THE HAUSDORFF MEASURE OF GENERALIZED SIERPINSKI CARPETS

被引：11
|
作者：
Zhu Yucan(Department of Mathematics Fuzhou University Fuzhou 350002 RPC)andLou Jun(Department of Scientific Calculation & Compute ApplicationZhong Shan UniversityGuangzhou 510275PRC)
机构：
来源：
ApproximationTheoryandItsApplications | 2000年 / 02期
关键词：
Math; THE HAUSDORFF MEASURE OF GENERALIZED SIERPINSKI CARPETS;
D O I：
暂无
中图分类号：
O174.41 [逼近论];
学科分类号：
070104 ;
摘要：
Let 0<a<1/2,T(a,1) (x) =ax and T(a,2) (x) =ax+ 1 -a,and let Ka be a unique nonempty compact subset of R satisfying Ka=T(a,1)(Ka)∪T(a,2)(Ka). If1/4<a<1/2,then the Hausdorff measure of Ka×Ka is strictly less than 2(loga2), If0<a≤1/4,then the Hausdorff measure of Ka×Ka is equal to 2(-loga2).
引用
收藏
页码：13 / 18
页数：6
相关论文
共 50 条
  • [41] The upper estimate and conjecture on Hausdorff measure of Sierpinski gasket
    Wang, XH
    PROGRESS IN NATURAL SCIENCE, 1999, 9 (11) : 812 - 819
  • [42] Self-Assembling Rulers for Approximating Generalized Sierpinski Carpets
    Kautz, Steven M.
    Shutters, Brad
    ALGORITHMICA, 2013, 67 (02) : 207 - 233
  • [43] Uniformization of Sierpinski Carpets by Square Carpets
    Ntalampekos, Dimitrios
    POTENTIAL THEORY ON SIERPINSKI CARPETS: WITH APPLICATIONS TO UNIFORMIZATION, 2020, 2268 : 91 - 177
  • [44] Self-Assembling Rulers for Approximating Generalized Sierpinski Carpets
    Steven M. Kautz
    Brad Shutters
    Algorithmica, 2013, 67 : 207 - 233
  • [45] Bounds on the Hausdorff measure of level-N Sierpinski gaskets
    Rivera, Andrea Arauza
    Lin, Edwin
    INVOLVE, A JOURNAL OF MATHEMATICS, 2022, 15 (03): : 379 - 391
  • [46] The Hausdorff measure of the level sets of Brownian motion on the Sierpinski carpet
    Yuag, CG
    MARKOV PROCESSES AND CONTROLLED MARKOV CHAINS, 2002, : 351 - 361
  • [47] Application of genetic algorithm to hausdorff measure estimation of sierpinski carpet
    Xiao, Qili
    Xi, Lifeng
    KNOWLEDGE-BASED INTELLIGENT INFORMATION AND ENGINEERING SYSTEMS: KES 2007 - WIRN 2007, PT II, PROCEEDINGS, 2007, 4693 : 182 - 188
  • [48] Quantum transport in Sierpinski carpets
    van Veen, Edo
    Yuan, Shengjun
    Katsnelson, Mikhail I.
    Polini, Marco
    Tomadin, Andrea
    PHYSICAL REVIEW B, 2016, 93 (11)
  • [49] Harmonic Functions on Sierpinski Carpets
    Ntalampekos, Dimitrios
    POTENTIAL THEORY ON SIERPINSKI CARPETS: WITH APPLICATIONS TO UNIFORMIZATION, 2020, 2268 : 9 - 89
  • [50] THE PACKING MEASURE OF A CLASS OF GENERALIZED SIERPINSKI CARPET
    Jia Baoguo( Zhongshan University
    AnalysisinTheoryandApplications, 2004, (01) : 69 - 76
12345