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General relativistic self-similar waves that induce an anomalous acceleration into the standard model of cosmology / / Joel Smoller, Blake Temple
| General relativistic self-similar waves that induce an anomalous acceleration into the standard model of cosmology / / Joel Smoller, Blake Temple |
| Autore | Smoller Joel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (69 p.) |
| Disciplina | 531/.1133 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Einstein field equations
Shock waves - Mathematical models Relativistic quantum theory General relativity (Physics) |
| ISBN | 0-8218-9012-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. Self-Similar Coordinates for the k=0 FRW Spacetime""; ""Chapter 3. The Expanding Wave Equations""; ""Chapter 4. Canonical Co-moving Coordinates and Comparison with the k=0 FRW Spacetimes""; ""Chapter 5. Leading Order Corrections to the Standard Model Induced by the Expanding Waves""; ""Chapter 6. A Foliation of the Expanding Wave Spacetimes into Flat Spacelike Hypersurfaces with Modified Scale Factor R(t)=ta.""; ""Chapter 7. Expanding Wave Corrections to the Standard Model in Approximate Co-moving Coordinates""
""Chapter 8. Redshift vs Luminosity Relations and the Anomalous Acceleration""""Chapter 9. Appendix: The Mirror Problem""; ""Chapter 10. Concluding Remarks""; ""Bibliography"" |
| Record Nr. | UNINA-9910812544403321 |
Smoller Joel
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| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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General relativity and the Einstein equations [[electronic resource] /] / Yvonne Choquet-Bruhat
| General relativity and the Einstein equations [[electronic resource] /] / Yvonne Choquet-Bruhat |
| Autore | Choquet-Bruhat Yvonne |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2009 |
| Descrizione fisica | 1 online resource (812 p.) |
| Disciplina | 530.11 |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
General relativity (Physics) - Mathematics
Einstein field equations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-99870-2
9786611998707 0-19-155226-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; I: Lorentz geometry; 1 Introduction; 2 Manifolds; 3 Differentiable mappings; 4 Vectors and tensors; 4.1 Tangent and cotangent space; 4.2 Vector fields; 4.3 Tensors and tensor fields; 5 Pseudo-Riemannian metrics; 5.1 General properties; 5.2 Riemannian and Lorentzian metrics; 6 Riemannian connection; 7 Geodesics; 8 Curvature; 9 Geodesic deviation; 10 Maximum of length and conjugate points; 11 Linearized Ricci and Einstein tensors; 12 Second derivative of the Ricci tensor; II: Special Relativity; 1 Newton's mechanics; 1.1 The Galileo-Newton spacetime
1.2 Newton's dynamics - the Galileo group2 Maxwell's equations; 3 Minkowski spacetime; 3.1 Definition; 3.2 Maxwell's equations on M[sub(4)]; 4 Poincaré group; 5 Lorentz group; 5.1 General formulae; 5.2 Transformation of electric and magnetic vector fields (case n = 3); 5.3 Lorentz contraction and dilatation; 6 Special Relativity; 6.1 Proper time; 6.2 Proper frame and relative velocities; 7 Dynamics of a pointlike mass; 7.1 Newtonian law; 7.2 Relativistic law; 7.3 Equivalence of mass and energy; 8 Continuous matter; 8.1 Case of dust (incoherent matter); 8.2 Perfect fluids III: General relativity and Einstein's equations1 Introduction; 2 Newton's gravity law; 3 General relativity; 3.1 Physical motivations; 4 Observations and experiments; 4.1 Deviation of light rays; 4.2 Proper time, gravitational time delay; 5 Einstein's equations; 5.1 Vacuum case; 5.2 Equations with sources; 6 Field sources; 6.1 Electromagnetic sources; 6.2 Electromagnetic potential; 6.3 Yang-Mills fields; 6.4 Scalar fields; 6.5 Wave maps; 6.6 Energy conditions; 7 Lagrangians; 7.1 Einstein-Hilbert Lagrangian; 7.2 Lagrangians and stress energy tensors of sources; 7.3 Coupled Lagrangian 8 Fluid sources9 Einsteinian spacetimes; 9.1 Definition; 9.2 Regularity hypotheses; 10 Newtonian approximation; 10.1 Equations for potentials; 10.2 Equations of motion; 11 Gravitational waves; 11.1 Minkowskian approximation; 11.2 General linear waves; 