Fractals on Graphs: Graph Fractaloids - Couverture souple

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9783639194470: Fractals on Graphs: Graph Fractaloids
Couverture souple
ISBN 10 : 3639194470 ISBN 13 : 9783639194470
Editeur : VDM Verlag, 2009

Synopsis

Recently, graphs have been studied and applied in various math and science fileds. In this monograph, we consider graphs with fractal property. Starting with graphs (combinatorial objects), we construct the corresponding groupoids (algebraic objects). The fractal property of graphs and groupoids is detected by the automata labelings (automata-theoretic objects). The groupoids with fractal property will be called graph fractaloids. By defining suitable representations of groupoids, we establish von Neumann algebras (operator-algebraic objects). As elements of the von Neumann algebras, we define the labeling operators (operator-theoretic objects) of graph fractaloids. In Part 1, by computing the free moments (free-probabilistic data) of the operators, we verify how the graph fractaloids act in the von Neumann algebras. Also, based on such computations, we can classify the graph fractaloids, in Part 2. Our classification shows the richness of graph fractaloids which are not fractal groups, in general. In Part 3, we show that, for any finite graph, there always exists a finite fractal graph containing it as its part.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Recently, graphs have been studied and applied in various math and science fileds. In this monograph, we consider graphs with fractal property. Starting with graphs (combinatorial objects), we construct the corresponding groupoids (algebraic objects). The fractal property of graphs and groupoids is detected by the automata labelings (automata-theoretic objects). The groupoids with fractal property will be called graph fractaloids. By defining suitable representations of groupoids, we establish von Neumann algebras (operator-algebraic objects). As elements of the von Neumann algebras, we define the labeling operators (operator-theoretic objects) of graph fractaloids. In Part 1, by computing the free moments (free-probabilistic data) of the operators, we verify how the graph fractaloids act in the von Neumann algebras. Also, based on such computations, we can classify the graph fractaloids, in Part 2. Our classification shows the richness of graph fractaloids which are not fractal groups, in general. In Part 3, we show that, for any finite graph, there always exists a finite fractal graph containing it as its part.

Biographie de l'auteur

Master Degrees (Math): Sungkyunkwan Univ. (Korea), Univ. of Iowa (U. S.), Ph. D Degree (Math): Univ. of Iowa (U. S.), Currenct Position (from 2005): Assistant Professor at St. Ambrose Univ., Dep. of Mathematics.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag
Date d'édition
2009
Langue
anglais
ISBN 10 
3639194470
ISBN 13 
9783639194470
Reliure
Broché
Nombre de pages
92
Coordonnées du fabricant
non disponible
Personne responsable
non disponible