A non-equilibrium statistical mechanics [[electronic resource] ] : without the assumption of molecular chaos / / Tian-Quan Chen |
Autore | Chen Tian-Quan |
Pubbl/distr/stampa | River Edge, N.J., : World Scientific, c2003 |
Descrizione fisica | 1 online resource (xvi, 420 p.) |
Disciplina | 530.13 |
Soggetto topico |
Statistical mechanics
Sturm-Liouville equation |
Soggetto genere / forma | Electronic books. |
ISBN |
1-281-93562-X
9786611935627 981-279-519-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Introduction. 1.1. Historical background. 1.2. Outline of the book -- 2. H-functional. 2.1. Hydrodynamic random fields. 2.2. H-Functional -- 3. H-functional equation. 3.1. Derivation of H-functional equation. 3.2. H-functional equation. 3.3. Balance equations. 3.4. Reformulation -- 4. K-Functional. 4.1. Definition of K-functional -- 5. Some useful formulas. 5.1. Some useful formulas. 5.2. A remark on H-functional equation -- 6. Turbulent Gibbs distributions. 6.1. Asymptotic analysis for Liouville equation. 6.2. Turbulent Gibbs distributions. 6.3. Gibbs mean -- 7. Euler K-functional equation. 7.1. Expressions of B[symbol] and B[symbol]. 7.2. Euler K-functional equation. 7.3. Reformulation. 7.4. Special cases. 7.5. Case of deterministic flows -- 8. Functionals and distributions. 8.1. K-functionals and turbulent Gibbs distributions. 8.2. Turbulent Gibbs measures. 8.3. Asymptotic analysis -- 9. Local stationary Liouville equation. 9.1. Gross determinism. 9.2. Temporal part of material derivative of T[symbol]. 9.3 Spatial part of material derivative of T[symbol]. 9.4. Stationary local Liouville equation -- 10. Second order approximate solutions. 10.1. Case of Reynolds-Gibbs distributions. 10.2. A poly-spherical coordinate system. 10.3. A solution to the equation (10.24)[symbol]. 10.4. A solution to the equation (10.24)[symbol]. 10.5. A solution to the equation (10.24)[symbol]. 10.6. A solution to the equation (10.24)[symbol]. 10.7. A solution to the equation (10.24)[symbol]. 10.8. A solution to the equation (10.24)[symbol]. 10.9. Equipartition of energy -- 11. A finer K-functional equation. 11.1. The expression of B[symbol]. 11.2. The contribution of G[symbol] to B[symbol]. 11.3. The contribution of G[symbol] to B[symbol]. 11.4. The contribution of G[symbol] to B[symbol]. 11.5. The expression of B[symbol]. 11.6. The contribution of G[symbol] to B[symbol]. 11.7. The contribution of G[symbol] to B[symbol]. 11.8. The contribution of G[symbol] to B[symbol]. 11.9. The contribution of G[symbol] to B[symbol]. 11.10. The contribution of G[symbol] to B[symbol]. 11.11. The contribution of G[symbol] to B[symbol]. 11.12. A finer K-functional equation -- 12. Conclusions. 12.1. A view on turbulence. 12.2. Features of the finer K-functional equation. 12.3. Justification of the finer K-functional equation. 12.4. Open problems. |
Record Nr. | UNINA-9910454294703321 |
Chen Tian-Quan | ||
River Edge, N.J., : World Scientific, c2003 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
A non-equilibrium statistical mechanics [[electronic resource] ] : without the assumption of molecular chaos / / Tian-Quan Chen |
Autore | Chen Tian-Quan |
Pubbl/distr/stampa | River Edge, N.J., : World Scientific, c2003 |
Descrizione fisica | 1 online resource (xvi, 420 p.) |
Disciplina | 530.13 |
Soggetto topico |
Statistical mechanics
Sturm-Liouville equation |
ISBN |
1-281-93562-X
9786611935627 981-279-519-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Introduction. 1.1. Historical background. 1.2. Outline of the book -- 2. H-functional. 2.1. Hydrodynamic random fields. 2.2. H-Functional -- 3. H-functional equation. 3.1. Derivation of H-functional equation. 3.2. H-functional equation. 3.3. Balance equations. 3.4. Reformulation -- 4. K-Functional. 4.1. Definition of K-functional -- 5. Some useful formulas. 5.1. Some useful formulas. 5.2. A remark on H-functional equation -- 6. Turbulent Gibbs distributions. 6.1. Asymptotic analysis for Liouville equation. 6.2. Turbulent Gibbs distributions. 6.3. Gibbs mean -- 7. Euler K-functional equation. 7.1. Expressions of B[symbol] and B[symbol]. 7.2. Euler K-functional equation. 7.3. Reformulation. 7.4. Special cases. 7.5. Case of deterministic flows -- 8. Functionals and distributions. 8.1. K-functionals and turbulent Gibbs distributions. 8.2. Turbulent Gibbs measures. 8.3. Asymptotic analysis -- 9. Local stationary Liouville equation. 9.1. Gross determinism. 9.2. Temporal part of material derivative of T[symbol]. 9.3 Spatial part of material derivative of T[symbol]. 9.4. Stationary local Liouville equation -- 10. Second order approximate solutions. 10.1. Case of Reynolds-Gibbs distributions. 