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齐次Moran集积集的Packing维数

发表时间:2009-01-15  浏览量:2153  下载量:922
全部作者: 黄精华
作者单位: 中国地质大学数学与物理学院
摘 要: 分形积集的维数是分形几何研究中的重要内容。本文讨论了一类齐次Moran集积集的Packing维数。设(I, {nk}k≥1, {ck}k≥1)是由I, {nk}k≥1, {ck}k≥1确定的Moran集类,利用Moran集的齐次结构,运用自然覆盖法的特别估计法,对E,F∈在一定条件下,确定了积集E×F的Packing维数公式,进一步得到:积集E×F的Packing维数严格小于集E,F的Packing维数之和。
关 键 词: 分形几何;齐次Moran集;齐次Cantor集;偏齐次Cantor集;Packing维数
Title: Packing dimension of product sets for homogeneous Moran sets
Author: HUANG Jinghua
Organization: School of Mathematics and Physics, China University of Geosciences
Abstract: It is important to research the dimension of product sets in fractal geometry. The paper discusses the Packing dimension of product sets for homogeneous Moran sets. Let (I, {nk}k≥1, {ck}k≥1) denote the Moran collection determined by the closed interval I, the positive integer series {nk}k≥1, and a positive real series {ck}k≥1. Use the homogeneous structure of Moran sets and a special method of natrual covering to estimate the Packing dimension formula for E×F, where E, F∈ is satisfied with some conditions. And the Packing dimension of E×F is strictly less than the sum of Packing dimensions for E, F.
Key words: fractal geometry; homogeneous Moran sets; homogeneous Cantor sets; partial homogeneous Cantor sets; Packing dimension
发表期数: 2009年1月第1期
引用格式: 黄精华. 齐次Moran集积集的Packing维数[J]. 中国科技论文在线精品论文,2009,2(1):48-53.
 
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