LEADER 02625nam 2200625 450 001 9910818127503321 005 20170816143339.0 010 $a1-4704-0232-7 035 $a(CKB)3360000000464827 035 $a(EBL)3114539 035 $a(SSID)ssj0000973921 035 $a(PQKBManifestationID)11578173 035 $a(PQKBTitleCode)TC0000973921 035 $a(PQKBWorkID)10984657 035 $a(PQKB)10890791 035 $a(MiAaPQ)EBC3114539 035 $a(RPAM)1670853 035 $a(PPN)195415272 035 $a(EXLCZ)993360000000464827 100 $a19980521h19981998 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral asymptotics on degenerating hyperbolic 3-manifolds /$fJo?zef Dodziuk, Jay Jorgenson 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1998] 210 4$dİ1998 215 $a1 online resource (90 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 643 300 $a"September 1998, volume 135, number 643 (third of 5 numbers)." 311 $a0-8218-0837-0 320 $aIncludes bibliographical references (pages 73-75). 327 $a""Contents""; ""Introduction""; ""A?1- Review of hyperbolic geometry""; ""A?2. Convergence of heat kernels""; ""A?3. Infinite cylinder estimates""; ""A?4. Heat kernels and regularized heat traces""; ""A?5. Degenerating heat traces""; ""A?6. Poisson kernel estimates""; ""A?7. Analysis of trace integrals""; ""A?8. Convergence of regularized heat traces""; ""A?9. Long time asymptotics""; ""A?10. Spectral zeta functions""; ""A?11- Selberg zeta functions""; ""A?12. Hurwitz- type zeta functions""; ""A?13. Asymptotics of spectral measures""; ""A?14. Eigenvalue counting problems"" 327 $a""A?15. Convergence of spectral projections""""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 643. 606 $aGeometry, Hyperbolic 606 $aHyperbolic spaces 606 $aSpectral theory (Mathematics) 606 $aAsymptotic expansions 615 0$aGeometry, Hyperbolic. 615 0$aHyperbolic spaces. 615 0$aSpectral theory (Mathematics) 615 0$aAsymptotic expansions. 676 $a510 s 676 $a516.9 700 $aDodziuk$b Jo?zef$f1947-$01673146 702 $aJorgenson$b Jay 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818127503321 996 $aSpectral asymptotics on degenerating hyperbolic 3-manifolds$94037040 997 $aUNINA LEADER 04426nam 2200733 450 001 9910831173403321 005 20240219153425.0 010 $a1-119-13467-6 024 7 $a10.1002/9781119134671 035 $a(CKB)2430000000040330 035 $a(CaBNVSL)mat07304003 035 $a(IDAMS)0b00006484a80f83 035 $a(IEEE)7304003 035 $a(SSID)ssj0000373594 035 $a(PQKBManifestationID)12145137 035 $a(PQKBTitleCode)TC0000373594 035 $a(PQKBWorkID)10440110 035 $a(PQKB)11102372 035 $a(PPN)26823454X 035 $a(EXLCZ)992430000000040330 100 $a20151222d2015 uy 101 0 $aeng 135 $aur|n||||||||| 181 $2rdacontent 182 $2isbdmedia 183 $2rdacarrier 200 10$aGuidance for the verification and validation of neural networks /$fLaura L. Pullum, Brian J. Taylor, Majorie A. Darrah 210 1$aHoboken, New Jersey :$cIEEE Computer Society,$dc2007. 210 2$a[Piscataqay, New Jersey] :$cIEEE Xplore,$d[2015] 215 $a1 PDF (ix, 133 pages) $cillustrations 225 1 $aEmerging technologies 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-470-08457-X 320 $aIncludes bibliographical references (p. 119-121) and index. 327 $aAreas of consideration for adaptive systems -- Verification and validation of neural networks-guidance -- Recent changes to IEEE std 1012. 330 $aGuidance for the Verification and Validation of Neural Networks is a supplement to the IEEE Standard for Software Verification and Validation, IEEE Std 1012-1998. Born out of a need by the National Aeronautics and Space Administration's safety- and mission-critical research, this book compiles over five years of applied research and development efforts. It is intended to assist the performance of verification and validation (V&V) activities on adaptive software systems, with emphasis given to neural network systems. The book discusses some of the difficulties with trying to assure adaptive systems in general, presents techniques and advice for the V&V practitioner confronted with such a task, and based on a neural network case study, identifies specific tasking and recommendations for the V&V of neural network systems. "As the demand for developing and assuring adaptive systems grows, this guidebook will provide practitioners with the insight and practical steps for verifying and validating neural networks. The work of the authors is a great step forward, offering a level of practical experience and advice for the software developers, assurance personnel, and those performing verification and validation of adaptive systems. This guide makes possible the daunting task of assuring this new technology. NASA is proud to sponsor such a realistic approach to what many might think a very futuristic subject. But adaptive systems with neural networks are here today and as the NASA Manager for Software Assurance and Safety, I believe this work by the authors will be a great resource for the systems we are building today and into tomorrow." -Martha S. Wetherholt, NASA Manager of Software Assurance and Software Safety NASA Headquarters, Office of Safety & Mission Assurance. 410 0$aEmerging technologies 606 $aNeural networks (Computer science) 606 $aComputer programs$xValidation 606 $aComputer programs$xVerification 606 $aNeural networks (Computer science)$xValidation 606 $aComputer programs$xVerification 606 $aComputer programs 606 $aEngineering & Applied Sciences$2HILCC 606 $aComputer Science$2HILCC 615 0$aNeural networks (Computer science) 615 0$aComputer programs$xValidation. 615 0$aComputer programs$xVerification. 615 0$aNeural networks (Computer science)$xValidation 615 0$aComputer programs$xVerification 615 0$aComputer programs 615 7$aEngineering & Applied Sciences 615 7$aComputer Science 676 $a006.32 700 $aPullum$b Laura L.$01602727 701 $aTaylor$b Brian J$01345186 701 $aDarrah$b Majorie A$01602728 801 0$bCaBNVSL 801 1$bCaBNVSL 801 2$bCaBNVSL 906 $aBOOK 912 $a9910831173403321 996 $aGuidance for the verification and validation of neural networks$93926772 997 $aUNINA