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Idempotent Analysis and Its Applications Mathematics and Its Applications

Victor P. Maslov

Published by Springer
ISBN 10: 0792345096 / ISBN 13: 9780792345091
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Title: Idempotent Analysis and Its Applications ...

Publisher: Springer

Binding: Hardcover

Book Condition: New

Book Type: Hardcover

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Hardcover. 305 pages. Dimensions: 9.3in. x 6.4in. x 1.0in.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 . This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9780792345091

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Synopsis: 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 .

Product Description: This monograph is about a branch of calculus the authors have called Idempotent Analysis, which deals with the semimodules of functions ranging in a semiring with idempotent addition. The theory is developed together with numerous applications to discrete mathematics, turnpike theory, mathematical economics, games and controlled Markov processes, the theory of generalised solutions of the Hamilton-Jacobi-Bellman differential equation, the theory of continuously observed and controlled quantum systems and the construction of WKB-like asymptotics of the heat equation and the Schrödinger equation.
Audience: This book will be of interest to mathematicians, engineers, college teachers and students.

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