Semirings and Affine Equations over Them: Theory and Applications [electronic resource] /
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.
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Format: | Texto biblioteca |
Language: | eng |
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Dordrecht : Springer Netherlands : Imprint: Springer,
2003
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Subjects: | Mathematics., Computer science, Associative rings., Rings (Algebra)., Mathematical models., Mathematical logic., Calculus of variations., Associative Rings and Algebras., Discrete Mathematics in Computer Science., Mathematical Modeling and Industrial Mathematics., Calculus of Variations and Optimal Control; Optimization., Mathematical Logic and Foundations., |
Online Access: | http://dx.doi.org/10.1007/978-94-017-0383-3 |
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KOHA-OAI-TEST:2132642018-07-30T23:46:56ZSemirings and Affine Equations over Them: Theory and Applications [electronic resource] / Golan, Jonathan S. author. SpringerLink (Online service) textDordrecht : Springer Netherlands : Imprint: Springer,2003.engSemiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.1: Semirings -- 2: Partially-Ordered Semirings -- 3: Complete Semirings -- 4: Residuated Semirings -- 5: Matrix Semirings -- 6: Symmetric Extension of a Semiring -- 7: Semimodules -- 8: Homomorphisms between Semimodules -- 9: Affine Maps between Semimodules -- 10: Partially-ordered Semimodules -- 11: Eigenelements -- 12: Permanents and Determinants -- Index of Applications -- Index of Terminology.Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.Mathematics.Computer scienceAssociative rings.Rings (Algebra).Mathematical models.Mathematical logic.Calculus of variations.Mathematics.Associative Rings and Algebras.Discrete Mathematics in Computer Science.Mathematical Modeling and Industrial Mathematics.Calculus of Variations and Optimal Control; Optimization.Mathematical Logic and Foundations.Springer eBookshttp://dx.doi.org/10.1007/978-94-017-0383-3URN:ISBN:9789401703833 |
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Mathematics. Computer science Associative rings. Rings (Algebra). Mathematical models. Mathematical logic. Calculus of variations. Mathematics. Associative Rings and Algebras. Discrete Mathematics in Computer Science. Mathematical Modeling and Industrial Mathematics. Calculus of Variations and Optimal Control; Optimization. Mathematical Logic and Foundations. Mathematics. Computer science Associative rings. Rings (Algebra). Mathematical models. Mathematical logic. Calculus of variations. Mathematics. Associative Rings and Algebras. Discrete Mathematics in Computer Science. Mathematical Modeling and Industrial Mathematics. Calculus of Variations and Optimal Control; Optimization. Mathematical Logic and Foundations. |
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Mathematics. Computer science Associative rings. Rings (Algebra). Mathematical models. Mathematical logic. Calculus of variations. Mathematics. Associative Rings and Algebras. Discrete Mathematics in Computer Science. Mathematical Modeling and Industrial Mathematics. Calculus of Variations and Optimal Control; Optimization. Mathematical Logic and Foundations. Mathematics. Computer science Associative rings. Rings (Algebra). Mathematical models. Mathematical logic. Calculus of variations. Mathematics. Associative Rings and Algebras. Discrete Mathematics in Computer Science. Mathematical Modeling and Industrial Mathematics. Calculus of Variations and Optimal Control; Optimization. Mathematical Logic and Foundations. Golan, Jonathan S. author. SpringerLink (Online service) Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
description |
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory. |
format |
Texto |
topic_facet |
Mathematics. Computer science Associative rings. Rings (Algebra). Mathematical models. Mathematical logic. Calculus of variations. Mathematics. Associative Rings and Algebras. Discrete Mathematics in Computer Science. Mathematical Modeling and Industrial Mathematics. Calculus of Variations and Optimal Control; Optimization. Mathematical Logic and Foundations. |
author |
Golan, Jonathan S. author. SpringerLink (Online service) |
author_facet |
Golan, Jonathan S. author. SpringerLink (Online service) |
author_sort |
Golan, Jonathan S. author. |
title |
Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
title_short |
Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
title_full |
Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
title_fullStr |
Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
title_full_unstemmed |
Semirings and Affine Equations over Them: Theory and Applications [electronic resource] / |
title_sort |
semirings and affine equations over them: theory and applications [electronic resource] / |
publisher |
Dordrecht : Springer Netherlands : Imprint: Springer, |
publishDate |
2003 |
url |
http://dx.doi.org/10.1007/978-94-017-0383-3 |
work_keys_str_mv |
AT golanjonathansauthor semiringsandaffineequationsoverthemtheoryandapplicationselectronicresource AT springerlinkonlineservice semiringsandaffineequationsoverthemtheoryandapplicationselectronicresource |
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