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Author : V. P. Maslov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841143
Total Pages : 228 pages
Book Rating : 4.8/5 (411 download)
Download or read book Idempotent Analysis written by V. P. Maslov and published by American Mathematical Soc.. This book was released on 1992 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ilia Itenberg
Publisher : Springer Science & Business Media
ISBN 13 : 3034600488
Total Pages : 113 pages
Book Rating : 4.0/5 (346 download)
Download or read book Tropical Algebraic Geometry written by Ilia Itenberg and published by Springer Science & Business Media. This book was released on 2009-05-30 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.
Author : Vassili N. Kolokoltsov
Publisher : Springer Science & Business Media
ISBN 13 : 9401589011
Total Pages : 318 pages
Book Rating : 4.4/5 (15 download)
Download or read book Idempotent Analysis and Its Applications written by Vassili N. Kolokoltsov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ยง1. 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 .
