03420nam 22005175 450 99646653580331620200706192224.03-540-78379-210.1007/978-3-540-78379-4(CKB)1000000000437232(SSID)ssj0000316330(PQKBManifestationID)11225812(PQKBTitleCode)TC0000316330(PQKBWorkID)10263930(PQKB)11498750(DE-He213)978-3-540-78379-4(MiAaPQ)EBC3068723(PPN)125218338(EXLCZ)99100000000043723220100301d2008 u| 0engurnn|008mamaatxtccrArithmetical Investigations[electronic resource] Representation Theory, Orthogonal Polynomials, and Quantum Interpolations /by Shai M. J. Haran1st ed. 2008.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2008.xii, 217 p. illLecture Notes in Mathematics,0075-8434Bibliographic Level Mode of Issuance: Monograph3-540-78378-4 Includes bibliographical references (p. [209]-213) and index.Introduction: Motivations from Geometry -- Gamma and Beta Measures -- Markov Chains -- Real Beta Chain and q-Interpolation -- Ladder Structure -- q-Interpolation of Local Tate Thesis -- Pure Basis and Semi-Group -- Higher Dimensional Theory -- Real Grassmann Manifold -- p-Adic Grassmann Manifold -- q-Grassmann Manifold -- Quantum Group Uq(su(1, 1)) and the q-Hahn Basis.In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.Lecture Notes in Mathematics,0075-8434Number theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Number theory.Number Theory.511.42Haran Shai M. Jauthttp://id.loc.gov/vocabulary/relators/aut724875BOOK996466535803316Arithmetical investigations1416595UNISA02596oam 2200625 450 991070976670332120180625095206.0(CKB)5470000002472578(OCoLC)183027199(EXLCZ)99547000000247257820071207j200607 ua 0engurcn|||||||||txtrdacontentcrdamediacrrdacarrierPetrographic methods of examining hardened concrete a petrographic manual /Hollis N. Walker, D. Stephen Lane, and Paul E. StutzmanRevised 2004.McLean, VA :U.S. Department of Transporation, Federal Highway Administration, Research, Development, and Technology, Turner-Fairbank Highway Research Center,July 2006.1 online resource (xviii, 333 pages) illustrations (some color)"July 2006.""Publication no. FHWA-HRT-04-150.""Performing organization: Virginia Transportation Research Council "--Technical report documentation page."Performing organization report number: VTRC 04-R21"--Technical report documentation page."Sponsoring agency: Virginia Department of Transportation and Federal Highway Administration, Office of Infrastructure R&D"--Technical report documentation page.Includes tables.Includes bibliographical references (pages 309-333).Petrographic methods of examining hardened concrete Pavements, ConcreteTestingHandbooks, manuals, etcConcreteTestingHandbooks, manuals, etcPetrographic microscopeHandbooks and manuals.lcgftPavements, ConcreteTestingConcreteTestingPetrographic microscope.Walker Hollis N.1401475Lane D. Stephen(Daniel Stephen),Stutzman Paul E.Virginia Transportation Research Council.Virginia.Department of Transportation,United States.Federal Highway Administration.Office of Infrastructure Research and Development,Turner-Fairbank Highway Research Center,JCRJCRCBTOCLCAOCLCFOCLCQOCLOCLCQGPOBOOK9910709766703321Petrographic methods of examining hardened concrete3470252UNINA