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Fractals and Reactions on Fractals
1989Many of the structures which surround us in nature (mountains, rivers, coastlines, clouds, the vascular system and other biological structures, for example) and systems of scientific interest (aggregates, macromolecules, rough surfaces, “strange” attractors, etc.) cannot be adequately described in terms of the concepts of Euclidean geometry.
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Chaos, Solitons & Fractals, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Montiel, M E, Aguado, A S, Zaluska, E
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Montiel, M E, Aguado, A S, Zaluska, E
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Siberian Mathematical Journal, 2012
The author constructs a self-similar fractal curve \({\mathfrak F}\) satisfying the following conditions: it is a quasi-conformal Jordan arc; it is not AC-removable, i.e., there exists a non-trivial function which is continuous in a domain \(D\supset {\mathfrak F}\) and holomorphic in \(D\setminus{\mathfrak F}\) but non-holomorphic on \({\mathfrak F}\);
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The author constructs a self-similar fractal curve \({\mathfrak F}\) satisfying the following conditions: it is a quasi-conformal Jordan arc; it is not AC-removable, i.e., there exists a non-trivial function which is continuous in a domain \(D\supset {\mathfrak F}\) and holomorphic in \(D\setminus{\mathfrak F}\) but non-holomorphic on \({\mathfrak F}\);
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Fractal walk and walk on fractals
Technical Physics, 2004The one-dimensional walk of a particle executing instantaneous jumps between the randomly distributed “atoms” at which it resides for a random time is considered. The random distances between the neighboring atoms and the time intervals between jumps are mutually independent. The asymptotic (t → ∞) behavior of this process is studied in connection with
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A REMARK ON WANG’S FRACTAL VARIATIONAL PRINCIPLE
, 2019Wang et al. established successfully a variational principle in a fractal space by the semi-inverse method.
Kang-le Wang, Chun-Hui He
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Interpolative operators: Fractal to multivalued fractal
Chaos, Solitons & Fractals, 2022Prithvi, B. V., Katiyar, S. K.
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Fractals of Brain, Fractals of Mind
1996This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic ...
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Fractal Geometry: Mathematical Foundations and Applications
, 1990K. Falconer
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