文献类型：期刊文献

中文题名：多重分形奇异谱的几何特性II.配分函数法

英文题名：Geometrical Characteristics of Singularity Spectra of Multifractals II. Partition Function Definition

作者：周炜星[1];吴韬[1];于遵宏[1]

机构：[1]华东理工大学洁净煤技术研究所,上海200237

年份：2000

卷号：26

期号：4

起止页码：390

中文期刊名：华东理工大学学报（自然科学版）

外文期刊名：Journal of East China University of Science and Technology

收录：CSTPCD;;EI(收录号：2001015498566);Scopus;北大核心:【北大核心1996】；CSCD:【CSCD2011_2012】；

基金：国家重点基础研究发展规划项目! (G19990 2 2 10 3)

语种：中文

中文关键词：多重分形;奇异谱;广义维数;配分函数法;几何特性

外文关键词：multifractal; singularity spectrum; generalized dimension; partition function

摘要：研究了用配分函数法定义的多重分形理论中奇异谱的几何特性 ,通过严格的数学推理证明了广义维数 Dq、质量指数 τ( q)、奇异性指数 α( q)和奇异谱 f( α( q) )的有关性质 ,明确提出了判定合理奇异谱 f( α( q) )的准则 ,给出了在参数 q→±∞时计算相应函数极限的解析算法。
To describe multiplicative cascade processes with unequal scales, formalism of multifractals defined via partition function should be adopted. The geometrical characteristics of singularity spectrum of these multifractals are studied. The relevant properties of generalized dimension D q , mass index τ(q) , singularity α(q) and singularity spectrum f(α(q)) are derived rigorously, which are somewhat similar to those obtained from multifractals defined via Renyi information but more general in mathematical form. The curve of generalized dimensions is similar to that of singularity strength when the parameter q tends to infinite. The singularity spectra curve lies in the first quadrant, whose endpoints are not necessary to be nought. The asymptotic behaviors are studied and the analytical algorithms calculating the limits of the relevant functions with q tending to infinity are presented. The criterion based on the fact that, the curve of the multifractal spectrum is tangent to the diagonal of the first quadrant is still valid in determining the proper singularity spectrum. This implies that f≤α for all q and no extreme point in the curve of the generalized dimensions.