Idempotent Analysis and Its Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
401 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An , n E N , over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring , namely, that of all languages over a finite alphabet, as well as linear equations in this sern- ing, was examined by S. Kleene [107] in 1956 . This noncommutative semiring was used in applications to compiling and parsing (see also [1]) . Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics, logic , mathematical physics , mathematical economics, and optimizat ion, is immense; e. g. , see [9, 10, 11, 12, 13, 15, 16 , 17, 22, 31 , 32, 35,36,37,38,39 ,40,41,52,53 ,54,55,61,62 ,63,64,68, 71, 72, 73,74,77,78, 79,80,81,82,83,84,85,86,88,114,125 ,128,135,136, 138,139,141,159,160, 167,170,173,174,175,176,177,178,179,180,185,186 , 187, 188, 189]. In §1. 2 we present the most important facts of the idempotent algebra formalism . The semimodules An are idempotent analogs of the finite-dimensional v- n, tor spaces lR and hence endomorphisms of these semi modules can naturally be called (idempotent) linear operators on An |
| Beschreibung: | 1 Online-Ressource (XII, 305 p) |
| ISBN: | 9789401589017 9789048148349 |
| DOI: | 10.1007/978-94-015-8901-7 |
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| 245 | 1 | 0 | |a Idempotent Analysis and Its Applications |c by Vassili N. Kolokoltsov, Victor P. Maslov |
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| 490 | 0 | |a Mathematics and Its Applications |v 401 | |
| 500 | |a The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An , n E N , over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring , namely, that of all languages over a finite alphabet, as well as linear equations in this sern- ing, was examined by S. Kleene [107] in 1956 . This noncommutative semiring was used in applications to compiling and parsing (see also [1]) . Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics, logic , mathematical physics , mathematical economics, and optimizat ion, is immense; e. g. , see [9, 10, 11, 12, 13, 15, 16 , 17, 22, 31 , 32, 35,36,37,38,39 ,40,41,52,53 ,54,55,61,62 ,63,64,68, 71, 72, 73,74,77,78, 79,80,81,82,83,84,85,86,88,114,125 ,128,135,136, 138,139,141,159,160, 167,170,173,174,175,176,177,178,179,180,185,186 , 187, 188, 189]. In §1. 2 we present the most important facts of the idempotent algebra formalism . The semimodules An are idempotent analogs of the finite-dimensional v- n, tor spaces lR and hence endomorphisms of these semi modules can naturally be called (idempotent) linear operators on An | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Economics | |
| 650 | 4 | |a Order, Lattices, Ordered Algebraic Structures | |
| 650 | 4 | |a Calculus of Variations and Optimal Control; Optimization | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Economic Theory | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Wirtschaft | |
| 700 | 1 | |a Maslov, Victor P. |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Kolokoltsov, Vassili N. |
| author_facet | Kolokoltsov, Vassili N. |
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| author_sort | Kolokoltsov, Vassili N. |
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| bvnumber | BV042424102 |
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| ctrlnum | (OCoLC)863963525 (DE-599)BVBBV042424102 |
| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
| dewey-sort | 3511.33 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8901-7 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401589017 9789048148349 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859519 |
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| spelling | Kolokoltsov, Vassili N. Verfasser aut Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov, Victor P. Maslov Dordrecht Springer Netherlands 1997 1 Online-Ressource (XII, 305 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 401 The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An , n E N , over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring , namely, that of all languages over a finite alphabet, as well as linear equations in this sern- ing, was examined by S. Kleene [107] in 1956 . This noncommutative semiring was used in applications to compiling and parsing (see also [1]) . Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics, logic , mathematical physics , mathematical economics, and optimizat ion, is immense; e. g. , see [9, 10, 11, 12, 13, 15, 16 , 17, 22, 31 , 32, 35,36,37,38,39 ,40,41,52,53 ,54,55,61,62 ,63,64,68, 71, 72, 73,74,77,78, 79,80,81,82,83,84,85,86,88,114,125 ,128,135,136, 138,139,141,159,160, 167,170,173,174,175,176,177,178,179,180,185,186 , 187, 188, 189]. In §1. 2 we present the most important facts of the idempotent algebra formalism . The semimodules An are idempotent analogs of the finite-dimensional v- n, tor spaces lR and hence endomorphisms of these semi modules can naturally be called (idempotent) linear operators on An Mathematics Algebra Differential equations, partial Mathematical optimization Economics Order, Lattices, Ordered Algebraic Structures Calculus of Variations and Optimal Control; Optimization Optimization Economic Theory Partial Differential Equations Mathematik Wirtschaft Maslov, Victor P. Sonstige oth https://doi.org/10.1007/978-94-015-8901-7 Verlag Volltext |
| spellingShingle | Kolokoltsov, Vassili N. Idempotent Analysis and Its Applications Mathematics Algebra Differential equations, partial Mathematical optimization Economics Order, Lattices, Ordered Algebraic Structures Calculus of Variations and Optimal Control; Optimization Optimization Economic Theory Partial Differential Equations Mathematik Wirtschaft |
| title | Idempotent Analysis and Its Applications |
| title_auth | Idempotent Analysis and Its Applications |
| title_exact_search | Idempotent Analysis and Its Applications |
| title_full | Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov, Victor P. Maslov |
| title_fullStr | Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov, Victor P. Maslov |
| title_full_unstemmed | Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov, Victor P. Maslov |
| title_short | Idempotent Analysis and Its Applications |
| title_sort | idempotent analysis and its applications |
| topic | Mathematics Algebra Differential equations, partial Mathematical optimization Economics Order, Lattices, Ordered Algebraic Structures Calculus of Variations and Optimal Control; Optimization Optimization Economic Theory Partial Differential Equations Mathematik Wirtschaft |
| topic_facet | Mathematics Algebra Differential equations, partial Mathematical optimization Economics Order, Lattices, Ordered Algebraic Structures Calculus of Variations and Optimal Control; Optimization Optimization Economic Theory Partial Differential Equations Mathematik Wirtschaft |
| url | https://doi.org/10.1007/978-94-015-8901-7 |
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