| Issue |
EPL
Volume 89, Number 5, March 2010
|
|
|---|---|---|
| Article Number | 50007 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/89/50007 | |
| Published online | 24 March 2010 | |
Generalization of multifractal theory within quantum calculus
1
Institute of Applied Physics, National Academy of Sciences of Ukraine - 58, Petropavlovskaya St., 40030 Sumy, Ukraine
2
Sumy State University - 2, Rimskii-Korsakov St., 40007 Sumy, Ukraine
Corresponding author: alex@ufn.ru
Received:
6
January
2010
Accepted:
19
February
2010
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 
= 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.
PACS: 02.20.Uw – Quantum groups / 05.45.Df – Fractals
© EPLA, 2010
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