On the existence of a nonzero mass density for a fractal set of independent pointlike masses with a power-type distribution
type: Item
instance of: scholarly article
title: On the existence of a nonzero mass density for a fractal set of independent pointlike masses with a power-type distribution
zbMATH Open document ID: 0946.60015
DOI: 10.1007/BF02432346
author: D. A. Korobko
author: V. V. Uchaikin
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-06-29T00:00:00Z
review text: The concept of global mass density (GMD) for deterministic and stochastic fractals is considered. For the construction of stochastic fractal, the Lévy-Mandelbrot algorithm and its modification are used. The probability density of GMD is investigated for all these cases. The main result is that this distribution has a nondegenerate limit under the following condition on the connection between the exponent of mass distribution and fractal dimension \(D=3\alpha\).
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 85A40
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1289194
zbMATH Keywords: concept of global mass density
zbMATH Keywords: deterministic and stochastic fractals
zbMATH Keywords: Levy-Mandelbrot algorithm
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1289194