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Title Generalization of multifractal theory within quantum calculus
Authors Oliemskoi, Oleksandr Ivanovych
Shuda, Iryna Oleksandrivna  
Borysiuk, Vadym Mykolaiovych
ORCID http://orcid.org/0000-0003-0184-8057
Keywords quantum calculus
multifractal theory
Type Article
Date of Issue 2010
URI http://essuir.sumdu.edu.ua/handle/123456789/3035
Publisher A Letters Journal Exploring the Frontiers of Physics
License
Citation Olemskoy, A.I. Generalization of multifractal theory within quantum calculus [Текст] / A.I. Olemskoy, I.A. Shuda, V.N. Borisyuk // A Letters Journal Exploring the Frontiers of Physics. — 2010. — vol.89. — p.6
Abstract On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over a self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τq= Dq(q −1). We find the equation for the set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and porous-surface condensates are considered as examples. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3035
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