10.2. A poly-spherical coordinate system. 10.3. A solution to the equation (10.24)[symbol]. 10.4. A solution to the equation (10.24)[symbol]. 10.5. A solution to the equation (10.24)[symbol]. 10.6. A solution to the equation (10.24)[symbol]. 10.7. A solution to the equation (10.24)[symbol]. 10.8. A solution to the equation (10.24)[symbol]. 10.9. Equipartition of energy -- 11. A finer K-functional equation. 11.1. The expression of B[symbol]. 11.2. The contribution of G[symbol] to B[symbol]. 11.3. The contribution of G[symbol] to B[symbol]. 11.4. The contribution of G[symbol] to B[symbol]. 11.5. The expression of B[symbol]. 11.6. The contribution of G[symbol] to B[symbol]. 11.7. The contribution of G[symbol] to B[symbol]. 11.8. The contribution of G[symbol] to B[symbol]. 11.9. The contribution of G[symbol] to B[symbol]. 11.10. The contribution of G[symbol] to B[symbol]. 11.11. The contribution of G[symbol] to B[symbol]. 11.12. A finer K-functional equation -- 12. Conclusions. 12.1. A view on turbulence. 12.2. Features of the finer K-functional equation. 12.3. Justification of the finer K-functional equation. 12.4. Open problems. |
Record Nr. | UNINA-9910782116003321 |
Chen Tian-Quan | ||
River Edge, N.J., : World Scientific, c2003 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
A non-equilibrium statistical mechanics : without the assumption of molecular chaos / / Tian-Quan Chen |
Autore | Chen Tian-Quan |
Edizione | [1st ed.] |
Pubbl/distr/stampa | River Edge, N.J., : World Scientific, c2003 |
Descrizione fisica | 1 online resource (xvi, 420 p.) |
Disciplina | 530.13 |
Soggetto topico |
Statistical mechanics
Sturm-Liouville equation |
ISBN |
1-281-93562-X
9786611935627 981-279-519-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Introduction. 1.1. Historical background. 1.2. Outline of the book -- 2. H-functional. 2.1. Hydrodynamic random fields. 2.2. H-Functional -- 3. H-functional equation. 3.1. Derivation of H-functional equation. 3.2. H-functional equation. 3.3. Balance equations. 3.4. Reformulation -- 4. K-Functional. 4.1. Definition of K-functional -- 5. Some useful formulas. 5.1. Some useful formulas. 5.2. A remark on H-functional equation -- 6. Turbulent Gibbs distributions. 6.1. Asymptotic analysis for Liouville equation. 6.2. Turbulent Gibbs distributions. 6.3. Gibbs mean -- 7. Euler K-functional equation. 7.1. Expressions of B[symbol] and B[symbol]. 7.2. Euler K-functional equation. 7.3. Reformulation. 7.4. Special cases. 7.5. Case of deterministic flows -- 8. Functionals and distributions. 8.1. K-functionals and turbulent Gibbs distributions. 8.2. Turbulent Gibbs measures. 8.3. Asymptotic analysis -- 9. Local stationary Liouville equation. 9.1. Gross determinism. 9.2. Temporal part of material derivative of T[symbol]. 9.3 Spatial part of material derivative of T[symbol]. 9.4. Stationary local Liouville equation -- 10. Second order approximate solutions. 10.1. Case of Reynolds-Gibbs distributions. 10.2. A poly-spherical coordinate system. 10.3. A solution to the equation (10.24)[symbol]. 10.4. A solution to the equation (10.24)[symbol]. 10.5. A solution to the equation (10.24)[symbol]. 10.6. A solution to the equation (10.24)[symbol]. 10.7. A solution to the equation (10.24)[symbol]. 10.8. A solution to the equation (10.24)[symbol]. 10.9. Equipartition of energy -- 11. A finer K-functional equation. 11.1. The expression of B[symbol]. 11.2. The contribution of G[symbol] to B[symbol]. 11.3. The contribution of G[symbol] to B[symbol]. 11.4. The contribution of G[symbol] to B[symbol]. 11.5. The expression of B[symbol]. 11.6. The contribution of G[symbol] to B[symbol]. 11.7. The contribution of G[symbol] to B[symbol]. 11.8. The contribution of G[symbol] to B[symbol]. 11.9. The contribution of G[symbol] to B[symbol]. 11.10. The contribution of G[symbol] to B[symbol]. 11.11. The contribution of G[symbol] to B[symbol]. 11.12. A finer K-functional equation -- 12. Conclusions. 12.1. A view on turbulence. 12.2. Features of the finer K-functional equation. 12.3. Justification of the finer K-functional equation. 12.4. Open problems. |
Record Nr. | UNINA-9910809092803321 |
Chen Tian-Quan | ||
River Edge, N.J., : World Scientific, c2003 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Recent developments in Sturm-Liouville theory / / Anton Zettl |
Autore | Zettl Anton |
Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter GmbH, , [2021] |
Descrizione fisica | 1 online resource (262 pages) |
Disciplina | 515.35 |
Collana | De Gruyter studies in mathematics |
Soggetto topico | Sturm-Liouville equation |
ISBN |
9783110719000
