Antieigenvalue analysis [[electronic resource] ] : with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization / / Karl Gustafson |
Autore | Gustafson Karl |
Pubbl/distr/stampa | Singapore, : World Scientific Pub. Co., 2012 |
Descrizione fisica | 1 online resource (259 p.) |
Disciplina | 519 |
Soggetto topico |
Eigenvalues
Mathematical analysis Numerical analysis Wavelets (Mathematics) Statistics Quantum theory |
ISBN |
1-280-66966-7
9786613646590 981-4366-29-3 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
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; Commentary
2.7 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 Schemes 4.6 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 Quotients 6.4 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 Rebalancing 8.5 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; Index |
Record Nr. | UNINA-9910779008403321 |
Gustafson Karl | ||
Singapore, : World Scientific Pub. Co., 2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Antieigenvalue analysis [[electronic resource] ] : with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization / / Karl Gustafson |
Autore | Gustafson Karl |
Edizione | [1st ed.] |
Pubbl/distr/stampa | Singapore, : World Scientific Pub. Co., 2012 |
Descrizione fisica | 1 online resource (259 p.) |
Disciplina | 519 |
Soggetto topico |
Eigenvalues
Mathematical analysis Numerical analysis Wavelets (Mathematics) Statistics Quantum theory |
ISBN |
1-280-66966-7
9786613646590 981-4366-29-3 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
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; Commentary
2.7 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 Schemes 4.6 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 Quotients 6.4 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 Rebalancing 8.5 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; Index |
Record Nr. | UNINA-9910823683803321 |
Gustafson Karl | ||
Singapore, : World Scientific Pub. Co., 2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.] |
Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
Descrizione fisica | 1 online resource (160 p.) |
Disciplina | 530.12 |
Altri autori (Persone) | JacakJanusz |
Soggetto topico |
Electrodynamics
Quantum theory Topology |
Soggetto genere / forma | Electronic books. |
ISBN |
1-299-28107-9
981-4412-03-1 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Acknowledgments; Preface; Contents; 1. Introduction; 2. Elements of Hall system physics in 2D spaces; 2.1 Laughlin function; 2.2 Composite fermions; 2.2.1 Composite fermions in Jain's model; 2.2.2 Composite fermions in Read's model; 2.2.3 Local gauge transformations corresponding to Jain's flux tubes and Read's vortices in the structure of composite fermions; 3. Topological methods for the description of many particle systems at various manifolds; 3.1 Braid groups; 3.1.1 Full braid groups for R3, R2, sphere S2 and torus T; 3.1.2 Pure braid group
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 Bosons, fermions, anyons and composite particles; 3.3.1 Anyons on the plane, sphere and torus; 3.3.2 Quantum statistics and braid groups; 3.4 Multidimensional unitary irreducible representations of braid groups; 4. Cyclotron braids for multi-particle-charged 2D systems in a strong magnetic field; 4.1 Insufficient length of cyclotron radii in 2D systems in a strong magnetic field; 4.2 Definition of the cyclotron braid subgroup and its unitary representations 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 Cyclotron structure of composite fermions; 4.5 The role of the Coulomb interaction; 4.6 Composite fermions in terms of cyclotron groups; 4.7 Hall metal in the description of cyclotron groups; 4.8 Comments on restrictions for the multi-loop structure of cyclotron braids; 4.8.1 Periodic character of wave packets' dynamics; 4.8.2 Quasi-classical character of quantization of the magnetic field flux; 4.9 Cyclotron groups in the case of graphene; 5. Recent progress in FQHE field 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 Development of Hall-type experiment in conventional semiconductor materials; 5.3 Topological insulators-new state of condensed matter; 5.3.1 Chern topological insulators; 5.3.2 Spin-Hall topological insulators; 5.4 Topological states in optical lattices; 6. Summary; 7. Comments and supplements; 7.1 The wave function for a completely filled lowest Landau level; 7.2 Paired Pfaffian states; 7.2.1 Fermi sea instability toward the creation of Cooper pairs in the presence of particle attraction 7.3 Basic definitions in group theory 7.4 Homotopy groups; 7.4.1 Definition of homotopy; 7.4.2 Homotopic transformations; 7.4.3 Properties of homotopy; 7.4.4 Loop homotopy; 7.5 Configuration space; 7.5.1 First homotopy group of configuration space for many particle systems; 7.5.2 Covering space; 7.6 Braid groups for the chosen manifolds; 7.6.1 Braid group for a two-dimensional Euclidean space R2; 7.6.2 Braid group for a sphere S2; 7.6.3 Braid group for a torus T; 7.6.4 The braid group for the three-dimensional Euclidean space R3; 7.6.5 Braid group for a line R1 and a circle S1 7.7 Exact sequences for braid groups |
