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Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors
| Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina | 512/.56 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Differential algebra
Darboux transformations Quantum theory - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-8535-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Preface""; ""Spectral/quadrature duality: Picardâ€?Vessiot theory and finite-gap potentials""; ""1. Introduction""; ""2. Background""; ""3. Integrability of equation (1) by Picardâ€?Vessiot""; ""4. Spectral/quadrature duality. An integration procedure""; ""5. The Î?-functons""; ""6. Integration as a linearly exponential Î?-extension""; ""7. Integrability and differential closedness""; ""8. Definition of through Liouvillian extension""; ""9. Non-finite-gap integrable counterexamples""; ""10. Concluding remarks""; ""References""
""Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty""""1. Introduction""; ""2. A brief outline of supersymmetric quantum mechanics""; ""3. EOP�s associated with broken supersymmetry""; ""4. Relation with higher order Darboux transformation""; ""5. Information-theoretic lengths for the partner potential of linear harmonic oscillator via supersymmetry""; ""6. Moment of the quantum mechanical states associated with the partner of harmonic oscillator via supersymmetry""; ""7. Discussion:""; ""References"" ""On orthogonal polynomials spanning a non-standard flag""""1. Introduction""; ""2. Preliminaries""; ""3. Codimension 1 flags""; ""4. Higher codimension flags""; ""Acknowledgements""; ""References""; ""On the Supersymmetric Spectra of two Planar Integrable Quantum Systems""; ""1. Introduction""; ""2. =2 supersymmetric planar quantum systems""; ""3. The planar quantum Kepler/Coulomb problem and supersymmetry""; ""4. The planar quantum Euler/Coulomb problem and supersymmetry""; ""5. Two center collapse in one center""; ""6. Further comments""; ""Acknowledgements""; ""References"" ""Solvable rational extension of translationally shape invariant potentials""""Introduction""; ""1. Solvable rational extensions of the harmonic oscillator""; ""2. Second category potentials""; ""3. Conclusion""; ""Acknowledgments""; ""References""; ""The pentagram map: geometry, algebra, integrability""; ""1. Introduction: The pentagram map""; ""2. Complete integrability of the pentagram map on the space _{ }""; ""3. Relation to the Boussinesq equation""; ""4. The space _{ } and 2-frieze patterns""; ""Acknowledgments""; ""References""; ""Jet Bundles, symmetries, Darboux transforms"" ""Elliptic beta integrals and solvable models of statistical mechanics"" |
| Record Nr. | UNINA-9910480116703321 |
| Providence, Rhode Island : , : American Mathematical Society | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors
| Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina | 512/.56 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Differential algebra
Darboux transformations Quantum theory - Mathematics |
| ISBN | 0-8218-8535-9 |
| Classificazione | 12H0533E3081Q6081Q8082B2333E99 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials -- 1. Introduction -- 2. Background -- 3. Integrability of equation (1) by Picard-Vessiot -- 4. Spectral/quadrature duality. An integration procedure -- 5. The Î?-functons -- 6. Integration as a linearly exponential Î?-extension -- 7. Integrability and differential closedness -- 8. Definition of through Liouvillian extension -- 9. Non-finite-gap integrable counterexamples -- 10. Concluding remarks -- References -- Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty -- 1. Introduction -- 2. A brief outline of supersymmetric quantum mechanics -- 3. EOP's associated with broken supersymmetry -- 4. Relation with higher order Darboux transformation -- 5. Information-theoretic lengths for the partner potential of linear harmonic oscillator via supersymmetry -- 6. Moment of the quantum mechanical states associated with the partner of harmonic oscillator via supersymmetry -- 7. Discussion: -- References -- On orthogonal polynomials spanning a non-standard flag -- 1. Introduction -- 2. Preliminaries -- 3. Codimension 1 flags -- 4. Higher codimension flags -- Acknowledgements -- References -- On the Supersymmetric Spectra of two Planar Integrable Quantum Systems -- 1. Introduction -- 2. =2 supersymmetric planar quantum systems -- 3. The planar quantum Kepler/Coulomb problem and supersymmetry -- 4. The planar quantum Euler/Coulomb problem and supersymmetry -- 5. Two center collapse in one center -- 6. Further comments -- Acknowledgements -- References -- Solvable rational extension of translationally shape invariant potentials -- Introduction -- 1. Solvable rational extensions of the harmonic oscillator -- 2. Second category potentials -- 3. Conclusion -- Acknowledgments -- References -- The pentagram map: geometry, algebra, integrability -- 1. Introduction: The pentagram map -- 2. Complete integrability of the pentagram map on the space _{ } -- 3. Relation to the Boussinesq equation -- 4. The space _{ } and 2-frieze patterns -- Acknowledgments -- References -- Jet Bundles, symmetries, Darboux transforms -- Elliptic beta integrals and solvable models of statistical mechanics. |
| Record Nr. | UNINA-9910788636203321 |
| Providence, Rhode Island : , : American Mathematical Society | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors
| Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics : Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia / / Primitivo B. Acosta-Humánez [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina | 512/.56 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Differential algebra
Darboux transformations Quantum theory - Mathematics |
| ISBN | 0-8218-8535-9 |
| Classificazione | 12H0533E3081Q6081Q8082B2333E99 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials -- 1. Introduction -- 2. Background -- 3. Integrability of equation (1) by Picard-Vessiot -- 4. Spectral/quadrature duality. An integration procedure -- 5. The Î?-functons -- 6. Integration as a linearly exponential Î?-extension -- 7. Integrability and differential closedness -- 8. Definition of through Liouvillian extension -- 9. Non-finite-gap integrable counterexamples -- 10. Concluding remarks -- References -- Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty -- 1. Introduction -- 2. A brief outline of supersymmetric quantum mechanics -- 3. EOP's associated with broken supersymmetry -- 4. Relation with higher order Darboux transformation -- 5. Information-theoretic lengths for the partner potential of linear harmonic oscillator via supersymmetry -- 6. Moment of the quantum mechanical states associated with the partner of harmonic oscillator via supersymmetry -- 7. Discussion: -- References -- On orthogonal polynomials spanning a non-standard flag -- 1. Introduction -- 2. Preliminaries -- 3. Codimension 1 flags -- 4. Higher codimension flags -- Acknowledgements -- References -- On the Supersymmetric Spectra of two Planar Integrable Quantum Systems -- 1. Introduction -- 2. =2 supersymmetric planar quantum systems -- 3. The planar quantum Kepler/Coulomb problem and supersymmetry -- 4. The planar quantum Euler/Coulomb problem and supersymmetry -- 5. Two center collapse in one center -- 6. Further comments -- Acknowledgements -- References -- Solvable rational extension of translationally shape invariant potentials -- Introduction -- 1. Solvable rational extensions of the harmonic oscillator -- 2. Second category potentials -- 3. Conclusion -- Acknowledgments -- References -- The pentagram map: geometry, algebra, integrability -- 1. Introduction: The pentagram map -- 2. Complete integrability of the pentagram map on the space _{ } -- 3. Relation to the Boussinesq equation -- 4. The space _{ } and 2-frieze patterns -- Acknowledgments -- References -- Jet Bundles, symmetries, Darboux transforms -- Elliptic beta integrals and solvable models of statistical mechanics. |
| Record Nr. | UNINA-9910822597303321 |
| Providence, Rhode Island : , : American Mathematical Society | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910453278503321 |
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910782491403321 |
|
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential-algebraic systems : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910828870603321 |
|
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||