）≤40961956×（87634）s≈0.587847293 is obtained.On the other hand,we derived the inequality μ（V）≤1.88｜V｜s.Using this inequality and the mass distribution principle,a better lower bound estimation value of the Koch curve Hs（K）≥0.531914893 is obtained. |
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| Keywords: | Koch curve Hausdorff measure estimate |
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