Soliton equations and Hamiltonian systems [[electronic resource] /] / L.A. Dickey |
Autore | Dickey Leonid A |
Edizione | [2nd ed.] |
Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
Descrizione fisica | 1 online resource (421 p.) |
Disciplina | 530.12/4 |
Collana | Advanced series in mathematical physics |
Soggetto topico |
Solitons
Hamiltonian systems |
ISBN |
1-281-93445-3
9786611934453 981-279-451-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Contents ; Preface to the Second Edition ; Introduction to the First Edition ; Chapter 1 Integrable Systems Generated by Linear Differential nth Order Operators ; 1.1 Differential Algebra A ; 1.2 Space of Functionals A ; 1.3 Ring of Pseudodifferential Operators
1.4 Lax Pairs. GD Hierarchies of Equations 1.5 First Integrals (Constants of Motion) ; 1.6 Compatibility of the Equations of a Hierarchy ; 1.7 Soliton Solutions ; 1.8 Resolvent. Adler Mapping ; Chapter 2 Hamiltonian Structures ; 2.1 Finite-Dimensional Case ; 2.2 Hamilton Mapping 2.3 Variational Principles 2.4 Symplectic Form on an Orbit of the Coadjoint Representation of a Lie Group ; 2.5 Purely Algebraic Treatment of the Hamiltonian Structure ; 2.6 Examples ; Chapter 3 Hamiltonian Structure of the GD Hierarchies ; 3.1 Lie Algebra V Dual Space Q1 and Module Q0 3.2 Proof of Theorem 3.1.2 3.3 Poisson Bracket ; 3.4 Reduction to the Submanifold Un-1 = 0 ; 3.5 Variational Derivative of the Resolvent ; 3.6 Hamiltonians of the GD Hierarchies ; 3.7 Theory of the KdV-Hierarchy (n = 2) Independent of the General Case Chapter 4 Modified KdV and GD. The Kupershmidt-Wilson Theorem 4 1 Miura Transformation. The Kupershmidt-Wilson Theorem ; 4.2 Modified KdV Equation. Backlund Transformations ; 4.3 More on Modified GD Equations ; Chapter 5 The KP Hierarchy ; 5.1 Definition of the KP Hierarchy 5.2 Reduction of the KP Hierarchy to GD |
Record Nr. | UNINA-9910782287503321 |
Dickey Leonid A
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River Edge, NJ, : World Scientific, c2003 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Soliton equations and Hamiltonian systems / / L.A. Dickey |
Autore | Dickey Leonid A |
Edizione | [2nd ed.] |
Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
Descrizione fisica | 1 online resource (421 p.) |
Disciplina | 530.12/4 |
Collana | Advanced series in mathematical physics |
Soggetto topico |
Solitons
Hamiltonian systems |
ISBN |
1-281-93445-3
9786611934453 981-279-451-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Contents ; Preface to the Second Edition ; Introduction to the First Edition ; Chapter 1 Integrable Systems Generated by Linear Differential nth Order Operators ; 1.1 Differential Algebra A ; 1.2 Space of Functionals A ; 1.3 Ring of Pseudodifferential Operators
1.4 Lax Pairs. GD Hierarchies of Equations 1.5 First Integrals (Constants of Motion) ; 1.6 Compatibility of the Equations of a Hierarchy ; 1.7 Soliton Solutions ; 1.8 Resolvent. Adler Mapping ; Chapter 2 Hamiltonian Structures ; 2.1 Finite-Dimensional Case ; 2.2 Hamilton Mapping 2.3 Variational Principles 2.4 Symplectic Form on an Orbit of the Coadjoint Representation of a Lie Group ; 2.5 Purely Algebraic Treatment of the Hamiltonian Structure ; 2.6 Examples ; Chapter 3 Hamiltonian Structure of the GD Hierarchies ; 3.1 Lie Algebra V Dual Space Q1 and Module Q0 3.2 Proof of Theorem 3.1.2 3.3 Poisson Bracket ; 3.4 Reduction to the Submanifold Un-1 = 0 ; 3.5 Variational Derivative of the Resolvent ; 3.6 Hamiltonians of the GD Hierarchies ; 3.7 Theory of the KdV-Hierarchy (n = 2) Independent of the General Case Chapter 4 Modified KdV and GD. The Kupershmidt-Wilson Theorem 4 1 Miura Transformation. The Kupershmidt-Wilson Theorem ; 4.2 Modified KdV Equation. Backlund Transformations ; 4.3 More on Modified GD Equations ; Chapter 5 The KP Hierarchy ; 5.1 Definition of the KP Hierarchy 5.2 Reduction of the KP Hierarchy to GD |
Record Nr. | UNINA-9910813735703321 |
Dickey Leonid A
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||
River Edge, NJ, : World Scientific, c2003 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
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Solitons / / Boling Guo [and three others] |
Autore | Guo Boling |
Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] |
Descrizione fisica | 1 online resource (376 pages) |
Disciplina | 530.12/4 |
Soggetto topico |
Solitons
Wave-motion, Theory of |
Soggetto genere / forma | Electronic books. |
