可逆测度与拟可逆测度的等价性

本文讨论了一类速度函数的可逆与拟可逆测度间的关系,证明了在[2]的条件下,可逆测度与拟可逆测度是等价的。     

关于重分形形式有效性的一个新的充分条件(英文)

本文研究了关于重分形形式有效性的充分条件.利用Hausdorff重分形预测度Hμ和Hausdorff重分形测度Hq,tμ之间的关系,得到了重分形形式有效性的一个新的充分条件,推广了文献[2]中给出的关于重分形形式有效性充分条件的结果.     

典型 Gibbs 态与可逆测度

本文给出[1]提出的一类一般的无穷质点系的随机演化模型作为 Feller 过程的一个充分条件,证明了在某些条件下,可逆随机场(从而典型 Gibbs 态)与可逆测度等价.在势为有界可测的条件下构造出全部典型 Gibbs 态、可逆随机场和可逆测度.证明了若存在正可逆测度,则速度函数有势,且正可逆测度集与正典型 Gibbs 态集相等.     

等价度量下的直径型填充测度

本文研究了在等价度量下,直径型填充测度之间的关系,证明了对任意紧度量空间(X,ρ),Pρ,g和Pcρ,g等价当且仅当纲函数g满足加倍条件.所得结论揭示了填充测度与加倍条件之间的关系.     

球上的对数Carleson测度

本文研究多复变数单位球上的Carleson测度,利用Bloch函数对有界及消没对数Carleson测度进行刻画,得到了在Bloch空间上类似于Hardy空间和Bergman空间上的Carleson定理.并推广的Cesáro算子在Bloch空间上有界和紧的等价条件.     

类切饼集的测度维数

本文考虑了满足一定条件的类切饼集,主要利用密度定理,获得其Hausdorff测度和填充测度是等价的.同时,给出这类类切饼集维数和测度的统计解释.     

集值Vitali-Hahn-Saks-Nikodym定理

本文通过强可加集值测度的一个等价叙述引入集值测度一致强可加的概念,并建立了集值测度的Vitali-Hahn-Saks-Nikodym定理.     

Cookie-Cutter~集上的~Gibbs~测度

Cookie-Cutter集不仅是动力系统中重要的研究对象,而且是分形中一类重要的集合.而支撑在其上的Gibbs测度对计算分形维数和热力学机制的熵起关键性作用.本文借助于定理2.1构造了支撑在其上的Gibbs测度,并用遍历性证明了该测度的唯一性.     

分形统计测度构建及其在投资组合中的应用研究

准确测量证券的风险和收益无论是对投资管理,还是对金融理论研究,甚至对理论成果向实践应用转化都至关重要。本文在证券价格具有分形特征的现实背景下,基于分形理论构建了分形期望和分形方差两个分形统计测度,以克服非分形统计测度在风险收益方面测不准或不可测的缺陷。在此基础上,应用分形统计测度构建了投资组合模型,给出了分形组合模型的解析解;随后,利用实证分析验证了分形统计测度在投资组合应用中的有效性。本文创新之处在于针对证券价格具有分形特征的现实背景构建了分形期望和分形方差两个分形统计测度;并基于分形统计测度构建了投资组合模型,将证券价格普遍存在的分形特征纳入投资组合的研究框架。     

关于自相似测度绝对连续的测度的点密度测度

本文研究了一类关于自相似测度绝对连续的概率测度的点密度测度的问题.利用迭代函数系,量子系数和H(o|¨)lder不等式,在自相似集满足强分离条件下,获得了此点密度测度,推广了自相似测度为Lebesgue测度的结果.     

THE MULTIFRACTAL HAUSDORFF AND PACKING MEASURE OF GENERAL SIERPINSKI CARPETS

1 IntroductionThe self-affine sets include self-similar sets as their special case. Although the fractalproperties of self-similar sets are well understood, little is known about self-affine sets in general.McMullen[1] studied a class of self~affine sets called generlized Sierpinski carpets, and got theirHausdorff and box dimensions. King[2] got the singular spectrum of general Sierpinski carpets.In [3] Olsen introduced the multifratal Hausdorff ajnd packing measure. and use them tostudy th…     

MULTIFRACTAL DECOMPOSITION OF CERTAIN RECURSIVE SETS WITHOUT THE OPEN SET CONDITION

1 IntroductionMultifractal decomposition has been investigated by rnany authors, it has become a use-ful tool in the fractal allalysis. Cawley and Mauldin had given good results on Moran fractaldecomPosition[3], Edgar and Mauldin studied the degraph multifractals[4], Falconer random-nized Cawley's results and the latest results on random selfsidrilar multifractals were doneby Arbeiter and Patzschke under rather weak .o1ldition.I2J. However, all these results wereestablished on certain sepa…     

Multifractal analysis of a measure of multifractal exact dimension

We focus on the multifractal generalization of the centered Hausdorff measure and dimension. We analyze the correlation among different approaches to the definition of the multifractal exact dimension of locally finite and Borel regular measures on the basis of fractal analysis of essential supports of these measures. Using characteristic multifractal measures, we carry out the multifractal analysis of singular probability measures and prove theorems on the structural representation of these measures.     

A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps

By now the multifractal structure of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self-similar sets which do not satisfy the Open Set Condition (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multifractal structure and product of matrices

There is a well established multifractal theory for self-similar measures generated by non-overtapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attentionto the important classes of self-similar measures that have matrix representations. The dimension spectra andthe L-spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifrac-tal structure and they will be discussed in detail.     

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．     

The multifractal structure of the product of two stable occupation measures

We study the multifractal structure of the product of two stable occupation measures and obtain the multifractal spectrum.     

Dynamical multifractal zeta-functions,multifractal pressure and fine multifractal spectra

We introduce multifractal pressure and dynamical multifractal zeta-functions, providing precise information on a very general class of multifractal spectra, including, for example, the fine multifractal spectra of self-conformal measures and the fine multifractal spectra of ergodic Birkhoff averages of continuous functions.