05499nam 2200661Ia 450 991045353630332120200520144314.01-281-91199-29786611911997981-277-230-8(CKB)1000000000538154(EBL)1681504(OCoLC)815748131(SSID)ssj0000103011(PQKBManifestationID)11138340(PQKBTitleCode)TC0000103011(PQKBWorkID)10061338(PQKB)10788639(MiAaPQ)EBC1681504(WSP)00002047 (PPN)168148110(Au-PeEL)EBL1681504(CaPaEBR)ebr10255619(CaONFJC)MIL191199(EXLCZ)99100000000053815420071223d2008 uy 0engur|n|---|||||txtccrAnalytic hyperbolic geometry and Albert Einstein's special theory of relativity[electronic resource] /Abraham Albert UngarSingapore ;Hackensack, NJ World Scientificc20081 online resource (649 p.)Description based upon print version of record.981-277-229-4 Includes bibliographical references (p. 605-620) and index.Contents; Preface; Acknowledgements; 1. Introduction; 1.1 A Vector Space Approach to Euclidean Geometry and A Gyrovector Space Approach to Hyperbolic Geometry; 1.2 Gyrolanguage; 1.3 Analytic Hyperbolic Geometry; 1.4 The Three Models; 1.5 Applications in Quantum and Special Relativity Theory; 2. Gyrogroups; 2.1 Definitions; 2.2 First Gyrogroup Theorems; 2.3 The Associative Gyropolygonal Gyroaddition; 2.4 Two Basic Gyrogroup Equations and Cancellation Laws; 2.5 Commuting Automorphisms with Gyroautomorphisms; 2.6 The Gyrosemidirect Product Group; 2.7 Basic Gyration Properties3. Gyrocommutative Gyrogroups3.1 Gyrocommutative Gyrogroups; 3.2 Nested Gyroautomorphism Identities; 3.3 Two-Divisible Two-Torsion Free Gyrocommutative Gyrogroups; 3.4 From M obius to Gyrogroups; 3.5 Higher Dimensional M obius Gyrogroups; 3.6 M obius gyrations; 3.7 Three-Dimensional M obius gyrations; 3.8 Einstein Gyrogroups; 3.9 Einstein Coaddition; 3.10 PV Gyrogroups; 3.11 Points and Vectors in a Real Inner Product Space; 3.12 Exercises; 4. Gyrogroup Extension; 4.1 Gyrogroup Extension; 4.2 The Gyroinner Product, the Gyronorm, and the Gyroboost; 4.3 The Extended Automorphisms4.4 Gyrotransformation Groups4.5 Einstein Gyrotransformation Groups; 4.6 PV (Proper Velocity) Gyrotransformation Groups; 4.7 Galilei Transformation Groups; 4.8 From Gyroboosts to Boosts; 4.9 The Lorentz Boost; 4.10 The (p :q)-Gyromidpoint; 4.11 The (p1 :p2 :...: pn)-Gyromidpoint; 5. Gyrovectors and Cogyrovectors; 5.1 Equivalence Classes; 5.2 Gyrovectors; 5.3 Gyrovector Translation; 5.4 Gyrovector Translation Composition; 5.5 Points and Gyrovectors; 5.6 The Gyroparallelogram Addition Law; 5.7 Cogyrovectors; 5.8 Cogyrovector Translation; 5.9 Cogyrovector Translation Composition5.10 Points and Cogyrovectors5.11 Exercises; 6. Gyrovector Spaces; 6.1 Definition and First Gyrovector Space Theorems; 6.2 Solving a System of Two Equations in a Gyrovector Space; 6.3 Gyrolines and Cogyrolines; 6.4 Gyrolines; 6.5 Gyromidpoints; 6.6 Gyrocovariance; 6.7 Gyroparallelograms; 6.8 Gyrogeodesics; 6.9 Cogyrolines; 6.10 Carrier Cogyrolines of Cogyrovectors; 6.11 Cogyromidpoints; 6.12 Cogyrogeodesics; 6.13 Various Gyrolines and Cancellation Laws; 6.14 M obius Gyrovector Spaces; 6.15 M obius Cogyroline Parallelism; 6.16 Illustrating the Gyroline Gyration Transitive Law6.17 Turning the M obius Gyrometric into the Poincar e Metric6.18 Einstein Gyrovector Spaces; 6.19 Turning Einstein Gyrometric into a Metric; 6.20 PV(ProperVelocity) Gyrovector Spaces; 6.21 Gyrovector Space Isomorphisms; 6.22 Gyrotriangle Gyromedians and Gyrocentroids; 6.22.1 In Einstein Gyrovector Spaces; 6.22.2 In M obius Gyrovector Spaces; 6.22.3 In PV Gyrovector Spaces; 6.23 Exercises; 7. Rudiments of Differential Geometry; 7.1 The Riemannian Line Element of Euclidean Metric; 7.2 The Gyroline and the Cogyroline Element; 7.3 The Gyroline Element of M obius Gyrovector Spaces7.4 The Cogyroline Element of M obius Gyrovector Spaces This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called <i>gyrovectors</i>. Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both Special relativity (Physics)Geometry, HyperbolicElectronic books.Special relativity (Physics)Geometry, Hyperbolic.516.9Ungar Abraham A850286MiAaPQMiAaPQMiAaPQBOOK9910453536303321Analytic hyperbolic geometry and Albert Einstein's special theory of relativity2098350UNINA02872 am 2200505 n 450 9910416473303321201907052-8107-1035-X10.4000/books.pumi.7227(CKB)4100000010352355(FrMaCLE)OB-pumi-7227(oapen)https://directory.doabooks.org/handle/20.500.12854/45531(PPN)243134614(EXLCZ)99410000001035235520200227j|||||||| ||| 0freuu||||||m||||txtrdacontentcrdamediacrrdacarrierDu lecteur à l’usager Ethnographie d’une Bibliothèque Universitaire /Mariangela Roselli, Marc PerrenoudToulouse Presses universitaires du Midi20191 online resource (284 p.) 2-8107-0085-0 Les usagers s’approprient les bibliothèques selon des modalités qui correspondent rarement aux attentes des professionnels. Ils y entrent avec ce qui les constitue : des habitudes de lecture, des demandes et des besoins particuliers, des origines sociales, un rapport spécifique au temps. Entre l’instant où ils en franchissent l’entrée et celui où ils en sortent, des parcours s’ébauchent, inscrits dans les espaces du lieu ; des relations singulières aux objets et aux personnes s’instaurent, des préférences s’expriment concrètement. Au gré d’une enquête ethnographique rigoureuse et vivante, cet ouvrage suit pas à pas les pratiques effectives des utilisateurs d’une bibliothèque universitaire française, celle de l’université de lettres et sciences humaines de Toulouse. Bien au-delà de la simple étude de cas, l’ouvrage alimentera la réflexion en cours sur le rapport des jeunes au livre et au savoir, dans un contexte marqué par l’essor du numérique et du multimédia, et par celui du nomadisme culturel. Cette analyse des pratiques du public « réel » d’une bibliothèque fournira des outils précieux aux professionnels de la documentation et aux enseignants, mais aussi, de façon plus générale, à tous ceux qui s’intéressent de près à la sociologie contemporaine des pratiques culturelles.Information Science &amp; Library ScienceSociologylecturebibliothèquedocumentationbibliothèquedocumentationlectureInformation Science &amp; Library ScienceSociologylecturebibliothèquedocumentationRoselli Mariangela1306162Perrenoud Marc1293972FR-FrMaCLEBOOK9910416473303321Du lecteur à l’usager3028346UNINA