Record Nr. | UNINA-9910465395803321 |
Singapore, : World Scientific, 2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Application of braid groups in 2D Hall system physics : composite fermion structure / Janusz Jacak ... [et al.] |
Pubbl/distr/stampa | Singapore ; Hackensack, NJ : World Scientific, c2012 |
Descrizione fisica | xi, 147 p. : ill. ; 24 cm |
Disciplina | 533.2 |
Altri autori (Persone) | Jacak, Januszauthor |
Soggetto topico |
Braid theory
Fermions Quantum Hall effect Electrodynamics Quantum theory Topology |
ISBN | 9789814412025 |
Classificazione |
LC QC793.5.F42
53.3.11 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991002102999707536 |
Singapore ; Hackensack, NJ : World Scientific, c2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.] |
Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
Descrizione fisica | 1 online resource (160 p.) |
Disciplina | 530.12 |
Altri autori (Persone) | JacakJanusz |
Soggetto topico |
Electrodynamics
Quantum theory Topology |
ISBN |
1-299-28107-9
981-4412-03-1 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Acknowledgments; Preface; Contents; 1. Introduction; 2. Elements of Hall system physics in 2D spaces; 2.1 Laughlin function; 2.2 Composite fermions; 2.2.1 Composite fermions in Jain's model; 2.2.2 Composite fermions in Read's model; 2.2.3 Local gauge transformations corresponding to Jain's flux tubes and Read's vortices in the structure of composite fermions; 3. Topological methods for the description of many particle systems at various manifolds; 3.1 Braid groups; 3.1.1 Full braid groups for R3, R2, sphere S2 and torus T; 3.1.2 Pure braid group
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 Bosons, fermions, anyons and composite particles; 3.3.1 Anyons on the plane, sphere and torus; 3.3.2 Quantum statistics and braid groups; 3.4 Multidimensional unitary irreducible representations of braid groups; 4. Cyclotron braids for multi-particle-charged 2D systems in a strong magnetic field; 4.1 Insufficient length of cyclotron radii in 2D systems in a strong magnetic field; 4.2 Definition of the cyclotron braid subgroup and its unitary representations 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 Cyclotron structure of composite fermions; 4.5 The role of the Coulomb interaction; 4.6 Composite fermions in terms of cyclotron groups; 4.7 Hall metal in the description of cyclotron groups; 4.8 Comments on restrictions for the multi-loop structure of cyclotron braids; 4.8.1 Periodic character of wave packets' dynamics; 4.8.2 Quasi-classical character of quantization of the magnetic field flux; 4.9 Cyclotron groups in the case of graphene; 5. Recent progress in FQHE field 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 Development of Hall-type experiment in conventional semiconductor materials; 5.3 Topological insulators-new state of condensed matter; 5.3.1 Chern topological insulators; 5.3.2 Spin-Hall topological insulators; 5.4 Topological states in optical lattices; 6. Summary; 7. Comments and supplements; 7.1 The wave function for a completely filled lowest Landau level; 7.2 Paired Pfaffian states; 7.2.1 Fermi sea instability toward the creation of Cooper pairs in the presence of particle attraction 7.3 Basic definitions in group theory 7.4 Homotopy groups; 7.4.1 Definition of homotopy; 7.4.2 Homotopic transformations; 7.4.3 Properties of homotopy; 7.4.4 Loop homotopy; 7.5 Configuration space; 7.5.1 First homotopy group of configuration space for many particle systems; 7.5.2 Covering space; 7.6 Braid groups for the chosen manifolds; 7.6.1 Braid group for a two-dimensional Euclidean space R2; 7.6.2 Braid group for a sphere S2; 7.6.3 Braid group for a torus T; 7.6.4 The braid group for the three-dimensional Euclidean space R3; 7.6.5 Braid group for a line R1 and a circle S1 7.7 Exact sequences for braid groups |
Record Nr. | UNINA-9910792056903321 |
Singapore, : World Scientific, 2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.] |
Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
Descrizione fisica | 1 online resource (160 p.) |
Disciplina | 530.12 |
Altri autori (Persone) | JacakJanusz |
Soggetto topico |
Electrodynamics
Quantum theory Topology |
ISBN |
1-299-28107-9
981-4412-03-1 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Acknowledgments; Preface; Contents; 1. Introduction; 2. Elements of Hall system physics in 2D spaces; 2.1 Laughlin function; 2.2 Composite fermions; 2.2.1 Composite fermions in Jain's model; 2.2.2 Composite fermions in Read's model; 2.2.3 Local gauge transformations corresponding to Jain's flux tubes and Read's vortices in the structure of composite fermions; 3. Topological methods for the description of many particle systems at various manifolds; 3.1 Braid groups; 3.1.1 Full braid groups for R3, R2, sphere S2 and torus T; 3.1.2 Pure braid group
