On the Hausdorff dimension of the expressible set of certain sequences
Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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H. Akkari, I. Bhouri, P. Dubois, M. H. Bedoui (2008)
Mathematical Modelling of Natural Phenomena
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The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination...
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Igudesman, K. (2003)
Lobachevskii Journal of Mathematics
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Conci, Aura, Aquino, Felipe R. (1999)
Journal for Geometry and Graphics
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Peter R. Massopust (1991)
Aequationes mathematicae
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Lu-ming Shen (2010)
Acta Arithmetica
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M. A. Navascués, M. V. Sebastián (2009)
Banach Center Publications
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The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional...
F. Przytycki, M. Urbański (1989)
Studia Mathematica
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Balázs Bárány (2009)
Fundamenta Mathematicae
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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...
Chen, Yanguang (2010)
Discrete Dynamics in Nature and Society
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James R. Lee, Manor Mendel, Mohammad Moharrami (2012)
Fundamenta Mathematicae
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For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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