| 一类变形的Mc Mullen集的维数及其应用 |
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| 引用本文： | 杨玉莲,龙伦海. 一类变形的Mc Mullen集的维数及其应用[J]. 海南大学学报(自然科学版), 2010, 28(4): 302-305 |
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| 作者姓名： | 杨玉莲 龙伦海 |
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| 作者单位： | 海南大学,信息科学技术学院,海南,海口,570228;海南大学,信息科学技术学院,海南,海口,570228 |
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| 基金项目： | 海南省教育厅自然科学资助项目 |
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| 摘 要： | 研究了平面上一类变形的Mc Mullen集R=∑∞k=1a00b-kxkyk,(xk,yk)R,其中整数a,b满足|a|≥|b|1或者|b|≥|a|1,有限整数点集R{(i,j),i=0,1,…,n-1,j=0,1,…,m-1},得到了这类自仿射集的Hausdorff维数和Box维数的计算公式.并且作为其应用给出了自仿射集R=∑∞k=1a bb a-kxkyk,(xk,yk)R相应的Hausdorff维数和Box维数,其中整数a,b满足|a-b|≥|a+b|1或者|a+b|≥|a-b|1有限整数点集R{(i+j,-i+j),i=0,1,…,|a-b|-1,j=0,1,…,|a+b|-1}.
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| 关 键 词： | 表示系统 自仿射集 Hausdorff维数 Box维数 |
Dimension of a Class of Modiffied Mc Mullen Sets and Its Application |
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| YANG Yu-lian,LONG Lun-hai. Dimension of a Class of Modiffied Mc Mullen Sets and Its Application[J]. Natural Science Journal of Hainan University, 2010, 28(4): 302-305 |
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| Authors: | YANG Yu-lian LONG Lun-hai |
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| Affiliation: | (College of Information Science and Technology,Hainan University,Haikou 570228,China) |
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| Abstract: | In the paper,a class of modified Mc Mullen sets R={∑∞k=1（a00b）-k（xkyk）/（xk,yk）R} was analyzed in which the integers satisfied ｜a｜≥｜b｜1 or ｜b｜≥｜a｜1 and the finite set {（i,j）/i=0,1,…,n-1,j=0,1,…,m-1}.and the Hausdorff dimension and Box dimension were obtained.As its application,the accordingly Hausdorff dimension and Box dimension for the following self-affine sets R={∑∞k=1（abba）-k（xkyk）/（xk,yk）R},were also obtained,in which a,b were integers satisfying ｜a-b｜≥｜a＋b｜1 or｜a＋b｜≥｜a-b｜1 and the finite set.R {（i＋j,-i＋j）/i=0,1,…,｜a-b｜-1,j=0,1,…,｜a＋b｜-1}. |
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| Keywords: | representing system self-affine sets Hausdorff dimension Box dimension |
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