一类Sierpinski垫片的Hausdorff测度的估计

数学季刊 ›› 2012, Vol. 27 ›› Issue (1): 59-62.

一类Sierpinski垫片的Hausdorff测度的估计

1. Department of Mathematics, East China Normal University 2. Department of Applied Mathematics, Nanjing Forest University

收稿日期:2009-09-24 出版日期:2012-03-30 发布日期:2023-04-06
作者简介:ZHANG Yun-xiu(1982-), female, native of Nanjing, Jiangsu, a lecturer of Nanjing Forest University, M.S.D., engages in fractal geometry and its applications; GU Hui(1982-), male, native of Nantong, Jiangsu, a doctoral student of East China Normal University, engages in fractal geometry and its applications.

Estimation of the Hausdorﬀ Measure of a Kind of Sierpinski Carpet

1. Department of Mathematics, East China Normal University 2. Department of Applied Mathematics, Nanjing Forest University

Received:2009-09-24 Online:2012-03-30 Published:2023-04-06
About author:ZHANG Yun-xiu(1982-), female, native of Nanjing, Jiangsu, a lecturer of Nanjing Forest University, M.S.D., engages in fractal geometry and its applications; GU Hui(1982-), male, native of Nantong, Jiangsu, a doctoral student of East China Normal University, engages in fractal geometry and its applications.

摘要/Abstract

摘要： Suppose F₀ is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F₀. We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F; meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.

关键词: Hausdorff measure, Sierpinski carpet, projection

Abstract: Suppose F₀is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F₀. We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F; meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.

Key words: Hausdorff measure, Sierpinski carpet, projection

中图分类号:

O174.12

张云秀, 顾惠. 一类Sierpinski垫片的Hausdorff测度的估计[J]. 数学季刊, 2012, 27(1): 59-62.

ZHANG Yun-xiu, GU Hui. Estimation of the Hausdorﬀ Measure of a Kind of Sierpinski Carpet[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(1): 59-62.

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