LEADER 04036nam 22006493 450 001 9910970826703321 005 20231110230533.0 010 $a9781470465308 010 $a1470465302 035 $a(CKB)4100000011975355 035 $a(MiAaPQ)EBC6661109 035 $a(Au-PeEL)EBL6661109 035 $a(OCoLC)1259594323 035 $a(RPAM)22488289 035 $a(EXLCZ)994100000011975355 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExistence of Unimodular Triangulations-Positive Results 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dĐ2021. 215 $a1 online resource (96 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.270 311 08$a9781470447168 311 08$a1470447169 320 $aIncludes bibliographical references. 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. What? -- 1.2. Why? Who? -- 1.3. What is new? -- 1.4. What is not here -- 1.5. What is left? -- Chapter 2. Methods -- 2.1. Pulling Triangulations -- 2.2. Push-forward subdivisions and pull-back subdivisions -- 2.3. Joins and (Fiber) Products -- 2.4. Toric Gro?bner Bases -- Chapter 3. Examples -- 3.1. Polytopes cut out by roots -- 3.2. Polytopes spanned by roots -- 3.3. Other Graph Polytopes -- 3.4. Lecture hall polytopes -- 3.5. Smooth Polytopes -- 3.6. The Gro?bner fan and the toric Hilbert scheme -- Chapter 4. Dilations and the KMW Theorem -- 4.1. KMW numbers in dimension three -- 4.2. Canonical triangulation of a dilated simplex -- 4.3. Reducing the volume of simplices in the dilation -- 4.4. A proof of the KMW Theorem -- 4.5. An effective version of the KMW-Theorem -- Bibliography -- Back Cover. 330 $a"Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aConvex polytopes 606 $aTriangularization (Mathematics) 606 $aCombinatorial geometry 606 $aConvex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry)$2msc 606 $aConvex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopes$2msc 606 $aCommutative algebra -- Arithmetic rings and other special rings -- Polynomial rings and ideals; rings of integer-valued polynomials$2msc 615 0$aConvex polytopes. 615 0$aTriangularization (Mathematics) 615 0$aCombinatorial geometry. 615 7$aConvex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry). 615 7$aConvex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopes. 615 7$aCommutative algebra -- Arithmetic rings and other special rings -- Polynomial rings and ideals; rings of integer-valued polynomials. 676 $a516/.08 686 $a52B20$a52B11$a13F20$2msc 700 $aHaase$b Christian$0288859 701 $aPaffenholz$b Andreas$01801796 701 $aPiechnik$b Lindsay C$01801797 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970826703321 996 $aExistence of Unimodular Triangulations-Positive Results$94347192 997 $aUNINA LEADER 04810oam 22011774 450 001 9910956788703321 005 20250426110835.0 010 $a9786613822550 010 $a9781462377060 010 $a1462377068 010 $a9781451996432 010 $a1451996438 010 $a9781282588769 010 $a1282588761 010 $a9781451908244 010 $a1451908245 035 $a(CKB)3360000000443290 035 $a(EBL)3014341 035 $a(SSID)ssj0000940740 035 $a(PQKBManifestationID)11532936 035 $a(PQKBTitleCode)TC0000940740 035 $a(PQKBWorkID)10955959 035 $a(PQKB)10425580 035 $a(OCoLC)440837441 035 $a(MiAaPQ)EBC3014341 035 $a(IMF)WPIEE2006028 035 $a(IMF)WPIEA2006028 035 $aWPIEA2006028 035 $a(EXLCZ)993360000000443290 100 $a20020129d2006 uf 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aZimbabwe's Export Performance : $eThe Impact of the Parallel Market and Governance Factors /$fSōnia Muņoz 205 $a1st ed. 210 1$aWashington, D.C. :$cInternational Monetary Fund,$d2006. 215 $a1 online resource (17 p.) 225 1 $aIMF Working Papers 300 $a"January 2006." 311 08$a9781451862881 311 08$a1451862881 320 $aIncludes bibliographical references (p. 14-15). 327 $a""Contents""; ""I. INTRODUCTION""; ""II. EXPORT PERFORMANCE IN ZIMBABWE""; ""III. ANALYSIS OF THE DETERMINANTS OF EXPORT BEHAVIOR""; ""IV. COMPARATIVE MEASURES OF COMPETITIVENESS""; ""V. CONCLUSIONS""; ""Appendix I. Description of Sources and Transformation""; ""REFERENCES"" 330 3 $aThis paper analyzes Zimbabwe's export performance in recent years and identifies the factors that could improve export performance, from both a quantitative and qualitative perspective. Improving export performance is critical to a turnaround in Zimbabwe's economic situation. The growth rate of total exports declined dramatically in the early 2000s, following a large real appreciation of the currency and the introduction of the fast-track land reform program. An important finding of the paper is that policies that reduce (eliminate) the parallel market premium and lower ethnic tensions would be key to promoting export growth. 410 0$aIMF Working Papers; Working Paper ;$vNo. 2006/028 606 $aExports$zZimbabwe$xEconometric models 606 $aInternational trade$xEconometric models 606 $aCurrency$2imf 606 $aDevelopment Planning and Policy: Trade Policy$2imf 606 $aExchange rates$2imf 606 $aExport performance$2imf 606 $aExports and Imports$2imf 606 $aExports$2imf 606 $aFactor Movement$2imf 606 $aForeign Exchange Policy$2imf 606 $aForeign Exchange$2imf 606 $aForeign exchange$2imf 606 $aFormal and Informal Sectors$2imf 606 $aInstitutional Arrangements$2imf 606 $aInternational economics$2imf 606 $aInternational trade$2imf 606 $aModels of Trade with Imperfect Competition and Scale Economies$2imf 606 $aMultiple currency practices$2imf 606 $aMultiple or Simultaneous Equation Models: Models with Panel Data$2imf 606 $aNatural Resources and Domestic and International Conflicts$2imf 606 $aReal exchange rates$2imf 606 $aShadow Economy$2imf 606 $aTrade: General$2imf 607 $aZimbabwe$2imf 615 0$aExports$xEconometric models. 615 0$aInternational trade$xEconometric models. 615 7$aCurrency 615 7$aDevelopment Planning and Policy: Trade Policy 615 7$aExchange rates 615 7$aExport performance 615 7$aExports and Imports 615 7$aExports 615 7$aFactor Movement 615 7$aForeign Exchange Policy 615 7$aForeign Exchange 615 7$aForeign exchange 615 7$aFormal and Informal Sectors 615 7$aInstitutional Arrangements 615 7$aInternational economics 615 7$aInternational trade 615 7$aModels of Trade with Imperfect Competition and Scale Economies 615 7$aMultiple currency practices 615 7$aMultiple or Simultaneous Equation Models: Models with Panel Data 615 7$aNatural Resources and Domestic and International Conflicts 615 7$aReal exchange rates 615 7$aShadow Economy 615 7$aTrade: General 700 $aMuņoz$b Sōnia$01815672 712 02$aInternational Monetary Fund.$bAfrican Dept. 801 0$bDcWaIMF 906 $aBOOK 912 $a9910956788703321 996 $aZimbabwe's Export Performance$94372052 997 $aUNINA