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Fractals, 1996
The concept of fractal form analysis is introduced, in which fractal metrication is defined for partial objects of fractals as a cmD or b mD with the fractal dimensionality D.
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The concept of fractal form analysis is introduced, in which fractal metrication is defined for partial objects of fractals as a cmD or b mD with the fractal dimensionality D.
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Fractal Analysis in Human Pathology
Annals of the New York Academy of Sciences, 1999.Living structures may be described as being in a self-organizing, fluctuating steady-state far from equilibrium. 1 Self-organization and a state far from equilibrium are characteristics of chaotic structures. Chaotic structures present fractal geometry, so is not too astonishing that the branching pattern of the airways in the lung or the arterial ...
LUZI P. +6 more
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SDSSU MULTIDISCIPLINARY RESEARCH JOURNAL, 2015
This paper provides the statistical foundations for fractal analysis of real-life data. It begins by developing a fractal probability distribution based on a power-law formulation and proceeds by estimating the parameters through (a) maximum likelihood estimation method, (b) exponential parameter estimation, and (c) regression approach.
Adriano Patac, Jr., Roberto Padua
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This paper provides the statistical foundations for fractal analysis of real-life data. It begins by developing a fractal probability distribution based on a power-law formulation and proceeds by estimating the parameters through (a) maximum likelihood estimation method, (b) exponential parameter estimation, and (c) regression approach.
Adriano Patac, Jr., Roberto Padua
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Meccanica, 2005
The author tries to establish a ``new analysis'' to study so-called irregular objects often modeled by fractal sets in order to formulate ``differential equation'' on nowhere differentiable sets or functions. Firstly, the analysis on the Sierpiński gasket is shown, includes the approximation of the Sierpiński gasket, the energy form, the Lagrangian ...
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The author tries to establish a ``new analysis'' to study so-called irregular objects often modeled by fractal sets in order to formulate ``differential equation'' on nowhere differentiable sets or functions. Firstly, the analysis on the Sierpiński gasket is shown, includes the approximation of the Sierpiński gasket, the energy form, the Lagrangian ...
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Fractal analysis of the uterine contractions.
Rivista di biologia, 2004The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of ...
Oczeretko, Edward +3 more
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Fractal Analysis in Neurodegenerative Diseases
2016Neurodegenerative diseases are defined by progressive nervous system dysfunction and death of neurons. The abnormal conformation and assembly of proteins is suggested to be the most probable cause for many of these neurodegenerative disorders, leading to the accumulation of abnormally aggregated proteins, for example, amyloid β (Aβ) (Alzheimer's ...
Daniel, Pirici +3 more
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Fractal Analysis in Medical Imaging
International Journal of Nonlinear Sciences and Numerical Simulation, 2002Summary: Anatomic and functional studies of the living body have revealed that organs have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. Such as lung vasculature or vermis of the cerebellum has a structure in which its small scale appears similar to its large-scale form.
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Catalysis Today, 1988
Abstract The fractal interpretation of porosimeter measurements leads to simple expressions which allow one to evaluate both cumulative pore volumes and surface areas over a range of three orders of magnitude. The pore system often consists of differently fractal regions which are superimposed on each other.
H. Spindler, M. Kraft
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Abstract The fractal interpretation of porosimeter measurements leads to simple expressions which allow one to evaluate both cumulative pore volumes and surface areas over a range of three orders of magnitude. The pore system often consists of differently fractal regions which are superimposed on each other.
H. Spindler, M. Kraft
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Fractals and nonstandard analysis
Journal of Mathematical Physics, 1984We describe and analyze a parametrization of fractal ‘‘curves’’ (i.e., fractal of topological dimension 1). The nondifferentiability of fractals and their infinite length forbid a complete description based on usual real numbers. We show that using nonstandard analysis it is possible to solve this problem: A class of nonstandard curves (whose standard ...
L. Nottale, J. Schneider
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Fractal analysis of macromolecules
Russian Chemical Reviews, 2000Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequlibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept, and of the possibility of modelling in terms of the percolation theory and ...
Viktor U Novikov, Georgii V Kozlov
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