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1.
The Hausdorff measure of a Sierpinski carpet 总被引:5,自引:0,他引:5
The exact value of the Hausdorff measure of a Sierpinski carpet has been obtained.
Project partially supported by the Science Foundation of Guangdong Province. 相似文献
2.
吴炯圻 《纯粹数学与应用数学》2003,19(3):206-212
在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM. 相似文献
3.
Yong Xin Gui 《数学学报(英文版)》2010,26(7):1369-1382
In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions 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 and finite. 相似文献
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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
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§ 1 . Introduction Infractalgeometry ,thestudyingonthetheoryandcalculationofHausdorffdimensionhasmadegreatprogress.ButasfarasHausdorffmeasureisconcerned ,onlyafewresultsareknown .ZHOUZuo linghasobtainedtheexactvalueofHausdorffmeasureforaSierpinskicar pet(see [3]) .MADong kuihasdevelopedthetechniquesin [3](see [4 ]) .ButineverystepofconstructingtheSierpinskicarpetsin [4 ],theremaininglittlesquaressatisfytheconditionthatfourofthemareatthefourvertexanglesoftheirimmediatepredecessorrespe… 相似文献
7.
ChenDan YangXiaoling 《分析论及其应用》2004,20(2):167-174
thenandIn this paper, a lemma as a new method to calculate the Hausdorff measure of fractal is given. And the exact values of Hausdorff measure of a class of Sierpinski sets which satisfy balance distribution ang dimension ≤1 are obtained 相似文献
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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. 相似文献
10.
In this paper we study a class of subset of Sierpinski carpets for which the allowed digits in the expansions fall into each fiber set with a prescribed frequency. We calculate the Hausdorff and packing dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff and packing measures to be finite. 相似文献
11.
用初等方法得到了Sierpinski地毯的Hausdorff测度. 相似文献
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By a new method, we obtain the lower and upper bounds of the Hausdorff measure of the Sierpinski gasket, which can approach the Hausdorff measure of the Sierpinski gasket infinitely. 相似文献
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In this paper we study a class of subsets of the general Sierpinski carpets for which the limiting frequency of a horizontal fibre falls into a prescribed closed interval. We obtain the explicit expression for the Hausdorff dimension of these subsets in terms of the parameters of the construction and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite. 相似文献
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设S_λ为压缩比为λ(λ≤1/3)的一类Sierpinski垫,s=-log_λ3为S_λ的Hausdorff维数,N为产生S_λ的所有基本三角形的集合.本文使用网测度方法,获得了S_λ的s-维Hausdorff测度的精确值H~s(S_λ)=1,同时证明了H~s(S_λ)可由S_λ关于网N的s-维Hausdorff测度H_N~s(S_λ)确定,获得了S_λ的非平凡的最佳覆盖. 相似文献
16.
Sierpinski地毯Hausdorff测度的一个初等证明 总被引:10,自引:0,他引:10
设Sm为压缩比为1/m(m≥4)的Sierpinski地毯,Sn为产生Sm的第n级基本正方形集合,U为平面点集,U的直径|U|>0,αn(U)表示Sn中与U相交的基本正方形的个数,本文用初等方法证明了对充分大的n有,从而证明了Sm的s-维Hausdorff测度Hs(Sm)=2s/2. 相似文献
17.
关于自相似集的Hausdorff测度的一个判据及其应用 总被引:5,自引:1,他引:5
讨论了满足开集条件的自相似集。对于此类分形,用自然覆盖类估计它的Hausdorff测度只能得到一个上限,因而如何判断某一个上限就是它的Hausdorff测度的准确值是一个重要的问题。本文给出了一个判据。作为应用,统一处理了一类自相似集,得到了平面上的一个Cantor集-Cantor尘的Hausdorff测度的准确值,并重新计算了直线上的Cantor集以及一个Sierpinski地毯的Hausdorff测度。 相似文献
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用相当简洁的初等办法,求出了维n欧氏空间中一类Sierpinski尘的Hausdorff测度的精确值. 相似文献
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通过在任意给定的凸四边形和三角形上构造一个不同于通常欧氏度量的度量,证明了如果把构造经典Sierpinski地毯的初始图形正方形换成任意一个凸四边形或者三角形,则得到的广义Sierpinski地毯与经典的Sierpinski地毯具有相同的Haus-dorff维数. 相似文献
20.
Baoguo Jia 《分析论及其应用》2006,22(4):362-376
By means of the idea of [2](Jia Baoguo,J.Math.Anal.Appl.In press) and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely. 相似文献