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A non-equilibrium statistical mechanics [[electronic resource] ] : without the assumption of molecular chaos / / Tian-Quan Chen
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
Opac: Controlla la disponibilità qui
A non-equilibrium statistical mechanics [[electronic resource] ] : without the assumption of molecular chaos / / Tian-Quan Chen
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
Opac: Controlla la disponibilità qui
A non-equilibrium statistical mechanics : without the assumption of molecular chaos / / Tian-Quan Chen
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
Opac: Controlla la disponibilità qui
Recent developments in Sturm-Liouville theory / / Anton Zettl
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
Opac: Controlla la disponibilità qui
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
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
Opac: Controlla la disponibilità qui
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
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
Opac: Controlla la disponibilità qui
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
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
Opac: Controlla la disponibilità qui
Sturm-Liouville theory / Anton Zettl
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
Opac: Controlla la disponibilità qui
Theory of a higher order Sturm-Liouville equation / / Vladimir Kozlov, Vladimir Maz'ya
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
Opac: Controlla la disponibilità qui
Theory of a higher order Sturm-Liouville equation / / Vladimir Kozlov, Vladimir Maz'ya
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
Opac: Controlla la disponibilità qui