共查询到20条相似文献,搜索用时 15 毫秒
1.
Zhiwei Zhu Zuoling Zhou Baoguo Jia 《分析论及其应用》2006,22(1):8-19
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 . 相似文献
2.
经典分形集测度上估的计算机搜索Ⅰ──对典型例子Sierpinski垫片编码技术的剖析 总被引:1,自引:1,他引:0
The upper estimation of Hausdorff measure for Sierpinski gasket has beengreatly hoprovd in Refs. [1, 2]. As the basis of these two works, the codingteclmique of the upper estimation seardsng for regular fractal sets on computerdiscusses thoroughly in this paper through a troical example of Sierpinski gasket. 相似文献
3.
经典分形集测度上估的计算机搜索Ⅰ──对典型例子Sierpinski垫片编码技术的剖析 总被引:2,自引:1,他引:1
分形集的Hausdorff测度是一个非线性科学的理论课题,至今结果甚少,即使对于一些生成很有规则的经典分形集亦是如此间.SISrpinski垫片就是这样一个经典分形集,但因其预分形的图形尚未被研究者解析地认识,所以对其Hausdorff测度的研究进展很慢.文献问猜测1十年之后,这个猜测才被文献问以估值否定.接着,文献同又得到更好的估值出由于采取了对Sierpinski垫片发生规则的编码技术,从而方便地得到H”(S)的一个上方估值函数o(x).上面提到的一系列猜测值或上方估值,依次由0(1/2),o(l/4),以司对给出,而则给出TH”(S)… 相似文献
4.
Zuoling Zhou 《中国科学A辑(英文版)》1997,40(10):1016-1021
By forming a sequence of coverings of the Sierpinski gasket, a descending sequence of the upper limits of Hausdorff measure is obtained. The limit of the sequence is the best upper limit of the Hausdorff measure known so far. 相似文献
5.
6.
RuanHuojun SuWeiyi 《分析论及其应用》2004,20(2):158-166
In this paper, we firstly define a decreasing sequence {P^n(S)} by the generation of the Sierpinski gasket where each P^n(S) can be obtained in finite steps. Then we prove that the Hausdorff measure H^8(S) of the Sierpinski gasket S can be approximated by {P^n(S)} with P^n(S)/(1 1/2^n-3)s ≤ H^8(S)≤ Pb(S).An algorithm is presented to get P^n(S) for n≤ 5. As an application, we obtain the best lower bound of H^8(S) till now: H^8(S) ≥ 0.5631. 相似文献
7.
指出了发表在《数学的实践与认识》上的两篇关于Sierpinski垫片和Sierpinski锥的Hausdorff测度的论文中主要结论的错误所在,并从若干方面讨论了相关的几个问题. 相似文献
8.
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension log3/log2. 相似文献
9.
Let {X(t),t≥0} be Brownian motion on Sierpinski gasket,The Hausdorff and packing dimensions of the image of a ompact set are studied,The uniform Hausdorff and packing dimensions of the inverse image are also discussed. 相似文献
10.
Yahan Xiong 《Journal of Mathematical Analysis and Applications》2005,305(1):121-129
In this paper we obtain the exact value of the Hausdorff measure of a class of Sierpinski carpets with Hausdorff dimension no more than 1 and show the fact that the Hausdorff measure of such Sierpinski carpets can be determined by coverings which only consist of basic squares. 相似文献
11.
In this paper, regular Sierpinski carpet as a new concept is given. The exact value of Hausdorff measure of the regular Sierpinski carpet and the range of Hausdorff measures for all forms of generalized Sierpinski carpets is also obtained. For any one of the generalized Sierpinski carpets we show that there exists a regular carpet such that they have the same Hausdorff measures. 相似文献
12.
In this paper, regular Sierpinski carpet as a new concept is given. The exact value of Hausdorff measure of the regular Sierpinski carpet and the range of Hausdorff measures for all forms of generalized Sierpinski carpets is also obtained. For any one of the generalized Sierpinski carpets we show that there exists a regular carpet such that they have the same Hausdorff measures. 相似文献
13.
Haudorff测度与等径不等式 总被引:1,自引:0,他引:1
对于:Hausdorff维数为s>0的满足开集条件的自相似集E(?)Rn(n>1),我们引入等径不等式Hs|E(X)≤|X|s,以及使该不等式等号成立而直径大于0的极限集U(?)Rn.这里,Hs|E(·)是限制到集合E上的s维Hausdorff测度,而|X|指集合X在欧氏度量下的直径.当s=n时,n维球是唯一的极限集;当s∈(1,n)时,除去一些反面例子以外,我们对上述等径不等式的极限集的基本性质所知甚少.可以看出,这些不等式与Hs(E)的准确值的计算有密切联系.作为特例,我们将考虑Sierpinski垫片,指出计算这一典型自相似集的In2/In3维Hausdorff测度准确值的困难何在.由此可以大致推想,为什么除去平凡情形以外,至今还没有一个具体的满足开集条件而维数大于1的自相似集的:Hausdorff测度准确值被计算出来. 相似文献
14.
Summary Upper and lower bounds are obtained for the transition densitiesp(t, x, y) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity ofp(t, x, y) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent, is shown to hold.Research partially supported by NSF Grant DMS 88-22053 相似文献
15.
Jun Kigami 《Mathematische Annalen》2008,340(4):781-804
We study the standard Dirichlet form and its energy measure,called the Kusuoka measure, on the Sierpinski gasket as aprototype
of “measurable Riemannian geometry”. The shortest pathmetric on the harmonic Sierpinski gasket is shown to be thegeodesic
distance associated with the “measurable Riemannianstructure”. The Kusuoka measure is shown to have the volumedoubling property
with respect to the Euclidean distance and alsoto the geodesic distance. Li–Yau type Gaussian off-diagonal heatkernel estimate
is established for the heat kernel associated withthe Kusuoka measure. 相似文献
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17.
Naotaka Kajino 《Potential Analysis》2012,36(1):67-115
For the measurable Riemannian structure on the Sierpinski gasket introduced by Kigami, various short time asymptotics of the
associated heat kernel are established, including Varadhan’s asymptotic relation, some sharp one-dimensional asymptotics at
vertices, and a non-integer-dimensional on-diagonal behavior at almost every point. Moreover, it is also proved that the asymptotic
order of the eigenvalues of the corresponding Laplacian is given by the Hausdorff and box-counting dimensions of the space. 相似文献
18.
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
19.
Sierpinski锥及其Hausdorff维数与Hausdorff测度 总被引:1,自引:1,他引:0
首先给出了 Sierpinski锥的概念及构造过程 ,然后求出其计盒维数、Hausdorff维数和 Hausdorff测度 . 相似文献
20.
三分Sierpinski垫上的α(=1+(log_2)/(log_3))维Hausdorff测度的Cauchy变换F(z)和二分的情形一样,表现出一些不平常的几何性质.本文考虑联系到F(z)的几个辅助函数,利用Laplace变换和Dong X.H.和Lau K.S.(2003)中的结果,得到了它们的一些重要性质.这些性质对研究F(z)的几何性质和渐近性质起关键作用. 相似文献