LEADER 03900nam 2200625 450 001 9910480096203321 005 20170822144228.0 010 $a1-4704-0597-0 035 $a(CKB)3360000000465167 035 $a(EBL)3114237 035 $a(SSID)ssj0000973338 035 $a(PQKBManifestationID)11552365 035 $a(PQKBTitleCode)TC0000973338 035 $a(PQKBWorkID)10960287 035 $a(PQKB)10269888 035 $a(MiAaPQ)EBC3114237 035 $a(PPN)195418727 035 $a(EXLCZ)993360000000465167 100 $a20150416h20102010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMetrics of positive scalar curvature and generalised Morse functions$iPart I /$fMark Walsh 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010. 210 4$dİ2010 215 $a1 online resource (80 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 983 300 $a"Volume 209, number 983 (second of 5 numbers)." 311 $a0-8218-5304-X 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background""; ""0.2. Main results""; ""0.3. The connection with generalised Morse functions and Part II""; ""0.4. Acknowledgements""; ""Chapter 1. Definitions and Preliminary Results""; ""1.1. Isotopy and concordance in the space of metrics of positive scalar curvature""; ""1.2. Warped product metrics on the sphere""; ""1.3. Torpedo metrics on the disk""; ""1.4. Doubly warped products and mixed torpedo metrics""; ""1.5. Inducing a mixed torpedo metric with an embedding""; ""Chapter 2. Revisiting the Surgery Theorem"" 327 $a""2.1. Surgery and cobordism""""2.2. Surgery and positive scalar curvature""; ""2.3. Outline of the proof of Theorem 2.3""; ""2.4. Part 1 of the proof: Curvature formulae for the first deformation""; ""2.5. Part 2 of the proof: A continuous bending argument""; ""2.6. Part 3 of the proof: Isotoping to a standard product""; ""2.7. Applying Theorem 2.3 over a compact family of psc-metrics""; ""2.8. The proof of Theorem 2.2 (The Improved Surgery Theorem)""; ""Chapter 3. Constructing Gromov-Lawson Cobordisms""; ""3.1. Morse Theory and admissible Morse functions"" 327 $a""3.2. A reverse Gromov-Lawson cobordism""""3.3. Continuous families of Morse functions""; ""Chapter 4. Constructing Gromov-Lawson Concordances""; ""4.1. Applying the Gromov-Lawson technique over a pair of cancelling surgeries""; ""4.2. Cancelling Morse critical points: The Weak and Strong Cancellation Theorems""; ""4.3. A strengthening of Theorem 4.2""; ""4.4. Standardising the embedding of the second surgery sphere""; ""Chapter 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries""; ""5.1. Connected sums of psc-metrics"" 327 $a""5.2. An analysis of the metric g'', obtained from the second surgery""""5.3. The proof of Theorem 5.1""; ""Chapter 6. Gromov-Lawson Concordance Implies Isotopy in the General Case""; ""6.1. A weaker version of Theorem 0.8""; ""6.2. The proof of the main theorem""; ""Appendix: Curvature Calculations from the Surgery Theorem""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 983. 606 $aCurvature 606 $aMorse theory 606 $aRiemannian manifolds 606 $aAlgebraic topology 608 $aElectronic books. 615 0$aCurvature. 615 0$aMorse theory. 615 0$aRiemannian manifolds. 615 0$aAlgebraic topology. 676 $a516.3/62 700 $aWalsh$b Mark $0894369 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480096203321 996 $aMetrics of positive scalar curvature and generalised Morse functions$91997902 997 $aUNINA LEADER 04096nam 22010213a 450 001 9910367751603321 005 20250203235433.0 010 $a9783038978213 010 $a3038978213 024 8 $a10.3390/books978-3-03897-821-3 035 $a(CKB)4100000010106201 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/53452 035 $a(ScCtBLL)5be3c837-a520-4fcc-90d2-3fb8d1d3205c 035 $a(OCoLC)1163809781 035 $a(oapen)doab53452 035 $a(EXLCZ)994100000010106201 100 $a20250203i20192019 uu 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aMicrowave Indices from Active and Passive Sensors for Remote Sensing Applications$fSimonetta Paloscia, Emanuele Santi 210 $cMDPI - Multidisciplinary Digital Publishing Institute$d2019 210 1$aBasel, Switzerland :$cMDPI,$d2019. 215 $a1 electronic resource (224 p.) 311 08$a9783038978206 311 08$a3038978205 330 $aPast research has comprehensively assessed the capabilities of satellite sensors operating at microwave frequencies, both active (SAR, scatterometers) and passive (radiometers), for the remote sensing of Earth's surface. Besides brightness temperature and backscattering coefficient, microwave indices, defined as a combination of data collected at different frequencies and polarizations, revealed a good sensitivity to hydrological cycle parameters such as surface soil moisture, vegetation water content, and snow depth and its water equivalent. The differences between microwave backscattering and emission at more frequencies and polarizations have been well established in relation to these parameters, enabling operational retrieval algorithms based on microwave indices to be developed. This Special Issue aims at providing an overview of microwave signal capabilities in estimating the main land parameters of the hydrological cycle, e.g., soil moisture, vegetation water content, and snow water equivalent, on both local and global scales, with a particular focus on the applications of microwave indices. 606 $aGeography$2bicssc 610 $atime series analysis 610 $apassive microwave soil moisture 610 $aSentinel-1 and Sentinel-2 610 $aSnow Depth and Snow Water Equivalent 610 $asnow cover characteristics 610 $avegetation biomass 610 $aroughness 610 $asea ice 610 $aSMOS 610 $amicrowave radiometry 610 $asoil moisture downscaling 610 $aVegetation Biomass 610 $avegetation index 610 $aTerra MODIS 610 $aSentinel-1 610 $aMicrowave Indices 610 $asoil moisture content 610 $adual-frequency ratios 610 $aSMAP 610 $apassive microwave 610 $awater-cloud model 610 $asnow 610 $aSentinel-1 backscatter 610 $aAMSR2 610 $adata fusion 610 $amicrowaves 610 $amountain region 610 $aSAR 610 $astart of season 610 $acrops 610 $aNDVI 610 $ascatterometer 610 $aRadarsat-2 610 $apolarization 610 $avegetation water content 610 $aco-pol ratio 610 $aactive microwaves 610 $amicrowave indices 610 $aharvest 610 $aMicrowave Radiometry 610 $asoil moisture 610 $aSoil Moisture Content 610 $asnow correlation length 610 $aradiometer 610 $aradar 610 $asoil scattering 610 $avegetation descriptor 610 $ascale gap 610 $asnow water equivalent 615 7$aGeography 700 $aPaloscia$b Simonetta$01787925 702 $aSanti$b Emanuele 801 0$bScCtBLL 801 1$bScCtBLL 906 $aBOOK 912 $a9910367751603321 996 $aMicrowave Indices from Active and Passive Sensors for Remote Sensing Applications$94322004 997 $aUNINA