| 一类三维自仿射谢宾斯基地毯的Hausdorff维数和Box维数 |
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| 引用本文： | 陈绍明,龙伦海,朱莉红.一类三维自仿射谢宾斯基地毯的Hausdorff维数和Box维数[J].海南大学学报(自然科学版),2012(3):199-202,205. |
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| 作者姓名： | 陈绍明 龙伦海 朱莉红 |
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| 作者单位： | 海南大学信息科学技术学院 |
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| 摘 要： | 给出了三维空间中一类自仿射集SierpinskiCarpets的Hausdofff维数的计算公式，并通过6个引理进行了论证．同时，给出了此类自仿射集SierpinskiCarpets的Box维数的表达式，并用Box维数的定义证明了该结论．
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| 关 键 词： | Sierpinski Carpets Hausdorff维数 Box维数 |
Hausdorff Dimension and Box Dimension of a Kind of 3-dimensional Self-affine Sierpinski Carpets |
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| CHEN Shao-ming,LONG Lun-hai,ZHU Li-hong.Hausdorff Dimension and Box Dimension of a Kind of 3-dimensional Self-affine Sierpinski Carpets[J].Natural Science Journal of Hainan University,2012(3):199-202,205. |
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| Authors: | CHEN Shao-ming LONG Lun-hai ZHU Li-hong |
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| Institution: | (College of Information Science & Technology,Hainan University,Haikou 570228,China) |
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| Abstract: | The formula of the Hausdorff dimension of a kind of 3-dimensional self-affine Sierpinski Carpets was given and proved through six lemmas.The formula of the Box dimensions of this kind of 3-dimensional self-affine Sierpinski Carpets was also obtained and proved through the definition of the box dimension. |
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| Keywords: | Sierpinski Carpets Hausdorff dimension Box dimension |
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