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hausdorff measure of Linear Cantor Set

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Wuhan University Journal of Natural Sciences 2004年第2期9卷 135-138页

作者： MaChao SchoolofMathematicsandStatistics WuhanUniversityWuhan430072HubeiChina

We study the hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and the first gap. This condition is easy to use. Key words linear Cantor set - hausdorff measure - strong seperated condition CLC number O 174. 12 Foundation item: Supported by the National Natural Science Foundation of China (10171028)Biography: Ma Chao (1975-), male, Ph. D. candidate, research direction: fractal geometry.

关键词： linear Cantor set hausdorff measure strong seperated condition

hausdorff measure OF UNIFORM SELF-SIMILAR FRACTALS

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Analysis in Theory and Applications 2010年第1期26卷 84-100页

作者： Wolfgang Kreitmeier University of Passau Innstraβe

Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the hausdorff dimension, by H^D（E） the hausdorff measure and by diam（E） the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the hausdorff dimension is smaller than one and H^O（E） = diam（E）^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D（E）〈 diam（E）^D, if c is small enough.

关键词： self-similar set hausdorff measure

THE hausdorff measure FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of Mathematics, Beijing Normal University Beijing 100875, China) Department of Mathematics Beijing Normal University Beijing 100875 China

It is proved that φ(s) = s2 log |logs| is the correct function to give the hausdorff measureof a sample path of the Westwater process.

关键词： hausdorff measure Wiener process Westwater process Sojourn time

Strong Mixing Subshift of Finite Type and hausdorff measure of Its Chaotic Set

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Acta Mathematica Sinica,English Series 2011年第4期27卷 789-798页

作者： Wan Gan SONG Zhi HU Hua Ming WU School of Mathematical Science Peking University Beijing 100871 P. R. China School of Computer Science and Technology Huaibei Coal Industry Teachers Huaibei 235000 P. R. China School of Mathematical and Computer Science Zhanjiang Teachers College Zhanjiang 524048 P. R. China

We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the hausdorff measur... 详细信息

关键词： Symbolic space a finite subshift chaotic set hausdorff measure

The upper estimate and conjecture on hausdorff measure of Sierpinski gasket

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Progress in Natural Science:Materials International 1999年第11期9卷 13-20页

作者：王兴华 China Department of Mathematics and Information Science Hangzhou 310028 Hangzhou University

For a binary decimal x with n bits, the pre-fracial of the level n + 1 of Sierpinski gasket S can be partially covered by a curved nonagon with the diameter 1 - x/2. The number of the small iriangles which are not com-pletely covered can be counted and a simple expression of the upper estimate function vn(x) for hausdorff measure of S can be derived. By minimized searching, a sequence with optimized estimates is obtained. The values and expressions of the first 16 terms are given, especially, the 16th term is exp(ln 97793. ln 3/ln 2)799250914 = 0.817 930 0..... On the above basis, a conjecture on the exact value of hausdorff measure is proposed.

关键词： Sierpinski gasket hausdorff measure symmetry curved nonagon binary decimal

On the Lower Bound of the hausdorff measure of the Koch Curve

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Acta Mathematica Sinica,English Series 2003年第4期19卷 715-728页

作者： ZhiWeiZHU ZuoLingZHOU BaoGuoJIA MathematicsDepartment ZhaoqingUniversityZhaoqing526061P.R.China LingnanCollege ZhongshanUniversityGuangzhou510275P.R.China MathematicsandScientificComputerCollege ZhongshanUniversityGuangzhou510275P.R.China

This paper gives a lower bound of the hausdorff measure of the Koch curve bymeans of the mass distribution principle.

关键词： Koch curve hausdorff dimension hausdorff measure

BOUNDS OF THE hausdorff measure OF SIERPINSKI CARPET

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Analysis in Theory and Applications 2006年第4期22卷 362-376页

作者： Baoguo Jia Zhongshan University China School of Mathematics and Scientific Computer Zhongshan University Guangzhou 510275 P. R. China

By means of the idea of [2]（Jia Baoguo,*** press） and the *** of Sierpinski carpet, we obtain the lower and upper bounds of the hausdorff measure of Sierpinski carpet, which can approach the hausdorff measure of Sie... 详细信息

关键词： hausdorff measure self-similar set Sierpinski carpet

A NEW LOWER BOUND OF THE hausdorff measure OF THE SIERPINSKI GASKET

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Analysis in Theory and Applications 2006年第1期22卷 8-19页

作者： Zhiwei Zhu Zuoling Zhou Baoguo Jia Zhaoqing University China Zhongshan University Ghina

For the Sierpinski gasket, by using a sort of cover consisting of special regular hexagons, we define a new measure that is equivalent to the hausdorff measure and obtain a lower bound of this measure. Moreover, the following lower bound of the Hausdroff measure of the Sierpinski gasket has been achieved H^s（S）≥0.670432,where S denotes the Sierpinski gasket, s = dimn（S） = log23, and H^s（S） denotes the s-dimensional hausdorff measure of S. The above result improves that developed in .

关键词： hausdorff measure regular hexagonal cover Sierpinski gasket

AN APPROXIMATION METHOD TO ESTIMATE THE hausdorff measure OF THE SIERPINSKI GASKET

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Analysis in Theory and Applications 2004年第2期20卷 158-166页

作者： RuanHuojun SuWeiyi ZhejiangUniversity China NanjingUniversity China

In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631.

关键词： hausdorff measure sierpinski gasket approximation method