LEADER 00999nam0-2200325---450- 001 990008409380403321 005 20070605103811.0 035 $a000840938 035 $aFED01000840938 035 $a(Aleph)000840938FED01 035 $a000840938 100 $a20061030d--------km-y0itay50------ba 101 1 $aita 102 $aIT 105 $a--------001yy 200 1 $a<>acustica nell'edilizia$eatti del Convegno tenutosi a Torino il 5 e 6 giugno 1979, presso l'Istituto elettrotecnico "Galileo Ferraris", con il patrocinio dell'associazione italiana di acustica$fa cura di R. Pisani 210 $aRoma$cE.S.A.$d[1980] 215 $a259 p.$d24 cm 610 0 $aAcustica 676 $a534 700 1$aPisani,$bR.$0501602 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990008409380403321 952 $a261007$b159$fDCATA 952 $a08 AA 121$b3827 C.E.$fDINED 959 $aDCATA 959 $aDINED 996 $aAcustica nell'edilizia$9726293 997 $aUNINA LEADER 06025nam 22006493 450 001 9910915797003321 005 20240723123144.0 010 $a1-4704-7540-5 035 $a(MiAaPQ)EBC30671915 035 $a(Au-PeEL)EBL30671915 035 $a(PPN)27210647X 035 $a(CKB)27902414500041 035 $a(EXLCZ)9927902414500041 100 $a20230804d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2023. 210 4$d©2023. 215 $a1 online resource (102 pages) 225 1 $aMemoirs of the American Mathematical Society Series ;$vv.287 311 08$aPrint version: Ratiu, Tudor S. Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems Providence : American Mathematical Society,c2023 9781470464394 327 $aCover -- Title page -- Chapter 1. Introduction -- Positive convexity results -- Negative convexity results -- Organization of the paper -- Acknowledgment -- Chapter 2. A brief overview of convexity in symplectic geometry and in integrable Hamiltonian systems -- 2.1. Kostant's Linear Convexity Theorem -- 2.2. Infinite dimensional Lie theory -- 2.3. "Linear" symplectic formulations -- 2.4. "Non-linear" symplectic formulations -- 2.5. Local-Global Convexity Principle -- 2.6. Convexity in integrable Hamiltonian systems -- Chapter 3. Toric-focus integrable Hamiltonian systems -- 3.1. Integrable systems -- 3.2. Local normal form of non-degenerate singularities -- 3.3. Semi-local structure of singularities -- 3.4. Topology and differential structure of the base space -- 3.5. Integral affine structure on the base space -- Chapter 4. Base spaces and affine manifolds with focus singularities -- 4.1. Monodromy and affine coordinates near elementary focus points -- 4.2. Affine coordinates near focus points in higher dimensions -- 4.3. Behavior of the affine structure near focus^{ } points -- 4.4. Definition of affine structures with focus points -- Chapter 5. Straight lines and convexity -- 5.1. Regular and singular straight lines -- 5.2. Singular straight lines in dimension 2 and branched extension -- 5.3. Straight lines in dimension near a focus point -- 5.4. Straight lines near a focus^{ } point -- 5.5. The notions of convexity and strong convexity -- Chapter 6. Local convexity at focus points -- 6.1. Convexity of focus boxes in dimension 2 -- 6.2. Convexity of focus boxes in higher dimensions -- 6.3. Existence of non-convex focus^{ } boxes -- Chapter 7. Global convexity -- 7.1. Local-global convexity principle -- 7.2. Angle variation of a curve on an affine surface -- 7.3. Convexity of compact affine surfaces with non-empty boundary. 327 $a7.4. Convexity in the non-compact proper case -- 7.5. Non-convex examples in the non-proper case -- 7.6. An affine black hole and non-convex ² -- 7.7. A globally convex ² example -- 7.8. Convexity of toric-focus base spaces in higher dimensions -- Bibliography -- Index -- Back Cover. 330 $a"This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities. We obtain a series of convexity results, both positive and negative, for such singular integral affine base spaces. In particular, near a focus singular point, they are locally convex and the local-global convexity principle still applies. They are also globally convex under some natural additional conditions. However, when the monodromy is sufficiently large, the local-global convexity principle breaks down and the base spaces can be globally non-convex, even for compact manifolds. As a surprising example, we construct a 2-dimensional "integral affine black hole", which is locally convex but for which a straight ray from the center can never escape"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society Series 606 $aConvex domains 606 $aAffine differential geometry 606 $aHamiltonian systems 606 $aToric varieties 606 $aDynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Completely integrable systems, topological structure of phase space, integratio$2msc 606 $aDifferential geometry -- Classical differential geometry -- Affine differential geometry$2msc 606 $aConvex and discrete geometry -- General convexity -- Axiomatic and generalized convexity$2msc 615 0$aConvex domains. 615 0$aAffine differential geometry. 615 0$aHamiltonian systems. 615 0$aToric varieties. 615 7$aDynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Completely integrable systems, topological structure of phase space, integratio 615 7$aDifferential geometry -- Classical differential geometry -- Affine differential geometry. 615 7$aConvex and discrete geometry -- General convexity -- Axiomatic and generalized convexity. 676 $a516/.08 676 $a516.08 686 $a37J35$a53A15$a52A01$2msc 700 $aRatiu$b Tudor S$041620 701 $aWacheux$b Christophe$01779813 701 $aZung$b Nguyen Tien$0499013 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910915797003321 996 $aConvexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems$94303373 997 $aUNINA LEADER 03801nam 22006495 450 001 9910254084403321 005 20200706233841.0 010 $a9783319333014 024 7 $a10.1007/978-3-319-33301-4 035 $a(CKB)3710000000891687 035 $a(DE-He213)978-3-319-33301-4 035 $a(MiAaPQ)EBC4714754 035 $a(PPN)19632520X 035 $a(EXLCZ)993710000000891687 100 $a20161008d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntegral and Discrete Inequalities and Their Applications $eVolume I: Linear Inequalities /$fby Yuming Qin 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016. 215 $a1 online resource (XVI, 989 p. 9 illus.) 311 $a3-319-33300-3 311 $a3-319-33301-1 320 $aIncludes bibliographical references and index. 327 $aPreface -- Linear One-Dimensional Continuous Integral Inequalities -- Linear One-Dimensional Discrete (Difference) Inequalities -- Linear One-Dimensional Discontinuous Integral Inequalities -- Applications of Linear One-Dimensional Inequalities -- Linear Multi-Dimensional Continuous Integral Inequalities -- Linear Multi-Dimensional Discrete (Difference) Inequalities -- Linear Multi-Dimensional Discontinuous Integral Inequalities -- Applications of Linear Multi-Dimensional Integral and Difference Inequalities. 330 $aThis book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author?s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations. 606 $aFunctions of real variables 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aIntegral equations 606 $aDifference equations 606 $aFunctional equations 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 615 0$aFunctions of real variables. 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 0$aIntegral equations. 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aReal Functions. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aIntegral Equations. 615 24$aDifference and Functional Equations. 676 $a515.8 700 $aQin$b Yuming$4aut$4http://id.loc.gov/vocabulary/relators/aut$0314000 906 $aBOOK 912 $a9910254084403321 996 $aIntegral and discrete inequalities and their applications$91520333 997 $aUNINA