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Displaying 101 – 110 of 110

Multifractal dimensions for invariant subsets of piecewise monotonic interval maps

Franz Hofbauer, Peter Raith, Thomas Steinberger (2003)

Fundamenta Mathematicae

The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.

Multifractals and projections.

Fadhila Bahroun, Imen Bhouri (2006)

Extracta Mathematicae

In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.

Multi-multifractal decomposition of digraph recursive fractals.

Dominique Simpelaere (2001)

Revista Matemática Iberoamericana

In many situations, both deterministic and probabilistic, one is interested in measure theory in local behaviours, for example in local dimensions, local entropies or local Lyapunov exponents. It has been relevant to study dynamical systems, since the study of multifractal can be further developed for a large class of measures invariant under some map, particularly when there exist strange attractors or repelers (hyperbolic case). Multifractal refers to a notion of size, which emphasizes the local...

Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times

Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao (2011)

Annales de l'I.H.P. Probabilités et statistiques

By using a wavelet method we prove that the harmonisable-type N-parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.

Multiplication, distributivity and fuzzy-integral. I

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.

Multiplication, distributivity and fuzzy-integral. II

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...

Multiplication, distributivity and fuzzy-integral. III

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.

Multiplications aléatoires et dimensions de Hausdorff

Jean-Pierre Kahane (1987)

Annales de l'I.H.P. Probabilités et statistiques

Multiresolution analysis and Radon measures on a locally compact Abelian group

Félix Galindo, Javier Sanz (2001)

Czechoslovak Mathematical Journal

A multiresolution analysis is defined in a class of locally compact abelian groups $G$ . It is shown that the spaces of integrable functions $ℒ^{p} (G)$ and the complex Radon measures $M (G)$ admit a simple characterization in terms of this multiresolution analysis.

Multivalued fractals in b-metric spaces

Monica Boriceanu, Marius Bota, Adrian Petruşel (2010)

Open Mathematics

Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal...

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