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fractal measures
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  分形测度
     The relationship between fractal measures in Rd1, Rd2 and their product measures in Rd1+d2 has been developed by many authors.
     在R~(d_1),R~(d_2)中的分形测度和R~(d_1)+r_2中乘积测度之间的关系已经被许多作者发展。
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     Chapter 2 introduces the preliminary knowledge which include the concepts and basic characters of fractal measures and fractal dimensions.
     第二章给出了预备知识。 给出分形测度、分形维数的概念与本文要用到的性质,以及分式Brown运动的概念与基本性质。
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     Fractal dimension and multifractal singularity spectrum are very important quantitative parameters describing fractal measures.
     分形维数和多重分形奇异谱是描述分形测度的重要的定量参数;
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     Some Estimates Related to the Laplacians and Fractal Measures on Manifolds
     流形上与Laplace算子及分形测度有关的一些估计
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     thusthis enable introduction of a measure theory definition of fractal measures.
     这使得我们能够引入分形测度的测度论定义。
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  相似匹配句对
     Hausdorff Measures of Two Classes of Fractal Sets
     两类分形集的Hausdorff测度
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     Some Problems of Fractal V ——Calculation of Hausdorff Measures
     分形几何若干前沿问题Ⅴ——分形测度的计算
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     Fractal Graphics
     Fractal图形学
短句来源
     FRACTAL AND PHYSICS
     FRACTAL与物理学
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     intervention measures;
     ④干预措施;
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  fractal measures
Fractal measures and polynomial sampling: I.F.S.-Gaussian integration
      
A general theory of uniform probability is developed for compact metric spaces, which agrees with Lebesgue measure, Haar measure, and various fractal measures in specific cases.
      
We highlight a correspondence between order-two densities and wavelet-like transforms of certain fractal measures.
      
The fractal measures that the author had introduced in the early 1970s are described, including new developments.
      
Such is, in particular, the case for fractal measures and for fractal graphs, often called hierarchical lattices.
      
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A new method of texture description is proposed using the texture model of fractal random field based on DFBIR. The theory of anisotropic DFBIR field has been extended. It is pointed out that the anisotropic DFBIR field is quite similar to natural image texture. A fractal statistical model for image is developed. The method for estimating the fractal measure and direction measure of the anisotropic DFBIR field is also proposed and has been successfully used in texture description.

本文在DFBIR场的基础上,提出了利用分形随机纹理模型的纹理描述方法,拓广DFBIR场为各向异性的DFBIR场,指明各向异性的DFBIR场与自然纹理最接近.文中对纹理的产生和分割进行了研究,提出了分割的特征量,并指明分形的标度区,对大量的图像进行了实验研究,实验结果证明了理论分折的正确性,为图像的分割与描述建立了新的途径.

Let A be the Laplace-Beltrami operator on a Riemannian manifold M. The main aim of this paper is to study the Lp-boundedness of the map (I-t)-β,Lp(M,d)→Lp(M,dx). In particular, the author gives a new generalization of Wiener's theorem. Here,is a locally uniformly a-dimensional fractal measure on M,and dx is the volume element on M.

设Δ是Riemann流形M上的Laplace-Beltrami算子。本文主要研究映照(I—tΔ)~(-β):L~p(M,dμ)→L~p(M,dx)的L~p有界性,特别获得了Wiener定理的一种新推广。此处,μ是M上局部一致α维分形测度,dx是由M上Riemann度量确定的体积元。

Based on the defination of set fractal a quantitative analysis is made towards the route of "Period-doubling leads to Chaos" by calculecting its fractal measure fractal characteristic number and fractal dimension. It is discovered that the fractal dimension is 0.5 070968…. which is universal when it enters into chaos through Period-doubling.

本文基于集合分形的定义,对“倍周期分支通向混沌”这一途径的分形度量──分形示性数及分形维数进行数值分析,揭示倍周期分支进入混沌时的分形维数为d_Fd_F(X∞)=0.5070968…具有普适性。

 
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