Results 11 to 20 of about 86,947 (328)
Classifying Cantor Sets by their Fractal Dimensions [PDF]
Proceedings of the American Mathematical Society, 2010 In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this
Cabrelli, Carlos A. +2 more
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Optimization on fractal sets [PDF]
Optimization Letters, 2021 We outline necessary and sufficient condition to the existence of extrmas of a function on a self-similar set, and we describe discrete gradient algorithm to find the extrema.
Nizare Riane, Claire David
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Turbulence on a Fractal Fourier Set [PDF]
Physical Review Letters, 2015 A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension, D, from the ...
Lanotte, As +4 more
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From Fractal Groups to Fractal Sets [PDF]
, 2003 This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and renormalizable dynamical systems.
Bartholdi, Laurent +2 more
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FRACTAL DIMENSIONS OF k-AUTOMATIC SETS
The Journal of Symbolic Logic, 2023 AbstractThis paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal geometry of “k-automatic” sets, subsets of $[0,1]^d$ that are recognized by Büchi automata.
Alexi Block Gorman +1 more
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Angular projections of fractal sets [PDF]
Europhysics Letters (EPL), 1997 We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small.
Durrer R +7 more
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Fractals, 2009 The formulation of a new analysis on a zero measure Cantor set C(⊂I = [0,1]) is presented. A non-Archimedean absolute value is introduced in C exploiting the concept of relative infinitesimals and a scale invariant ultrametric valuation of the form log ε-1 (ε/x) for a given scale ε > 0 and infinitesimals 0 < x < ε, x ∈ I\C.
Raut, Santanu, Datta, Dhurjati Prasad
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Set-Valued $$\alpha $$-Fractal Functions
Constructive Approximation, 2023 In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal functions. Further, we estimate the perturbation error between the given continuous function and its $\alpha$-fractal ...
Pandey, Megha +2 more
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Fractal Curves on Banach Algebras
Fractal and Fractional, 2022 Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as ...
María A. Navascués
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Furstenberg sets for a fractal set of directions [PDF]
Proceedings of the American Mathematical Society, 2010 In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the set of directions defining it. For any pair α
Ursula Molter, Ezequiel Rela
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