00960nam 2200253la 450 991048153350332120210618142901.0(UK-CbPIL)2090348729(CKB)5500000000105171(EXLCZ)99550000000010517120210618d1543 uy |itaurcn||||a|bb|Lettere volgari di diuersi nobilissimi huomini et eccellentissimi ingegni scritte in diuerse materie ... Libro primo[electronic resource]Venice Aldine Press1543Online resource (187, [5] c., 8°)Reproduction of original in Biblioteca Nazionale Centrale di Firenze.Manuzio Paolo1512-1574.327584Uk-CbPILUk-CbPILBOOK9910481533503321Lettere volgari di diuersi nobilissimi huomini et eccellentissimi ingegni scritte in diuerse materie ... Libro primo2230567UNINA03536nam 22006855 450 991029977030332120220426233942.04-431-55702-410.1007/978-4-431-55702-9(CKB)3710000000444539(EBL)3567544(SSID)ssj0001534899(PQKBManifestationID)11856008(PQKBTitleCode)TC0001534899(PQKBWorkID)11497729(PQKB)10390972(DE-He213)978-4-431-55702-9(MiAaPQ)EBC3567544(PPN)187687838(EXLCZ)99371000000044453920150707d2015 u| 0engur|n|---|||||txtccrVirtual turning points /by Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei1st ed. 2015.Tokyo :Springer Japan :Imprint: Springer,2015.1 online resource (133 p.)SpringerBriefs in Mathematical Physics,2197-1757 ;4Description based upon print version of record.4-431-55701-6 Includes bibliographical references and index.1. Definition and basic properties of virtual turning Points -- 2. Application to the Noumi-Yamada system with a large Parameter -- 3. Exact WKB analysis of non-adiabatic transition problems for 3-levels -- A. Integral representation of solutions and the Borel resummed WKBsolutions.The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.SpringerBriefs in Mathematical Physics,2197-1757 ;4Mathematical physicsDifferential equationsQuantum theoryMathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Quantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Mathematical physics.Differential equations.Quantum theory.Mathematical Physics.Ordinary Differential Equations.Quantum Physics.515.353Honda Naofumiauthttp://id.loc.gov/vocabulary/relators/aut755709Kawai Takahiroauthttp://id.loc.gov/vocabulary/relators/autTakei Yoshitsuguauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299770303321Virtual Turning Points2544374UNINA