共查询到20条相似文献,搜索用时 31 毫秒
1.
Hun Ki Baek 《Proceedings Mathematical Sciences》2008,118(2):273-279
First, we prove the decomposition theorem for the regularities of multifractal Hausdorff measure and packing measure in ”
d
. This decomposition theorem enables us to split a set into regular and irregular parts, so that we can analyze each separately,
and recombine them without affecting density properties. Next, we give some properties related to multifractal Hausdorff and
packing densities. Finally, we extend the density theorem in [6] to any measurable set. 相似文献
2.
Thomas S. Mountford 《Journal of Theoretical Probability》2007,20(1):25-46
We establish the correct Hausdorff measure function for the level sets of additive strictly stable processes derived from
strictly stable processes satisfying Taylor’s condition (A). This leads naturally to a characterization of local time in terms
of the corresponding Hausdorff measure function of the level set.
相似文献
3.
Shui Cao ZHENG Huo Nan LIN Di He HU 《数学学报(英文版)》2005,21(5):1137-1148
In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф(r) = r^N-d/α (log log l/r)d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d, α) strictly stable processes. 相似文献
4.
We study the partial regularity of weak solutions to the 2-dimensional LandauLifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C ∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points. 相似文献
5.
设μ为 Rd上 Borel概率测度,q,t∈R,记 Hμq,t为 Olsen定义的重分形 Hausdorff测度,证明了当μ为测度时,Hμq,t的有限测度子集存在. 相似文献
6.
We present some general methods for the estimation of the local Hausdorff measure of nodal sets of solutions to elliptic and parabolic equations. Our main results (Theorems 3.1 and 4.1) improve previous results of Lin Fanghua in [1]. 相似文献
7.
We analyze the local behavior of the Hausdorff centered measure for selfsimilar sets. If E is a self-similar set satisfying the open set condition, then Cs(E∩B(x,r)) ≤(2r)s for all x ∈ E and r 0, where Csdenotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure. 相似文献
8.
Zhen-long Chen San-yang Liu 《应用数学学报(英文版)》2005,21(4):623-636
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N). 相似文献
9.
本文研究了度量空间中Hausdorff测度与度量及纲函数的关系.利用拓扑学及Hausdorff测度论中一些性质,构造了两反例来说明存在不等价纲函数g,h和某一紧度量空间(ρ,X),使得Hρ,g与Hρ,h对此紧度量空间等价等问题.这些反例有助于从另一个角度理解文胜友、文志英[4]中主要结果. 相似文献
10.
Wolfgang Kreitmeier 《分析论及其应用》2010,26(1):84-100
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
D
(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. 相似文献
11.
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
12.
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
13.
14.
Valentino Magnani 《Central European Journal of Mathematics》2006,4(1):82-109
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence
of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple
examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence
of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg
group. 相似文献
15.
We consider subsets F of $\mathbb{R}^n$ generated by iterated function systems with contracting conformal C1+γ-diffeomorphisms whose Hausdorff dimension is s. The unique s-self-conformal probability measure μ agrees with the normalised s-dimensional Hausdorff measure on F. Using the associated dynamical system and ergodic theory we develop a potential theoretic representation of the average densities of μ at almost all points of F. Before we formulate some general relationships between average densities and local dimensions of measures. 相似文献
16.
17.
§ 1 . Introduction Infractalgeometry ,thestudyingonthetheoryandcalculationofHausdorffdimensionhasmadegreatprogress.ButasfarasHausdorffmeasureisconcerned ,onlyafewresultsareknown .ZHOUZuo linghasobtainedtheexactvalueofHausdorffmeasureforaSierpinskicar pet(see [3]) .MADong kuihasdevelopedthetechniquesin [3](see [4 ]) .ButineverystepofconstructingtheSierpinskicarpetsin [4 ],theremaininglittlesquaressatisfytheconditionthatfourofthemareatthefourvertexanglesoftheirimmediatepredecessorrespe… 相似文献
18.
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
19.
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
20.
Zuoling Zhou 《中国科学A辑(英文版)》1998,41(7):723-728
The self-similar sets satisfying the open condition have been studied. An estimation of fractal, by the definition can only
give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exact value or not is important.
A negative criterion has been given. As a consequence, the Marion’s conjecture on the Hausdorff measure of the Koch curve
has been proved invalid.
Project partially supported by the State Scientific Commission and the State Education Commission. 相似文献