12 High-frequency gravitational waves; 12.1 Phase and polarizations; 12.2 Radiative coordinates; 12.3 Energy conservation; 13 Coupled electromagnetic and gravitational waves; 13.1 Phase and polarizations; 13.2 Propagation equations; IV: Schwarzschild spacetime and black holes; 1 Introduction; 2 Spherically symmetric spacetimes 3 Schwarzschild metric4 Other coordinates; 4.1 Isotropic coordinates; 4.2 Wave coordinates; 4.3 Painlevé-Gullstrand-like coordinates; 4.4 Regge-Wheeler coordinates; 5 Schwarzschild spacetime; 6 The motion of the planets and perihelion precession; 6.1 Equations; 6.2 Results of observations; 6.3 Escape velocity; 7 Stability of circular orbits; 8 Deflection of light rays; 8.1 Theoretical prediction; 8.2 Results of observation; 8.3 Fermat's principle and light travel parameter time; 9 Red shift and time delay; 10 Spherically symmetric interior solutions; 10.1 Static solutions. Upper limit on mass 10.2 Matching with an exterior solution |
| Record Nr. | UNINA-9910465797503321 |
|
Choquet-Bruhat Yvonne
|
||
| Oxford ; ; New York, : Oxford University Press, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
General relativity and the Einstein equations [[electronic resource] /] / Yvonne Choquet-Bruhat
| General relativity and the Einstein equations [[electronic resource] /] / Yvonne Choquet-Bruhat |
| Autore | Choquet-Bruhat Yvonne |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2009 |
| Descrizione fisica | xxiv, 785 p. : ill |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
General relativity (Physics) - Mathematics
Einstein field equations |
| ISBN |
9780191552267
0191552267 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795716303321 |
|
Choquet-Bruhat Yvonne
|
||
| Oxford ; ; New York, : Oxford University Press, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
General relativity and the Einstein equations / / Yvonne Choquet-Bruhat
| General relativity and the Einstein equations / / Yvonne Choquet-Bruhat |
| Autore | Choquet-Bruhat Yvonne |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2009 |
| Descrizione fisica | xxiv, 785 p. : ill |
| Disciplina | 530.11 |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
General relativity (Physics) - Mathematics
Einstein field equations |
| ISBN |
9780191552267
0191552267 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- CONTENTS -- I: Lorentz geometry -- 1 Introduction -- 2 Manifolds -- 3 Differentiable mappings -- 4 Vectors and tensors -- 4.1 Tangent and cotangent space -- 4.2 Vector fields -- 4.3 Tensors and tensor fields -- 5 Pseudo-Riemannian metrics -- 5.1 General properties -- 5.2 Riemannian and Lorentzian metrics -- 6 Riemannian connection -- 7 Geodesics -- 8 Curvature -- 9 Geodesic deviation -- 10 Maximum of length and conjugate points -- 11 Linearized Ricci and Einstein tensors -- 12 Second derivative of the Ricci tensor -- II: Special Relativity -- 1 Newton's mechanics -- 1.1 The Galileo-Newton spacetime -- 1.2 Newton's dynamics - the Galileo group -- 2 Maxwell's equations -- 3 Minkowski spacetime -- 3.1 Definition -- 3.2 Maxwell's equations on M[sub(4)] -- 4 Poincaré group -- 5 Lorentz group -- 5.1 General formulae -- 5.2 Transformation of electric and magnetic vector fields (case n = 3) -- 5.3 Lorentz contraction and dilatation -- 6 Special Relativity -- 6.1 Proper time -- 6.2 Proper frame and relative velocities -- 7 Dynamics of a pointlike mass -- 7.1 Newtonian law -- 7.2 Relativistic law -- 7.3 Equivalence of mass and energy -- 8 Continuous matter -- 8.1 Case of dust (incoherent matter) -- 8.2 Perfect fluids -- III: General relativity and Einstein's equations -- 1 Introduction -- 2 Newton's gravity law -- 3 General relativity -- 3.1 Physical motivations -- 4 Observations and experiments -- 4.1 Deviation of light rays -- 4.2 Proper time, gravitational time delay -- 5 Einstein's equations -- 5.1 Vacuum case -- 5.2 Equations with sources -- 6 Field sources -- 6.1 Electromagnetic sources -- 6.2 Electromagnetic potential -- 6.3 Yang-Mills fields -- 6.4 Scalar fields -- 6.5 Wave maps -- 6.6 Energy conditions -- 7 Lagrangians -- 7.1 Einstein-Hilbert Lagrangian -- 7.2 Lagrangians and stress energy tensors of sources -- 7.3 Coupled Lagrangian.