ISBN |
3-11-054941-7
3-11-054963-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Contents -- 1. Introduction -- 2. Inverse scattering transform -- 3. Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations -- 4. Interaction of solitons and its asymptotic properties -- 5. Hirota method -- 6. Bäcklund transformations and the infinitely many conservation laws -- 7. Multi-dimensional solitons and their stability -- 8. Numerical computation methods for some nonlinear evolution equations -- 9. The geometric theory of solitons -- 10. Global existence and blow up for the nonlinear evolution equations -- 11. The soliton movements of elementary particles in nonlinear quantum field -- 12. The theory of soliton movement of superconductive features -- 13. The soliton movements in condensed state systems -- Bibliography |
Record Nr. | UNINA-9910467342203321 |
Guo Boling
![]() |
||
Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Solitons / / Boling Guo [and three others] |
Autore | Guo Boling |
Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] |
Descrizione fisica | 1 online resource (376 pages) |
Disciplina | 530.12/4 |
Soggetto topico |
Solitons
Wave-motion, Theory of |
ISBN |
3-11-054941-7
3-11-054963-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Contents -- 1. Introduction -- 2. Inverse scattering transform -- 3. Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations -- 4. Interaction of solitons and its asymptotic properties -- 5. Hirota method -- 6. Bäcklund transformations and the infinitely many conservation laws -- 7. Multi-dimensional solitons and their stability -- 8. Numerical computation methods for some nonlinear evolution equations -- 9. The geometric theory of solitons -- 10. Global existence and blow up for the nonlinear evolution equations -- 11. The soliton movements of elementary particles in nonlinear quantum field -- 12. The theory of soliton movement of superconductive features -- 13. The soliton movements in condensed state systems -- Bibliography |
Record Nr. | UNINA-9910796899103321 |
Guo Boling
![]() |
||
Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Solitons / / Boling Guo [and three others] |
Autore | Guo Boling |
Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] |
Descrizione fisica | 1 online resource (376 pages) |
Disciplina | 530.12/4 |
Soggetto topico |
Solitons
Wave-motion, Theory of |
ISBN |
3-11-054941-7
3-11-054963-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Contents -- 1. Introduction -- 2. Inverse scattering transform -- 3. Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations -- 4. Interaction of solitons and its asymptotic properties -- 5. Hirota method -- 6. Bäcklund transformations and the infinitely many conservation laws -- 7. Multi-dimensional solitons and their stability -- 8. Numerical computation methods for some nonlinear evolution equations -- 9. The geometric theory of solitons -- 10. Global existence and blow up for the nonlinear evolution equations -- 11. The soliton movements of elementary particles in nonlinear quantum field -- 12. The theory of soliton movement of superconductive features -- 13. The soliton movements in condensed state systems -- Bibliography |
Record Nr. | UNINA-9910824716803321 |
Guo Boling
![]() |
||
Berlin ; ; Boston : , : Walter de Gruyter, GmbH, , [2018] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Solving the Schrödinger equation [[electronic resource] ] : has everything been tried? / / editor, Paul Popelier |
Pubbl/distr/stampa | London, : Imperial College Press, c2011 |
Descrizione fisica | 1 online resource (375 p.) |
Disciplina | 530.12/4 |
Altri autori (Persone) | PopelierPaul L. A |
Soggetto topico |
Schrödinger equation
Wave functions Wave mechanics |
Soggetto genere / forma | Electronic books. |
ISBN |
1-283-43320-6
9786613433206 1-84816-725-3 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Contents; Bibliography; Preface; 1. Intracule Functional Theory Deborah L. Crittenden and Peter M.W. Gill; 1.1 Introduction; 1.2 Intracules; 1.3 Electron Correlation Models; 1.4 Dynamic and Static Correlation; 1.5 Dispersion Energies; 1.6 Future Prospects; Bibliography; 2. Explicitly Correlated Electronic Structure Theory Frederick R. Manby; 2.1 Introduction; 2.1.1 Basis-set expansions; 2.2 F12 Theory; 2.2.1 MP2-F12; 2.2.2 Explicitly correlated coupled-cluster theory; 2.3 Five Thoughts for F12 Theory; 2.3.1 Thought 1: Do we need (products of) virtuals?
2.3.2 Thought 2: Are there better two-electron basis sets?2.3.3 Thought 3: Do we need the resolution of the identity?; 2.3.4 Thought 4: Could we have explicit correlation for higher excitations?; 2.3.5 Thought 5: Can we avoid three-electron errors in two-electron systems?; 2.4 Conclusions; Acknowledgments; Bibliography; 3. Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG) Garnet Kin-Lic Chan and Sandeep Sharma; 3.1 The Problem of Strong Correlation; 3.2 The Density Matrix Renormalization Group Wavefunction; 3.3 Locality and Entanglement in the DMRG 3.4 Other Properties of the DMRG3.5 Relation to the Renormalization Group; 3.6 Dynamic Correlation - the Role of Canonical Transformations; 3.7 What Can the DMRG Do? A Brief History; 3.8 The Future: Higher Dimensional Analogues; Bibliography; 4. Reduced-Density-Matrix Theory for Many-electron Correlation David A. Mazziotti; 4.1 Introduction; 4.2 Variational 2-RDM Method; 4.2.1 Energy as a 2-RDM functional; 4.2.2 Positivity conditions; 4.2.2.1. Two-positivity; 4.2.2.2. Three-positivity; 4.2.3 Semidefinite programming; 4.2.4 Applications; 4.2.4.1. Dissociation of the N molecule 4.2.4.2. Metal to insulator transition in the H lattice4.2.4.3. Polyradical character of the acene chains; 4.3 Contracted Schr dinger Theory; 4.3.1 ACSE and cumulant reconstruction; 4.3.2 Solving the ACSE for ground and excited states; 4.3.3 Applications; 4.3.3.1. Energy barriers of bicyclobutane's transition states; 4.3.3.2. Conical intersections in CH 's triplet excited states; 4.4 Parametric 2-RDM Method; 4.4.1 Parametrization of the 2-RDM; 4.4.2 Applications; 4.4.2.1. Correlation energies at equilibrium geometries; 4.4.2.2. Dissociation of the HF molecule 4.4.2.3. Isomerization of nitrosomethane4.5 Looking Ahead; Acknowledgments; 5. Finite Size Scaling for Criticality of the Schr dinger Equation Sabre Kais; 5.1 Introduction; 5.2 Criticality for Large-dimensional Models; 5.3 Finite Size Scaling: A Brief History; 5.4 Finite Size Scaling for the Schr dinger Equation; 5.5 The Hulthen Potential; 5.5.1 Analytical solution; 5.5.2 Basis set expansion; 5.5.3 Finite element method; 5.5.4 Finite size scaling results; 5.6 Finite Size Scaling and Criticality of M-electron Atoms; 5.7 Conclusions; Acknowledgments; Bibliography 6. The Generalized Sturmian Method James Avery and John Avery |
Record Nr. | UNINA-9910457162103321 |
London, : Imperial College Press, c2011 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Solving the Schrödinger equation [[electronic resource] ] : has everything been tried? / / editor, Paul Popelier |
Pubbl/distr/stampa | London, : Imperial College Press, c2011 |
Descrizione fisica | 1 online resource (375 p.) |
Disciplina | 530.12/4 |
Altri autori (Persone) | PopelierPaul L. A |
Soggetto topico |
Schrödinger equation
Wave functions Wave mechanics |
ISBN |
1-283-43320-6
9786613433206 1-84816-725-3 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Contents; Bibliography; Preface; 1. Intracule Functional Theory Deborah L. Crittenden and Peter M.W. Gill; 1.1 Introduction; 1.2 Intracules; 1.3 Electron Correlation Models; 1.4 Dynamic and Static Correlation; 1.5 Dispersion Energies; 1.6 Future Prospects; Bibliography; 2. Explicitly Correlated Electronic Structure Theory Frederick R. Manby; 2.1 Introduction; 2.1.1 Basis-set expansions; 2.2 F12 Theory; 2.2.1 MP2-F12; 2.2.2 Explicitly correlated coupled-cluster theory; 2.3 Five Thoughts for F12 Theory; 2.3.1 Thought 1: Do we need (products of) virtuals?
2.3.2 Thought 2: Are there better two-electron basis sets?2.3.3 Thought 3: Do we need the resolution of the identity?; 2.3.4 Thought 4: Could we have explicit correlation for higher excitations?; 2.3.5 Thought 5: Can we avoid three-electron errors in two-electron systems?; 2.4 Conclusions; Acknowledgments; Bibliography; 3. Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG) Garnet Kin-Lic Chan and Sandeep Sharma; 3.1 The Problem of Strong Correlation; 3.2 The Density Matrix Renormalization Group Wavefunction; 3.3 Locality and Entanglement in the DMRG 3.4 Other Properties of the DMRG3.5 Relation to the Renormalization Group; 3.6 Dynamic Correlation - the Role of Canonical Transformations; 3.7 What Can the DMRG Do? A Brief History; 3.8 The Future: Higher Dimensional Analogues; Bibliography; 4. Reduced-Density-Matrix Theory for Many-electron Correlation David A. Mazziotti; 4.1 Introduction; 4.2 Variational 2-RDM Method; 4.2.1 Energy as a 2-RDM functional; 4.2.2 Positivity conditions; 4.2.2.1. Two-positivity; 4.2.2.2. Three-positivity; 4.2.3 Semidefinite programming; 4.2.4 Applications; 4.2.4.1. Dissociation of the N molecule 4.2.4.2. Metal to insulator transition in the H lattice4.2.4.3. Polyradical character of the acene chains; 4.3 Contracted Schr dinger Theory; 4.3.1 ACSE and cumulant reconstruction; 4.3.2 Solving the ACSE for ground and excited states; 4.3.3 Applications; 4.3.3.1. Energy barriers of bicyclobutane's transition states; 4.3.3.2. Conical intersections in CH 's triplet excited states; 4.4 Parametric 2-RDM Method; 4.4.1 Parametrization of the 2-RDM; 4.4.2 Applications; 4.4.2.1. Correlation energies at equilibrium geometries; 4.4.2.2. Dissociation of the HF molecule 4.4.2.3. Isomerization of nitrosomethane4.5 Looking Ahead; Acknowledgments; 5. Finite Size Scaling for Criticality of the Schr dinger Equation Sabre Kais; 5.1 Introduction; 5.2 Criticality for Large-dimensional Models; 5.3 Finite Size Scaling: A Brief History; 5.4 Finite Size Scaling for the Schr dinger Equation; 5.5 The Hulthen Potential; 5.5.1 Analytical solution; 5.5.2 Basis set expansion; 5.5.3 Finite element method; 5.5.4 Finite size scaling results; 5.6 Finite Size Scaling and Criticality of M-electron Atoms; 5.7 Conclusions; Acknowledgments; Bibliography 6. The Generalized Sturmian Method James Avery and John Avery |
Record Nr. | UNINA-9910778827903321 |
London, : Imperial College Press, c2011 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Solving the Schrödinger equation : has everything been tried? / / editor, Paul Popelier |
Edizione | [1st ed.] |
Pubbl/distr/stampa | London, : Imperial College Press, c2011 |
Descrizione fisica | 1 online resource (375 p.) |
Disciplina | 530.12/4 |
Altri autori (Persone) | PopelierPaul L. A |
Soggetto topico |
Schrödinger equation
Wave functions Wave mechanics |
ISBN |
1-283-43320-6
9786613433206 1-84816-725-3 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Contents; Bibliography; Preface; 1. Intracule Functional Theory Deborah L. Crittenden and Peter M.W. Gill; 1.1 Introduction; 1.2 Intracules; 1.3 Electron Correlation Models; 1.4 Dynamic and Static Correlation; 1.5 Dispersion Energies; 1.6 Future Prospects; Bibliography; 2. Explicitly Correlated Electronic Structure Theory Frederick R. Manby; 2.1 Introduction; 2.1.1 Basis-set expansions; 2.2 F12 Theory; 2.2.1 MP2-F12; 2.2.2 Explicitly correlated coupled-cluster theory; 2.3 Five Thoughts for F12 Theory; 2.3.1 Thought 1: Do we need (products of) virtuals?