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 Bosons, fermions, anyons and composite particles; 3.3.1 Anyons on the plane, sphere and torus; 3.3.2 Quantum statistics and braid groups; 3.4 Multidimensional unitary irreducible representations of braid groups; 4. Cyclotron braids for multi-particle-charged 2D systems in a strong magnetic field; 4.1 Insufficient length of cyclotron radii in 2D systems in a strong magnetic field; 4.2 Definition of the cyclotron braid subgroup and its unitary representations 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 Cyclotron structure of composite fermions; 4.5 The role of the Coulomb interaction; 4.6 Composite fermions in terms of cyclotron groups; 4.7 Hall metal in the description of cyclotron groups; 4.8 Comments on restrictions for the multi-loop structure of cyclotron braids; 4.8.1 Periodic character of wave packets' dynamics; 4.8.2 Quasi-classical character of quantization of the magnetic field flux; 4.9 Cyclotron groups in the case of graphene; 5. Recent progress in FQHE field 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 Development of Hall-type experiment in conventional semiconductor materials; 5.3 Topological insulators-new state of condensed matter; 5.3.1 Chern topological insulators; 5.3.2 Spin-Hall topological insulators; 5.4 Topological states in optical lattices; 6. Summary; 7. Comments and supplements; 7.1 The wave function for a completely filled lowest Landau level; 7.2 Paired Pfaffian states; 7.2.1 Fermi sea instability toward the creation of Cooper pairs in the presence of particle attraction 7.3 Basic definitions in group theory 7.4 Homotopy groups; 7.4.1 Definition of homotopy; 7.4.2 Homotopic transformations; 7.4.3 Properties of homotopy; 7.4.4 Loop homotopy; 7.5 Configuration space; 7.5.1 First homotopy group of configuration space for many particle systems; 7.5.2 Covering space; 7.6 Braid groups for the chosen manifolds; 7.6.1 Braid group for a two-dimensional Euclidean space R2; 7.6.2 Braid group for a sphere S2; 7.6.3 Braid group for a torus T; 7.6.4 The braid group for the three-dimensional Euclidean space R3; 7.6.5 Braid group for a line R1 and a circle S1 7.7 Exact sequences for braid groups |
Record Nr. | UNINA-9910816078403321 |
Singapore, : World Scientific, 2012 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Application of distributions to the theory of elementary particles in quantum mechanics / Laurent Schwartz |
Autore | Schwartz, Laurent |
Pubbl/distr/stampa | New York : Gordon and Breach Science Publishers, 1968 |
Descrizione fisica | 134 p. ; 24 cm. |
Collana | Documents on modern physics |
Soggetto topico |
Particles (Nuclear physics)
Quantum theory |
Classificazione |
53.3.1
510.46.40 531.16 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991000813999707536 |
Schwartz, Laurent | ||
New York : Gordon and Breach Science Publishers, 1968 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Applied matrix and tensor analysis / by John A. Eisele and Robert M. Mason |
Autore | Eisele, John A. |
Pubbl/distr/stampa | New York : Wiley-Interscience Publ., c1970 |
Descrizione fisica | x, 337 p. : ill. ; 24 cm. |
Disciplina | 512.5 |
Altri autori (Persone) | Mason, Robert M. |
Soggetto topico |
Calculus of tensors
Matrices Quantum theory Relativity |
ISBN | 0471234656 |
Classificazione | AMS 15-00 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991000690519707536 |
Eisele, John A. | ||
New York : Wiley-Interscience Publ., c1970 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Applied quantum mechanics / Walter A. Harrison |
Autore | Harrison, Walter Ashley |
Pubbl/distr/stampa | Singapore ; River Edge, N.J. : World Scientific, c2000 |
Descrizione fisica | xvi, 353 p. : ill. ; 23 cm |
Disciplina | 530.12 |
Soggetto topico | Quantum theory |
ISBN |
9810243758
9810243944 |
Classificazione |
53.1.4
LC QC174.12 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991001884659707536 |
Harrison, Walter Ashley | ||
Singapore ; River Edge, N.J. : World Scientific, c2000 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Arthur E. Haas -- the hidden pioneer of quantum mechanics : a biography / / Michael Wiescher |
Autore | Wiescher Michael |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
Descrizione fisica | 1 online resource (558 pages) |
Disciplina | 530.092 |
Collana | Springer Biographies |
Soggetto topico |
Quantum theory
Physicists Jewish scientists |
ISBN | 3-030-80606-5 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISA-996466845503316 |
Wiescher Michael | ||
Cham, Switzerland : , : Springer, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|