LEADER 04180nam 2200805 a 450 001 9910958721903321 005 20220310021344.0 010 $a9786613290953 010 $a9781283290951 010 $a1283290952 010 $a9781400840588 010 $a1400840589 024 7 $a10.1515/9781400840588 035 $a(CKB)2670000000122120 035 $a(EBL)784515 035 $a(OCoLC)768165026 035 $a(SSID)ssj0000554343 035 $a(PQKBManifestationID)11392535 035 $a(PQKBTitleCode)TC0000554343 035 $a(PQKBWorkID)10514353 035 $a(PQKB)11109901 035 $a(StDuBDS)EDZ0000406839 035 $a(DE-B1597)447101 035 $a(OCoLC)979968552 035 $a(DE-B1597)9781400840588 035 $a(Au-PeEL)EBL784515 035 $a(CaPaEBR)ebr10503246 035 $a(CaONFJC)MIL329095 035 $z(PPN)199244502 035 $a(PPN)187958394 035 $a(Perlego)735304 035 $a(FR-PaCSA)88838022 035 $a(MiAaPQ)EBC784515 035 $a(FRCYB88838022)88838022 035 $a(EXLCZ)992670000000122120 100 $a20110714d2012 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 14$aThe ambient metric /$fCharles Fefferman, C. Robin Graham 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (124 p.) 225 1 $aAnnals of mathematics studies ;$vno. 178 300 $aDescription based upon print version of record. 311 08$a9780691153131 311 08$a0691153132 311 08$a9780691153148 311 08$a0691153140 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tChapter One. Introduction --$tChapter Two. Ambient Metrics --$tChapter Three. Formal Theory --$tChapter Four. Poincaré Metrics --$tChapter Five. Self-dual Poincaré Metrics --$tChapter Six. Conformal Curvature Tensors --$tChapter Seven. Conformally Flat and Conformally Einstein Spaces --$tChapter Eight. Jet Isomorphism --$tChapter Nine. Scalar Invariants --$tBibliography --$tIndex 330 $aThis book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory. 410 0$aAnnals of mathematics studies ;$vno. 178. 606 $aConformal geometry 606 $aConformal invariants 615 0$aConformal geometry. 615 0$aConformal invariants. 676 $a516.3/7 686 $aMAT012020$2bisacsh 700 $aFefferman$b Charles$f1949-$0476528 701 $aGraham$b C. Robin$f1954-$01799005 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910958721903321 996 $aThe ambient metric$94342083 997 $aUNINA LEADER 05032nam 22007455 450 001 9910254182003321 005 20200630023450.0 010 $a3-319-21623-6 024 7 $a10.1007/978-3-319-21623-2 035 $a(CKB)3710000000467431 035 $a(EBL)4178416 035 $a(SSID)ssj0001546631 035 $a(PQKBManifestationID)16141349 035 $a(PQKBTitleCode)TC0001546631 035 $a(PQKBWorkID)14796087 035 $a(PQKB)11254153 035 $a(DE-He213)978-3-319-21623-2 035 $a(MiAaPQ)EBC4178416 035 $a(PPN)188461442 035 $a(EXLCZ)993710000000467431 100 $a20150828d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced Control of Piezoelectric Micro-/Nano-Positioning Systems /$fby Qingsong Xu, Kok Kiong Tan 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (266 p.) 225 1 $aAdvances in Industrial Control,$x1430-9491 300 $aDescription based upon print version of record. 311 $a3-319-21622-8 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aIntroduction -- Part I Hysteresis Model-Based Feedforward Control -- Feedforward Control Based on an Inverse Hysteresis Model -- Feedforward Control without Modeling Inverse Hysteresis -- Part II Hysteresis-Model-Free, State-Observer-Based Feedback Control -- Model Predictive Discrete-Time Sliding-Mode Control -- Model Predictive Output Integral Discrete-Time Sliding-Mode Control -- Part III Hysteresis-Model-Free, State-Observer-Free Feedback Control -- Digital Sliding-Mode Control of Second-Order Systems -- Digital Sliding-Mode Control of High-Order System -- Digital Sliding-Mode Prediction Control -- Model-Reference Adaptive Control with Perturbation Estimation -- Part IV Applications to Micromanipulation -- Adaptive Impedance Control of Piezoelectric Microgripper -- Position/Force-Switching Control of a Miniature Gripper. Glossary. 330 $aThis book explores emerging methods and algorithms that enable precise control of micro-/nano-positioning systems. The text describes three control strategies: hysteresis-model-based feedforward control and hysteresis-model-free feedback control based on and free from state observation. Each paradigm receives dedicated attention within a particular part of the text. Readers are shown how to design, validate and apply a variety of new control approaches in micromanipulation: hysteresis modelling, discrete-time sliding-mode control and model-reference adaptive control. Experimental results are provided throughout and build up to a detailed treatment of practical applications in the fourth part of the book. The applications focus on control of piezoelectric grippers. Advanced Control of Piezoelectric Micro-/Nano-Positioning Systems will assist academic researchers and practising control and mechatronics engineers interested in suppressing sources of nonlinearity such as hysteresis and drift when combining position and force control of precision systems with piezoelectric actuation. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control. 410 0$aAdvances in Industrial Control,$x1430-9491 606 $aAutomatic control 606 $aNanotechnology 606 $aIndustrial engineering 606 $aProduction engineering 606 $aMechatronics 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aNanotechnology and Microengineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T18000 606 $aIndustrial and Production Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T22008 606 $aMechatronics$3https://scigraph.springernature.com/ontologies/product-market-codes/T19030 615 0$aAutomatic control. 615 0$aNanotechnology. 615 0$aIndustrial engineering. 615 0$aProduction engineering. 615 0$aMechatronics. 615 14$aControl and Systems Theory. 615 24$aNanotechnology and Microengineering. 615 24$aIndustrial and Production Engineering. 615 24$aMechatronics. 676 $a629.8 700 $aXu$b Qingsong$4aut$4http://id.loc.gov/vocabulary/relators/aut$0760809 702 $aTan$b Kok Kiong$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254182003321 996 $aAdvanced Control of Piezoelectric Micro-$94451398 997 $aUNINA