LEADER 06265nam 22017895 450 001 9910154746903321 005 20190708092533.0 010 $a1-4008-8241-9 024 7 $a10.1515/9781400882410 035 $a(CKB)3710000000627786 035 $a(SSID)ssj0001651256 035 $a(PQKBManifestationID)16425852 035 $a(PQKBTitleCode)TC0001651256 035 $a(PQKBWorkID)12623624 035 $a(PQKB)11346273 035 $a(MiAaPQ)EBC4738718 035 $a(DE-B1597)468030 035 $a(OCoLC)979580918 035 $a(DE-B1597)9781400882410 035 $a(EXLCZ)993710000000627786 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 /$fVictor Guillemin 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1989 215 $a1 online resource (236 pages) $cillustrations 225 0 $aAnnals of Mathematics Studies ;$v352 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08514-5 311 $a0-691-08513-7 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tContents -- $tForeword -- $tPart I. A relativistic approach to Zoll phenomena -- $tPart II. The general theory of Zollfrei deformations -- $tPart III. Zollfrei deformations of M2,1 -- $tPart IV. The generalized x-ray transform -- $tPart V. The Floquet theory -- $tBibliography 330 $aThe subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal. 410 0$aAnnals of mathematics studies ;$vno. 121. 606 $aCosmology$xMathematical models 606 $aGeometry, Differential 606 $aLorentz transformations 610 $aAutomorphism. 610 $aBijection. 610 $aC0. 610 $aCanonical form. 610 $aCanonical transformation. 610 $aCauchy distribution. 610 $aCausal structure. 610 $aCayley transform. 610 $aCodimension. 610 $aCohomology. 610 $aCokernel. 610 $aCompactification (mathematics). 610 $aComplexification (Lie group). 610 $aComputation. 610 $aConformal geometry. 610 $aConformal map. 610 $aConformal symmetry. 610 $aConnected sum. 610 $aContact geometry. 610 $aCorank. 610 $aCovariant derivative. 610 $aCovering space. 610 $aDeformation theory. 610 $aDiagram (category theory). 610 $aDiffeomorphism. 610 $aDifferentiable manifold. 610 $aDifferential operator. 610 $aDimension (vector space). 610 $aEinstein field equations. 610 $aEquation. 610 $aEuler characteristic. 610 $aExistential quantification. 610 $aFiber bundle. 610 $aFibration. 610 $aFloquet theory. 610 $aFour-dimensional space. 610 $aFourier integral operator. 610 $aFourier transform. 610 $aFundamental group. 610 $aGeodesic. 610 $aHamilton?Jacobi equation. 610 $aHilbert space. 610 $aHolomorphic function. 610 $aHolomorphic vector bundle. 610 $aHyperfunction. 610 $aHypersurface. 610 $aIntegral curve. 610 $aIntegral geometry. 610 $aIntegral transform. 610 $aIntersection (set theory). 610 $aInvertible matrix. 610 $aK-finite. 610 $aLagrangian (field theory). 610 $aLie algebra. 610 $aLight cone. 610 $aLinear map. 610 $aManifold. 610 $aMaxima and minima. 610 $aMinkowski space. 610 $aModule (mathematics). 610 $aNotation. 610 $aOne-parameter group. 610 $aParametrix. 610 $aParametrization. 610 $aPrincipal bundle. 610 $aProduct metric. 610 $aPseudo-differential operator. 610 $aQuadratic equation. 610 $aQuadratic form. 610 $aQuadric. 610 $aRadon transform. 610 $aRiemann surface. 610 $aRiemannian manifold. 610 $aSeifert fiber space. 610 $aSheaf (mathematics). 610 $aSiegel domain. 610 $aSimply connected space. 610 $aSubmanifold. 610 $aSubmersion (mathematics). 610 $aSupport (mathematics). 610 $aSurjective function. 610 $aSymplectic manifold. 610 $aSymplectic vector space. 610 $aSymplectomorphism. 610 $aTangent space. 610 $aTautology (logic). 610 $aTensor product. 610 $aTheorem. 610 $aTopological space. 610 $aTopology. 610 $aTwo-dimensional space. 610 $aUnit vector. 610 $aUniversal enveloping algebra. 610 $aVariable (mathematics). 610 $aVector bundle. 610 $aVector field. 610 $aVector space. 610 $aVerma module. 610 $aVolume form. 610 $aX-ray transform. 615 0$aCosmology$xMathematical models. 615 0$aGeometry, Differential. 615 0$aLorentz transformations. 676 $a523.1/072/4 700 $aGuillemin$b Victor, $040563 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154746903321 996 $aCosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121$92788032 997 $aUNINA LEADER 04367nam 22006975 450 001 996503551403316 005 20240223120039.0 010 $a3-031-21853-1 024 7 $a10.1007/978-3-031-21853-8 035 $a(MiAaPQ)EBC7156550 035 $a(Au-PeEL)EBL7156550 035 $a(CKB)25657527200041 035 $a(DE-He213)978-3-031-21853-8 035 $a(EXLCZ)9925657527200041 100 $a20221208d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPartial Differential Equations in Action$b[electronic resource] $eFrom Modelling to Theory /$fby Sandro Salsa, Gianmaria Verzini 205 $a4th ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (692 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v147 311 08$aPrint version: Salsa, Sandro Partial Differential Equations in Action Cham : Springer International Publishing AG,c2023 9783031218521 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and Vibration -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational Formulation of Elliptic Problems -- 9 Weak Formulation of Evolution Problems -- 10 More Advanced Topics -- 11 Systems of Conservation Laws -- Appendix A: Measures and Integrals -- Appendix B: Identities and Formulas. 330 $aThis work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v147 606 $aDifferential equations 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aFunctional analysis 606 $aMathematical physics 606 $aDifferential Equations 606 $aMathematical and Computational Engineering Applications 606 $aFunctional Analysis 606 $aMathematical Methods in Physics 606 $aEquacions en derivades parcials$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aFunctional analysis. 615 0$aMathematical physics. 615 14$aDifferential Equations. 615 24$aMathematical and Computational Engineering Applications. 615 24$aFunctional Analysis. 615 24$aMathematical Methods in Physics. 615 7$aEquacions en derivades parcials 676 $a381 700 $aSalsa$b S.$061750 702 $aVerzini$b Gianmaria 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996503551403316 996 $aPartial differential equations in action$9715363 997 $aUNISA