RN中某些分形子集的Hausdorff维数与Hausdorff测度

给出了RN中某些分形子集的Hausdorff维数及其Hausdorff测度估计式.     

分形插值函数图象的Hausdorff维数

本文给出了插值点为的分形插值函数图象的Hausdorff维数的下界估计     

关于向量维Hausdorff测度

本文引进了向量维Hausdorff测度及其维向量的概念,研究了向量维Hausdorff测度的基本性质及其与经典Hausdorff测度(其维数为广义非负实数)的关系,引进两种类型的维向量,研究了它们之间的关系及其与经典Hausdorff维数的关系。     

Engel连分数中一个例外集的Hausdorff维数

本文研究了Engel连分数展式中部分商以某种速度增长的集合的Hausdorff维数.利用自然覆盖和质量分布原理,得到了集合B(α)={x∈(0,1):lim n→∞ log bn+1(x)/log bn(x)=α}的Hausdorff维数是1/α的结果.     

d维平稳高斯过程多重时的Hausdorff维数及Packing维数

设X^d(t∈R )是d维可分平衡高,过程,在一定条件下,本文得到了x^d(t)多重时Hausdorff维数及Packing维数,Polya过程为其特例。     

广义统计自相似集的Hausdorff维数估计

作者进一步研究了在文章［１］中构造的广义统计自相似集的分形性质，得到了这类集合的Hausdorff维数和确切Hausdorff测度函数。文中的结果是［4］中结果的延拓。     

限制零的m进制数集之Hausdorff测度

对于任意整数表示mkz的分数部分.给出了数集Fm的Hausdorff测度是Fm的HausdorfF维数.     

具阻尼的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计

本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计．     

加权Besicovitch集的Hausdorff维数

本文引入并研究符号空间上的加权Besicoritch集.通过构造一个伯努利测度,得到此集的Hausdorff维数,结果符合一个变分原理.     

一类广义齐次Moran集的Hausdorff维数

本文构造了一类具有类似高维Moran结构的集合,给出一些充分条件来计算其Hausdorff维数.     

Hausdorff Dimension in Convex Bornological Spaces

For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the classical notion.     

Fractal dimension for fractal structures: A Hausdorff approach revisited

In this paper, we use fractal structures to study a new approach to the Hausdorff dimension from both continuous and discrete points of view. We show that it is possible to generalize the Hausdorff dimension in the context of Euclidean spaces equipped with their natural fractal structure. To do this, we provide three definitions of fractal dimension for a fractal structure and study their relationships and mathematical properties.     

The Hausdorff measure of a class of Sierpinski carpets

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.     

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 dimension of self-similar sets with overlaps

We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausforff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.      

一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数

首先介绍广义Weierstrass型函数的Weyl-Marchaud分数阶导数,得到了带随机相位的广义Weierstrass型函数的Weyl-Marchaud分数阶导数图像的Hausdorff维数,证明了该分形函数图像的Hausdorff维数与Weyl-Marchaud分数阶导数的阶之间的线性关系.     

Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatoš [Andrej Zlatoš, Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216-252].     

Estimating the Hausdorff dimensions of univoque sets for self-similar sets

An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoque sets.     

满Parry测度的有限型子集的Hausdorff维数与测度

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.