LEADER 01199nam--2200349---450- 001 990003106670203316 005 20080514100703.0 010 $a3-8260-1268-2 035 $a000310667 035 $aUSA01000310667 035 $a(ALEPH)000310667USA01 035 $a000310667 100 $a20080514d1997----km-y0itay50------ba 101 $ager 102 $aDE 105 $a||||||||001yy 200 1 $aEuklids Geometrie und ihre mathematiktheoretische Grundlegung in der neuplatonischen Philosophie des Proklos$fMarkus Schmitz 210 $aWürzburg$cKönigshausen & Neumann$d1997 215 $a449 p.$d24 cm 225 2 $aEpistemata$iReihe Philosophie$v212 410 0$12001$aEpistemataReihe Philosophie 606 0 $aProclo Diadoco$xNeoplatonismo$xMatematica [di] Euclide$2BNCF 676 $a186.4 700 1$aSCHMITZ,$bMarkus$0601372 801 0$aIT$bsalbc$gISBD 912 $a990003106670203316 951 $aII.1.A. 1252$b207642 L.M.$cII.1.$d00210725 959 $aBK 969 $aUMA 979 $aCHIARA$b90$c20080514$lUSA01$h1007 996 $aEuklids Geometrie und ihre mathematiktheoretische Grundlegung in der neuplatonischen Philosophie des Proklos$91021126 997 $aUNISA LEADER 03536nam 22006855 450 001 9910299770303321 005 20220426233942.0 010 $a4-431-55702-4 024 7 $a10.1007/978-4-431-55702-9 035 $a(CKB)3710000000444539 035 $a(EBL)3567544 035 $a(SSID)ssj0001534899 035 $a(PQKBManifestationID)11856008 035 $a(PQKBTitleCode)TC0001534899 035 $a(PQKBWorkID)11497729 035 $a(PQKB)10390972 035 $a(DE-He213)978-4-431-55702-9 035 $a(MiAaPQ)EBC3567544 035 $a(PPN)187687838 035 $a(EXLCZ)993710000000444539 100 $a20150707d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aVirtual turning points /$fby Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei 205 $a1st ed. 2015. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2015. 215 $a1 online resource (133 p.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v4 300 $aDescription based upon print version of record. 311 $a4-431-55701-6 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aThe discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi?Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v4 606 $aMathematical physics 606 $aDifferential equations 606 $aQuantum theory 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 615 0$aMathematical physics. 615 0$aDifferential equations. 615 0$aQuantum theory. 615 14$aMathematical Physics. 615 24$aOrdinary Differential Equations. 615 24$aQuantum Physics. 676 $a515.353 700 $aHonda$b Naofumi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755709 702 $aKawai$b Takahiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTakei$b Yoshitsugu$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299770303321 996 $aVirtual Turning Points$92544374 997 $aUNINA