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1.
In this paper,we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E the self-similar sets generating in a unit regular pentagon on the plane.Under some conditions,we show the natural covering is the best one,and the Hausdorff measures of those sets are euqal to | E | s,where s=dim H E.  相似文献   

2.
THE HAUSDORFF MEASURE OF GENERALIZED SIERPINSKI CARPETS   总被引:1,自引:0,他引:1  
  相似文献   

3.
4.
Sierpinski垫片Hausdorff测度的上方估值   总被引:5,自引:0,他引:5  
Sierpinski垫片S是三个经典的自相似集之一具有Housdorff维数  相似文献   

5.
对于m2的任何整数m,本文定义了R~m中的一类广义 Sierpinski海绵,同时给出了该类海绵的填充测度的计算公式.  相似文献   

6.
Cantor dust is a classical fractal set .It is very important to compute its Hausdorff measure.In this Paper,we obtained the expression and approximation of Hausdorff measure of Cantor dust through the analysis of interpolation function of a certain of mass distribution defined on Cantor dust.  相似文献   

7.
王何宇  王兴华 《计算数学》1999,21(3):345-354
A upper estimate function ν(x) of Hausdorff measure Hs (S) ofSierpinski Gasket is given. A mathematical representation of the upperapproximate value νN (x) to ν(x) and a simple algorithm ofνN (x) based on lattice tracing technique are also derived. As asimple corollary, the estimation Hs(S)≤ min ν15 (n·10-5)=ν15 (0.50783)=0.81794 …is obtained.  相似文献   

8.
苏峰  赵兴球 《数学杂志》1995,15(4):396-400
设K为广义自相似集,μ为支撑于K上的无穷乘积测度,本文中证明了K的重fractal分解集Kα恰好由关于测度μ的点态维数为α的点所组成,并证明了Kα的packing维数与其Hausdorff维数一致,从而Kα为在Taylor[9]意义下的fractal集。  相似文献   

9.
In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.  相似文献   

10.
The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф*(x)=limsup logv(B(x,r))-qlogu(B(x,r))/logr are discussed and some applications are given.  相似文献   

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