LEADER 03318nam 22004695a 450 001 9910153279503321 005 20160630234501.0 010 $a3-03719-657-2 024 70$a10.4171/157 035 $a(CKB)3340000000002766 035 $a(CH-001817-3)204-160630 035 $a(PPN)194913732 035 $a(EXLCZ)993340000000002766 100 $a20160630j20160725 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAbsolute Arithmetic and $\mathbb F_1$-Geometry$b[electronic resource] /$fKoen Thas 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016 215 $a1 online resource (397 pages) 311 $a3-03719-157-0 327 $tThe Weyl functor. Introduction to Absolute Arithmetic /$rKoen Thas --$tBelian categories /$rAnton Deitmar --$tThe combinatorial-motivic nature of $\mathbb F_1$-schemes /$rKoen Thas --$tA blueprinted view on $\mathbb F_1$-geometry /$rOliver Lorscheid --$tAbsolute geometry and the Habiro topology /$rLieven Le Bruyn --$tWitt vectors, semirings, and total positivity /$rJames Borger --$tModuli operad over $\mathbb F_1$ /$rYuri I. Manin, Matilde Marcolli --$tA taste of Weil theory in characteristic one /$rKoen Thas. 330 $aIt has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, $\mathbb F_1$, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger-Manin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the $\mathbb F_1$-world, covers several areas in $\mathbb F_1$-theory, and is divided into four main parts - Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind $\mathbb F_1$, categorical foundations, the blend of different scheme theories over $\mathbb F_1$ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality. 606 $aCombinatorics & graph theory$2bicssc 606 $aCombinatorics$2msc 606 $aNumber theory$2msc 606 $aCommutative rings and algebras$2msc 606 $aAlgebraic geometry$2msc 615 07$aCombinatorics & graph theory 615 07$aCombinatorics 615 07$aNumber theory 615 07$aCommutative rings and algebras 615 07$aAlgebraic geometry 686 $a05-xx$a11-xx$a13-xx$a14-xx$2msc 701 $aThas$b Koen$f1977-$0726617 801 0$bch0018173 906 $aBOOK 912 $a9910153279503321 996 $aAbsolute Arithmetic and$92564511 997 $aUNINA LEADER 03280nam 2200745 a 450 001 9910825788703321 005 20200520144314.0 010 $a9786612112829 010 $a9781118210949 010 $a1118210948 010 $a9781282112827 010 $a1282112821 010 $a9780470403563 010 $a047040356X 010 $a9780470403556 010 $a0470403551 035 $a(CKB)1000000000719450 035 $a(EBL)427580 035 $a(OCoLC)476269135 035 $a(SSID)ssj0000227398 035 $a(PQKBManifestationID)11173569 035 $a(PQKBTitleCode)TC0000227398 035 $a(PQKBWorkID)10269839 035 $a(PQKB)11056633 035 $a(MiAaPQ)EBC427580 035 $a(Au-PeEL)EBL427580 035 $a(CaPaEBR)ebr10303825 035 $a(CaONFJC)MIL211282 035 $a(PPN)226206025 035 $a(OCoLC)228427375 035 $a(FINmELB)ELB178299 035 $a(Perlego)1008402 035 $a(EXLCZ)991000000000719450 100 $a20080509d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aPrinciples of modeling and simulation $ea multidisciplinary approach /$fedited by John A. Sokolowski, Catherine M. Banks 205 $a1st ed. 210 $aHoboken, N.J. $cJohn Wiley$dc2009 215 $a1 online resource (275 p.) 300 $aDescription based upon print version of record. 311 08$a9780470289433 311 08$a0470289430 320 $aIncludes bibliographical references and index. 327 $aPrinciples of Modeling and Simulation; Contents; Preface; Contributors; Part One Principles of Modeling and Simulation: A Multidisciplinary Approach; 1. What Is Modeling and Simulation?; 2. The Role of Modeling and Simulation; Part Two Theoretical Underpinnings; 3. Simulation: Models That Vary over Time; 4. Queue Modeling and Simulation; 5. Human Interaction with Simulations; 6. Verification and Validation; Part Three Practical Domains; 7. Uses of Simulation; 8. Modeling and Simulation: Real-World Examples; 9. The Future of Simulation; Index 330 $aExplores wide-ranging applications of modeling and simulation techniques that allow readers to conduct research and ask ""What if??"" Principles of Modeling and Simulation: A Multidisciplinary Approach is the first book to provide an introduction to modeling and simulation techniques across diverse areas of study. Numerous researchers from the fields of social science, engineering, computer science, and business have collaborated on this work to explore the multifaceted uses of computational modeling while illustrating their applications in common spreadsheets. The book is organized 606 $aMathematical models 606 $aSimulation methods 606 $aInterdisciplinary research 615 0$aMathematical models. 615 0$aSimulation methods. 615 0$aInterdisciplinary research. 676 $a003 701 $aSokolowski$b John A.$f1953-$01630190 701 $aBanks$b Catherine M.$f1960-$01630191 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825788703321 996 $aPrinciples of modeling and simulation$93968352 997 $aUNINA