05410nam 2200733 a 450 991045209660332120200520144314.01-280-66966-79786613646590981-4366-29-3(CKB)2550000000101468(EBL)919054(OCoLC)794328357(SSID)ssj0000654360(PQKBManifestationID)12216668(PQKBTitleCode)TC0000654360(PQKBWorkID)10661709(PQKB)10744267(MiAaPQ)EBC919054(WSP)00008247(Au-PeEL)EBL919054(CaPaEBR)ebr10563513(CaONFJC)MIL364659(EXLCZ)99255000000010146820120607d2012 uy 0engur|n|---|||||txtccrAntieigenvalue analysis[electronic resource] with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization /Karl GustafsonSingapore World Scientific Pub. Co.20121 online resource (259 p.)Description based upon print version of record.981-4366-28-5 Includes bibliographical references and index.Contents; Preface; 1. Introduction; Perspective; 1.1 A Recent Referee Speaks; 1.2 The Original Motivation; 1.3 The Essential Entities; 1.4 Simple Examples and a Picture; 1.5 Applications to-Date; 1.6 Organization of this Book; Commentary; 1.7 Exercises; 2. The Original Motivation: Operator Semigroups; Perspective; 2.1 Abstract Initial Value Problems; 2.2 The Hille-Yosida-Phillips-Lumer Theorem; 2.3 The Rellich-Kato-Nelson-Gustafson Theorem; 2.4 The Multiplicative Perturbation Theorem; 2.5 When are Positive Operator Products Positive?; 2.6 Nonnegative Contraction Semigroups; Commentary2.7 Exercises3. The Essentials of Antieigenvalue Theory; Perspective; 3.1 Convexity Properties of Norm Geometry; 3.2 The Min-Max Theorem; 3.3 The Euler Equation; 3.4 Higher Antieigenvalues and Antieigenvectors; 3.5 The Triangle Inequality; 3.6 Extended Operator Trigonometry; Commentary; 3.7 Exercises; 4. Applications in Numerical Analysis; Perspective; 4.1 Gradient Descent: Kantorovich Bound is Trigonometric; 4.2 Minimum Residual Ax = b Solvers; 4.3 Richardson Relaxation Schemes (e.g. SOR); 4.4 Very Rich Trigonometry Underlies ADI; 4.5 Domain Decomposition Multilevel Schemes4.6 Preconditioning and Condition NumbersCommentary; 4.7 Exercises; 5. Applications in Wavelets, Control, Scattering; Perspective; 5.1 The Time Operator of Wavelets; 5.2 Frame Operator Trigonometry; 5.3 Wavelet Reconstruction is Trigonometric; 5.4 New Basis Trigonometry; 5.5 Trigonometry of Lyapunov Stability; 5.6 Multiplicative Perturbation and Irreversibility; Commentary; 5.7 Exercises; 6. The Trigonometry of Matrix Statistics; Perspective; 6.1 Statistical Efficiency; 6.2 The Euler Equation versus the Inefficiency Equation; 6.3 Canonical Correlations and Rayleigh Quotients6.4 Other Statistics Inequalities6.5 Prediction Theory: Association Measures; 6.6 Antieigenmatrices; Commentary; 6.7 Exercises; 7. Quantum Trigonometry; Perspective; 7.1 Bell-Wigner-CHSH Inequalities; 7.2 Trigonometric Quantum Spin Identities; 7.3 Quantum Computing: Phase Issues; 7.4 Penrose Twistors; 7.5 Elementary Particles; 7.6 Trigonometry of Quantum States; Commentary; 7.7 Exercises; 8. Financial Instruments; Perspective; 8.1 Some Remarks on Mathematical Finance; 8.2 Quantos: Currency Options; 8.3 Multi-Asset Pricing: Spread Options; 8.4 Portfolio Rebalancing8.5 American Options with Random Volatility8.6 Risk Measures for Incomplete Markets; Commentary; 8.7 Exercises; 9. Other Directions; Perspective; 9.1 Operators; 9.2 Angles; 9.3 Optimization; 9.4 Equalities; 9.5 Geometry; 9.6 Applications; Commentary; 9.7 Exercises; Appendix A Linear Algebra; A.1 Matrix Analysis; A.2 Operator Theory; Appendix B Hints and Answers to Exercises; Chapter 1.; Chapter 2.; Chapter 3.; Chapter 4.; Chapter 5.; Chapter 6.; Chapter 7.; Chapter 8.; Chapter 9.; Bibliography; IndexKarl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.EigenvaluesMathematical analysisNumerical analysisWavelets (Mathematics)StatisticsQuantum theoryElectronic books.Eigenvalues.Mathematical analysis.Numerical analysis.Wavelets (Mathematics)Statistics.Quantum theory.519Gustafson Karl898982MiAaPQMiAaPQMiAaPQBOOK9910452096603321Antieigenvalue analysis2008602UNINA02039nam 2200469z- 450 991055777200332120231214133337.0(CKB)5400000000045640(oapen)https://directory.doabooks.org/handle/20.500.12854/74146(EXLCZ)99540000000004564020202111d2020 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierNeuro-Immune Connections to Enable Repair in CNS DisordersFrontiers Media SA20201 electronic resource (243 p.)2-88966-007-9 This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contactMedicinebicsscImmunologybicsscneuroimmunologycentral nervous systemimmune systemCNS repairCNS disordersMedicineImmunologyVanmierlo Timedt1293841Broux BiekeedtVan Horssen JackedtHellings NielsedtVanmierlo TimothBroux BiekeothVan Horssen JackothHellings NielsothBOOK9910557772003321Neuro-Immune Connections to Enable Repair in CNS Disorders3022771UNINA