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Fractals, coherent states and self-similarity induced noncommutative geometry
self-similarity fractals squeezed coherent states noncommutative geometry dissipation
2012/6/30
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are relate...
Electromagnetism on Anisotropic Fractals
Electromagnetism Anisotropic Fractals Mathematical Physics
2011/7/26
Abstract: We derive basic equations of electromagnetic fields in fractal media which are specified by three indepedent fractal dimensions {\alpha}_{i} in the respective directions x_{i} (i=1,2,3) of t...
Derivations and Dirichlet forms on fractals
Fredholm module derivation metric space Dirichlet form finitely ramified fractal
2011/7/27
Abstract: We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial...