# Generalization of multifractal theory within quantum calculus

@article{Olemskoi2010GeneralizationOM, title={Generalization of multifractal theory within quantum calculus}, author={Alexander I. Olemskoi and I. {\`A}. Shuda and Vadim Borisyuk}, journal={EPL}, year={2010}, volume={89}, pages={50007} }

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…

## 9 Citations

Statistical field theories deformed within different calculi

- Mathematics, Physics
- 2010

Abstract.
Within the framework of basic-deformed and finite-difference calculi,
as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis and
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q-analytic functions, fractals and generalized analytic functions

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- 2014

We introduce a new class of complex functions of complex argument which we call q-analytic functions. These functions satisfy q-Cauchy–Riemann equations and have real and imaginary parts as…

Polychronakos statistics and α-deformed Bose condensation of α-bosons

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In this paper, we consider the Polychronakos statistics for α < 0. We use the Stirling formula for the α-Gamma function to find the distribution function for the α-bosons. As application, we discuss…

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The cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods is surveyed, and the sources ofMultifractality are discussed.

Application of the Variational Iteration Method to the Initial Value Problems of Q-difference Equations-Some Examples

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- 2013

The q-difference equations are a class of important models both in q-calculus and applied sciences. The variational iteration method is extended to approximately solve the initial value problems of…

Formation of porous low-dimensional nickel systems during near equilibrium condensation in ultrapure inert environment

- Chemistry
- 2014

Abstract A new technique for synthesizing porous low-dimensional nickel has been developed, which involves the controlled sputter deposition of extremely small vapor fluxes in an ultrapure inert…

Structure formation mechanisms of low-dimensional porous titanium systems condensed under quasi-equilibrium steady-state conditions

- Materials Science
- 2011

Abstract In the present study porous titanium condensates have been deposited by means of ion-plasma sputtering under the quasi-equilibrium conditions and their structure formation mechanisms have…

Multifractal Analysis of the Surfaces of Protective (TiAlSiY)N, Me1−xN/CrN and Me1−xN/ZrN Coatings

- Materials ScienceLecture Notes in Mechanical Engineering
- 2019

In the present paper, a technique for the preparation of protective (TiAlSiY)N, MexN/CrN and Mex/ZrN coatings is shown. The algorithm of multifractal fluctuation analysis is described, and the…

Feature normalization based on non-extensive statistics for speech recognition

- Computer ScienceSpeech Commun.
- 2013

Highlights? We propose a feature normalization method for robust speech recognition. ? It operates in a spectral domain intermediate between log and linear. ? We name our method q-logarithmic…

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