3110719002 9783110719383 9783110718843 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Introduction -- Contents -- Part I: One-interval problems -- 1 Classical regular self-adjoint problems -- 2 Periodic coefficients -- 3 Extensions of the classical problem -- 4 Finite spectrum -- 5 Inverse Sturm-Liouville problems with finite spectrum -- 6 Eigenvalues below the essential spectrum -- 7 Spectral parameter in the boundary conditions -- Part II: Two-interval problems -- 8 Discontinuous boundary conditions -- 9 The Green's and characteristic functions -- 10 The Legendre equation and its operators -- A Notation -- B Open problems -- Bibliography -- Index |
Record Nr. | UNINA-9910554225603321 |
Zettl Anton | ||
Berlin ; ; Boston : , : Walter de Gruyter GmbH, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
Autore | Jirari Alouf <1965-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
Descrizione fisica | 1 online resource (154 p.) |
Disciplina | 515/.625 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0121-5 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
Record Nr. | UNINA-9910480338603321 |
Jirari Alouf <1965-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
Autore | Jirari Alouf <1965-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
Descrizione fisica | 1 online resource (154 p.) |
Disciplina | 515/.625 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
ISBN | 1-4704-0121-5 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
Record Nr. | UNINA-9910788756103321 |
Jirari Alouf <1965-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
Autore | Jirari Alouf <1965-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
Descrizione fisica | 1 online resource (154 p.) |
Disciplina | 515/.625 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
ISBN | 1-4704-0121-5 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
Record Nr. | UNINA-9910818934103321 |
Jirari Alouf <1965-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Sturm-Liouville theory / Anton Zettl |
Autore | Zettl, Anton |
Pubbl/distr/stampa | Providence, R.I. : American Mathematical Society, 2005 |
Descrizione fisica | xi, 328 p. ; 25 cm |
Disciplina | 515.35 |
Collana | Mathematical surveys and monographs, 0076-5376 ; 121 |
Soggetto topico | Sturm-Liouville equation |
ISBN | 0821839055 |
Classificazione |
AMS 34B20
AMS 34B24 LC QA379.Z48 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991001417219707536 |
Zettl, Anton | ||
Providence, R.I. : American Mathematical Society, 2005 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Theory of a higher order Sturm-Liouville equation / / Vladimir Kozlov, Vladimir Maz'ya |
Autore | Kozlov Vladimir <1954-> |
Edizione | [1st ed. 1997.] |
Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer-Verlag, , [1997] |
Descrizione fisica | 1 online resource (XII, 144 p.) |
Disciplina | 515.35 |
Collana | Lecture Notes in Mathematics |
Soggetto topico | Sturm-Liouville equation |
ISBN | 3-540-69122-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Basic equation with constant coefficients -- The operator M(? t ) on a semiaxis and an interval -- The operator M(? t )??0 with constant ?0 -- Green's function for the operator M(? t )??(t) -- Uniqueness and solvability properties of the operator M(? t ??(t) -- Properties of M(? t ??(t) under various assumptions about ?(t) -- Asymptotics of solutions at infinity -- Application to ordinary differential equations with operator coefficients. |
Record Nr. | UNINA-9910146287403321 |
Kozlov Vladimir <1954-> | ||
Berlin, Heidelberg : , : Springer-Verlag, , [1997] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Theory of a higher order Sturm-Liouville equation / / Vladimir Kozlov, Vladimir Maz'ya |
Autore | Kozlov Vladimir <1954-> |
Edizione | [1st ed. 1997.] |
Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer-Verlag, , [1997] |
Descrizione fisica | 1 online resource (XII, 144 p.) |
Disciplina | 515.35 |
Collana | Lecture Notes in Mathematics |
Soggetto topico | Sturm-Liouville equation |
ISBN | 3-540-69122-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Basic equation with constant coefficients -- The operator M(? t ) on a semiaxis and an interval -- The operator M(? t )??0 with constant ?0 -- Green's function for the operator M(? t )??(t) -- Uniqueness and solvability properties of the operator M(? t ??(t) -- Properties of M(? t ??(t) under various assumptions about ?(t) -- Asymptotics of solutions at infinity -- Application to ordinary differential equations with operator coefficients. |
Record Nr. | UNISA-996466576603316 |
Kozlov Vladimir <1954-> | ||
Berlin, Heidelberg : , : Springer-Verlag, , [1997] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|