LEADER 03263nam 2200673 450 001 996466480303316 005 20220304143001.0 010 $a3-540-47951-1 024 7 $a10.1007/BFb0078909 035 $a(CKB)1000000000437523 035 $a(SSID)ssj0000325766 035 $a(PQKBManifestationID)12087650 035 $a(PQKBTitleCode)TC0000325766 035 $a(PQKBWorkID)10264855 035 $a(PQKB)11745817 035 $a(DE-He213)978-3-540-47951-2 035 $a(MiAaPQ)EBC5592117 035 $a(Au-PeEL)EBL5592117 035 $a(OCoLC)1066187596 035 $a(MiAaPQ)EBC6842472 035 $a(Au-PeEL)EBL6842472 035 $a(OCoLC)793079033 035 $a(PPN)155237055 035 $a(EXLCZ)991000000000437523 100 $a20220304d1987 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPositive polynomials, convex integral polytopes, and a randomwalk problem /$fDavid E. Handelman 205 $a1st ed. 1987. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1987] 210 4$dİ1987 215 $a1 online resource (XIV, 138 p.) 225 1 $aLecture Notes in Mathematics ;$v1282 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-18400-7 311 $a3-540-18400-7 327 $aDefinitions and notation -- A random walk problem -- Integral closure and cohen-macauleyness -- Projective RK-modules are free -- States on ideals -- Factoriality and integral simplicity -- Meet-irreducibile ideals in RK -- Isomorphisms. 330 $aEmanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1282. 606 $aPolytopes 606 $aPolynomials 615 0$aPolytopes. 615 0$aPolynomials. 676 $a516.158 686 $a46L35$2msc 686 $a13B25$2msc 686 $a52A43$2msc 686 $a60G50$2msc 700 $aHandelman$b David$f1950-$058999 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466480303316 996 $aPositive polynomials, convex integral polytopes, and a randomwalk problem$92831094 997 $aUNISA