{"product_id":"9780792345091","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003eKolokoltsov, Vassili N.; Maslov, Victor P.\u003c\/h2\u003e \u003cp\u003eThe 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 .\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1997-04-30\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792345091\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-015-8901-7\u003c\/p\u003e \u003cp\u003eDimensions: 297cm x210cm\u003c\/p\u003e \u003cp\u003ePages: 305\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46539686543500,"sku":"9780792345091","price":224.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792345091.jpg?v=1775678918","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780792345091","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}