LEADER 04114nam 2200637Ia 450 001 9910454372203321 005 20200520144314.0 010 $a1-281-95164-1 010 $a9786611951641 010 $a981-281-010-2 035 $a(CKB)1000000000538027 035 $a(EBL)1679404 035 $a(SSID)ssj0000178208 035 $a(PQKBManifestationID)11156230 035 $a(PQKBTitleCode)TC0000178208 035 $a(PQKBWorkID)10221344 035 $a(PQKB)10244395 035 $a(MiAaPQ)EBC1679404 035 $a(WSP)00004691 035 $a(Au-PeEL)EBL1679404 035 $a(CaPaEBR)ebr10255391 035 $a(CaONFJC)MIL195164 035 $a(OCoLC)815754701 035 $a(EXLCZ)991000000000538027 100 $a20010307d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe index theorem and the heat equation method$b[electronic resource] /$fYanlin Yu 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$dc2001 215 $a1 online resource (309 p.) 225 1 $aNankai tracts in mathematics ;$vv. 2 300 $aDescription based upon print version of record. 311 $a981-02-4610-2 320 $aIncludes bibliographical references (p. 279-282) and index. 327 $aPREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation 327 $a2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 327 $a6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX 330 $aThis book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schro?dinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th 410 0$aNankai tracts in mathematics ;$vv. 2. 606 $aAtiyah-Singer index theorem 606 $aHeat equation 608 $aElectronic books. 615 0$aAtiyah-Singer index theorem. 615 0$aHeat equation. 676 $a514.74 700 $aYu$b Yanlin$0880508 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454372203321 996 $aThe index theorem and the heat equation method$91966077 997 $aUNINA LEADER 03613nam 22006254a 450 001 9910830573203321 005 20190813181726.0 010 $a1-280-45054-1 010 $a9786610450541 010 $a0-470-01056-8 010 $a0-470-01055-X 035 $a(CKB)1000000000357456 035 $a(EBL)258946 035 $a(OCoLC)657978312 035 $a(SSID)ssj0000244593 035 $a(PQKBManifestationID)11208841 035 $a(PQKBTitleCode)TC0000244593 035 $a(PQKBWorkID)10170833 035 $a(PQKB)11448429 035 $a(MiAaPQ)EBC258946 035 $a(PPN)162102534 035 $a(EXLCZ)991000000000357456 100 $a20060111d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aSevere dementia /$feditors, Alistair Burns, Bengt Winblad 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cJohn Wiley & Sons$dc2006 215 $a1 online resource (262 p.) 300 $aDescription based upon print version of record. 311 $a0-470-01054-1 320 $aIncludes bibliographical references and index. 327 $aSevere Dementia; Contents; List of Contributors; Introduction; Part 1 Introductory; Chapter 1 Assessment and Diagnosis of Severe Dementia; Chapter 2 Cholinergic and Serotonergic Systems in Severe Dementia; Chapter 3 The Molecular Pathology of Severe Dementia; Part 2 Clinical Features of Severe Dementia; Chapter 4 Cognitive Functions in Severe Dementia; Chapter 5 Behavioural and Psychological Symptoms of Dementia - Agitation; Chapter 6 Depression in Severe Dementia; Chapter 7 Physical Aspects of Severe Alzheimer's Disease; Chapter 8 Clinical Features of Severe Dementia: Staging 327 $aChapter 9 Clinical Features of Severe Dementia: FunctionPart 3 Management; Chapter 10 Drug Treatment: Memantine; Chapter 11 Drug Treatment: Cholinesterase Inhibitors; Chapter 12 Drug Treatment: Treatment of Behavioural and Psychological Symptoms of Dementia with Neuroleptics; Chapter 13 Non-pharmacological Treatment of Severe Dementia: An Overview; Chapter 14 Non-pharmacological Treatment of Severe Dementia:the Seattle Protocols; Chapter 15 Care by Families for Late Stage Dementia; Chapter 16 Person-centred Care for People with Severe Dementia 327 $aChapter 17 Palliative Care in Patients with Severe DementiaChapter 18 Narrative Ethics and Ethical Narratives in Dementia; Chapter 19 Health Economics of Severe Dementia; Index 330 $aThe later stages of dementia are as important, if not more so, as the earlier stages, since they harbour unique characteristics and events, which profoundly affect the lives of patients and their carers. Severe dementia has not had a high profile in the clinical literature as until recently prognosis was poor and there were few beneficial interventions. With the recent licensing of memantine, clinicians finally have a drug option that will delay disease progression. Severe Dementia is the first book to focus exclusively on severe dementia. It addresses both the clinical featur 606 $aDementia 606 $aDementia$xChemotherapy 606 $aDementia$xTreatment 615 0$aDementia. 615 0$aDementia$xChemotherapy. 615 0$aDementia$xTreatment. 676 $a616.83 676 $a616.831061 701 $aBurns$b Alistair S$01701535 701 $aWinblad$b Bengt$01342854 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830573203321 996 $aSevere dementia$94085342 997 $aUNINA