Cantor尘的Hausdorff测度估计

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.     

Partial compactness for Landau-Lifshitz maxwell equation in two-dimension

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.     

一类Sierpinski垫片的Hausdorff测度的估计(英文)

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.     

扩散 Cantor 集的最小Hausdorff 测度

In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek.     

通过反复无限细分定义测度

This paper generalizes the method of constructing measure by repeated finite subdivision in fractal geometry to that by infinite subdivision. Two conditions for the existing method are removed. A measure on the interval [0,1] is constructed using this generalized method.     

The Hausdorff dimension of sets related to the general Sierpinski carpets

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.     

Hausdorff-type Measures of the Sample Path of Gaussian Random Fields

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）.     

The Multifractal Formalism for Measures,Review and Extension to Mixed Cases

The multifractal formalism for single measure is reviewed.Next,a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures.Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.     

Constructing Restricted Patterson Measures for Geometrically Infinite Kleinian Groups

In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp.     

Hausdorff dimension and measure of a class of subsets of the general Sierpinski carpets

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.     

保形图递归集的Hausdorff维数和测度

本文确定了保形图递归集的 Ｈａｕｓｄｏｒｆｆ维数,证明了相应的 Ｈａｕｓｄｏｒｆｆ度是正σ－有限的,并且我们给出了 Ｈａｕｓｄｏｒｆｆ测度为正有限的充分必要条件．     

Hausdorff Measure of Homogeneous Cantor Set

This paper gives the Hausdorff measure of a class of homogeneous Cantor sets. Project supportedb y the National Climbing Project (Grant No. 92101090)     

两类Feigen baum映射的拟极限集的Hausdorff测度

本文计算了一类无穷多峰 Feigenbaum映射和一类单峰 Feigenbaum映射的拟极限集的Hausdorff测度     

Strong mixing subshift of finite type and Hausdorff measure of its chaotic set

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 measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.     

一类Sierpinski地毯的Hausdorff测度的估计

设Sr是压缩比为r(0.250≤r≤0.292)的Sierpinski地毯,该文证明了Sr的Hausdorff测度满足公式:21-s/2≤Hs(Sr)≤2s/2,其中s=-logr4.     

一类Sierpinski垫的Hausdorff测度

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.     

重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

均匀三部分康托集的Hausdorff中心测度

均匀三部分康托集K(λ,3)是满足开集条件的自相似分形集．本文通过一个概率测度μ在点x的上球密度的计算给出了K(λ,3)的s维Hausdorff中心测度的精确值,其中s=logλ1/3是K(λ,3)的Hausdorff维数．     

m分非均匀Cantor集的Hausdorff测度

证明了m分非均匀Cantor集的E的H ausdorff测度HS(E)=1.