2.3.2 Thought 2: Are there better two-electron basis sets?2.3.3 Thought 3: Do we need the resolution of the identity?; 2.3.4 Thought 4: Could we have explicit correlation for higher excitations?; 2.3.5 Thought 5: Can we avoid three-electron errors in two-electron systems?; 2.4 Conclusions; Acknowledgments; Bibliography; 3. Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG) Garnet Kin-Lic Chan and Sandeep Sharma; 3.1 The Problem of Strong Correlation; 3.2 The Density Matrix Renormalization Group Wavefunction; 3.3 Locality and Entanglement in the DMRG 3.4 Other Properties of the DMRG3.5 Relation to the Renormalization Group; 3.6 Dynamic Correlation - the Role of Canonical Transformations; 3.7 What Can the DMRG Do? A Brief History; 3.8 The Future: Higher Dimensional Analogues; Bibliography; 4. Reduced-Density-Matrix Theory for Many-electron Correlation David A. Mazziotti; 4.1 Introduction; 4.2 Variational 2-RDM Method; 4.2.1 Energy as a 2-RDM functional; 4.2.2 Positivity conditions; 4.2.2.1. Two-positivity; 4.2.2.2. Three-positivity; 4.2.3 Semidefinite programming; 4.2.4 Applications; 4.2.4.1. Dissociation of the N molecule 4.2.4.2. Metal to insulator transition in the H lattice4.2.4.3. Polyradical character of the acene chains; 4.3 Contracted Schr dinger Theory; 4.3.1 ACSE and cumulant reconstruction; 4.3.2 Solving the ACSE for ground and excited states; 4.3.3 Applications; 4.3.3.1. Energy barriers of bicyclobutane's transition states; 4.3.3.2. Conical intersections in CH 's triplet excited states; 4.4 Parametric 2-RDM Method; 4.4.1 Parametrization of the 2-RDM; 4.4.2 Applications; 4.4.2.1. Correlation energies at equilibrium geometries; 4.4.2.2. Dissociation of the HF molecule 4.4.2.3. Isomerization of nitrosomethane4.5 Looking Ahead; Acknowledgments; 5. Finite Size Scaling for Criticality of the Schr dinger Equation Sabre Kais; 5.1 Introduction; 5.2 Criticality for Large-dimensional Models; 5.3 Finite Size Scaling: A Brief History; 5.4 Finite Size Scaling for the Schr dinger Equation; 5.5 The Hulthen Potential; 5.5.1 Analytical solution; 5.5.2 Basis set expansion; 5.5.3 Finite element method; 5.5.4 Finite size scaling results; 5.6 Finite Size Scaling and Criticality of M-electron Atoms; 5.7 Conclusions; Acknowledgments; Bibliography 6. The Generalized Sturmian Method James Avery and John Avery |
Record Nr. | UNINA-9910813877403321 |
London, : Imperial College Press, c2011 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Stability of KAM tori for nonlinear Schrödinger equation / / Hongzi Cong, Jianjun Liu, Xiaoping Yuan |
Autore | Cong Hongzi <1982-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2015] |
Descrizione fisica | 1 online resource (100 pages) |
Disciplina | 530.12/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Gross-Pitaevskii equations
Nonlinear wave equations Perturbation (Mathematics) |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-2751-6 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNINA-9910480924903321 |
Cong Hongzi <1982->
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [2015] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Stability of KAM tori for nonlinear Schrödinger equation / / Hongzi Cong, Jianjun Liu, Xiaoping Yuan |
Autore | Cong Hongzi <1982-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2015] |
Descrizione fisica | 1 online resource (100 pages) |
Disciplina | 530.12/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Gross-Pitaevskii equations
Nonlinear wave equations Perturbation (Mathematics) |
ISBN | 1-4704-2751-6 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNINA-9910796559303321 |
Cong Hongzi <1982->
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , [2015] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|