Results 221 to 230 of about 16,389 (269)

The fractal neighbor distance measure

Pattern Recognition, 2002
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Teewoon Tan, Hong Yan 0001
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HERMITE EXPANSIONS AND FRACTAL MEASURES

Acta Mathematica Scientia, 1998
For each \(\lambda \in Z^n_+\), let \(\Phi_\lambda\) denote the associated Hermite function. These Hermite functions are the orthonormal eigenfunctions of the operator \(H = -\Delta + | x| ^2\), and so one can use them to form various multipliers, in particular the Abel-Poisson means \[ P_t F = \sum_\lambda t^{| \lambda| } \Phi_\lambda \langle F,\Phi_ ...
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The Fractal Dimension as a Measure of the Quality of Habitats

Acta Biotheoretica, 2004
Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones.
Imre, A,, Bogaert, Jan
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Scattering on fractal measures

Journal of Physics A: Mathematical and General, 1996
We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude r(p) and t(p) of an incoming wave e(ipx) are well defined. We also show that the scattering problem on fractal potentials can be obtained as a limit case of scattering on ...
Guerin, Charles-Antoine, Holschneider, Matthias   +1 more
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Fractal Probability Measures of Learning

Methods, 2001
Herein we introduce a technique for determining the fractal dimension of time series obtained from complex systems, in particular brain-wave data in which the fractal dimension is arguably a measure of awareness and learning. The technique is based on determining the probability distribution for the degree of irregularity in random time series and has ...
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Quantifying the closeness of fractal measures

Physical Review E, 1994
Numerically, fractal measures are represented by finite sets of discrete points, e.g., those generated by trajectories. We introduce a cross-correlation integral to evaluate the distinctness and overlap of two such sets, and present a criterion to determine up to what precision the two sets are realizations of the same measure.
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Fractal measures in multiparticle production

Physical Review D, 1990
A new set of moments {ital G}{sub {ital q}} of the multiplicity distribution in a narrow rapidity window is suggested for analysis so that the chaotic fluctuations of the rapidity distribution can be described in the formalism of multifractals. Phenomenological evidence is given to show that there is a fractal structure in the data of multiparticle ...
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Measuring the complexity of non-fractal shapes by a fractal method

Pattern Recognition Letters, 2000
Summary: The divider-step method is commonly used to measure the fractal dimension \(D\) of fractal objects. We propose to use an approximate Hausdorff measure in the dimension \(D\) to estimate the complexity of non-fractal objects.
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Measuring of Spectral Franctal Dimension

New Mathematics and Natural Computation, 2007
There were great expectations in the 1980s in connection with the practical applications of mathematical processes which were built mainly upon the fractal dimension, mathematical basis. Results were achieved in the first times in several fields: examination of material structure, simulation of chaotic phenomena (earthquake, tornado), modeling real ...
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A note on fractal sets and the measurement of fractal dimension

Physica A: Statistical Mechanics and its Applications, 1996
Abstract The fractal dimension of a set in the Euclidean n-space may depend on the applied concept of fractal dimension. Several concepts are considered here, and in a first part, properties are given for sets such that they have the same fractal dimension for all concepts. In particular, self-similar sets hold these properties. The second part deals
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