| Applications of Hyperstructure Theory 2003 Edition Contributor(s): Corsini, P. (Author), Leoreanu, V. (Author) |
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ISBN: 1402012225 ISBN-13: 9781402012228 Publisher: Springer OUR PRICE: $237.49 Product Type: Hardcover - Other Formats Published: March 2003 Annotation: This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers. |
| Additional Information |
| BISAC Categories: - Computers | Machine Theory - Mathematics | Group Theory - Mathematics | Discrete Mathematics |
| Dewey: 004.015 |
| LCCN: 2003044516 |
| Series: Advances in Mathematics |
| Physical Information: 0.93" H x 6.34" W x 9.92" (1.48 lbs) 322 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Some mathematical disciplines can be presented and developed in the context of other disciplines, for instance Boolean algebras, that Stone has converted in a branch of ring theory, projective geome- tries, characterized by Birkhoff as lattices of a special type, projec- tive, descriptive and spherical geometries, represented by Prenowitz, as multigroups, linear geometries and convex sets presented by Jan- tosciak and Prenowitz as join spaces. As Prenowitz and Jantosciak did for geometries, in this book we present and study several ma- thematical disciplines that use the Hyperstructure Theory. Since the beginning, the Hyperstructure Theory and particu- larly the Hypergroup Theory, had applications to several domains. Marty, who introduced hypergroups in 1934, applied them to groups, algebraic functions and rational fractions. New applications to groups were also found among others by Eaton, Ore, Krasner, Utumi, Drbohlav, Harrison, Roth, Mockor, Sureau and Haddad. Connections with other subjects of classical pure Mathematics have been determined and studied: - Fields by Krasner, Stratigopoulos and Massouros Ch. - Lattices by Mittas, Comer, Konstantinidou, Serafimidis, Leoreanu and Calugareanu - Rings by Nakano, Kemprasit, Yuwaree - Quasigroups and Groupoids by Koskas, Corsini, Kepka, Drbohlav, Nemec - Semigroups by Kepka, Drbohlav, Nemec, Yuwaree, Kempra- sit, Punkla, Leoreanu - Ordered Structures by Prenowitz, Corsini, Chvalina IX x - Combinatorics by Comer, Tallini, Migliorato, De Salvo, Scafati, Gionfriddo, Scorzoni - Vector Spaces by Mittas - Topology by Mittas, Konstantinidou - Ternary Algebras by Bandelt and Hedlikova. |