8 Fluid sources -- 9 Einsteinian spacetimes -- 9.1 Definition -- 9.2 Regularity hypotheses -- 10 Newtonian approximation -- 10.1 Equations for potentials -- 10.2 Equations of motion -- 11 Gravitational waves -- 11.1 Minkowskian approximation -- 11.2 General linear waves -- 12 High-frequency gravitational waves -- 12.1 Phase and polarizations -- 12.2 Radiative coordinates -- 12.3 Energy conservation -- 13 Coupled electromagnetic and gravitational waves -- 13.1 Phase and polarizations -- 13.2 Propagation equations -- IV: Schwarzschild spacetime and black holes -- 1 Introduction -- 2 Spherically symmetric spacetimes -- 3 Schwarzschild metric -- 4 Other coordinates -- 4.1 Isotropic coordinates -- 4.2 Wave coordinates -- 4.3 Painlevé-Gullstrand-like coordinates -- 4.4 Regge-Wheeler coordinates -- 5 Schwarzschild spacetime -- 6 The motion of the planets and perihelion precession -- 6.1 Equations -- 6.2 Results of observations -- 6.3 Escape velocity -- 7 Stability of circular orbits -- 8 Deflection of light rays -- 8.1 Theoretical prediction -- 8.2 Results of observation -- 8.3 Fermat's principle and light travel parameter time -- 9 Red shift and time delay -- 10 Spherically symmetric interior solutions -- 10.1 Static solutions. Upper limit on mass -- 10.2 Matching with an exterior solution -- 10.3 Non-static solutions -- 11 The Schwarzschild black hole -- 11.1 The event horizon -- 11.2 The Eddington-Finkelstein extension -- 11.3 Eddington-Finkelstein white hole -- 11.4 Kruskal complete spacetime -- 11.5 Observations -- 12 Spherically symmetric gravitational collapse -- 12.1 Tolman metric -- 12.2 Monotonically decreasing density -- 13 The Reissner-Nordström solution -- 14 Schwarzschild spacetime in dimension n + 1 -- 14.1 Standard coordinates -- 14.2 Wave coordinates -- V: Cosmology -- 1 Introduction -- 2 Cosmological principle. 3 Isotropic and homogeneous Riemannian manifolds -- 3.1 Isotropy -- 3.2 Homogeneity -- 4 Robertson-Walker spacetimes -- 4.1 Space metrics -- 4.2 Robertson-Walker spacetime metrics -- 4.3 Robertson-Walker dynamics -- 4.4 Einstein static universe -- 4.5 Cosmological red shift and the Hubble constant -- 4.6 De Sitter spacetime -- 4.7 Anti de Sitter (AdS) spacetime -- 5 Friedmann-Lemaître models. -- 5.1 Equation of state -- 5.2 General properties -- 5.3 Friedmann models -- 5.4 Some other models -- 5.5 Confrontation with observations -- 6 Homogeneous non-isotropic cosmologies -- 7 Bianchi class I universes -- 7.1 Kasner solutions -- 7.2 Models with matter -- 8 Bianchi type IX -- 9 The Kantowski-Sachs models -- 10 Taub and Taub NUT spacetimes -- 10.1 Taub spacetime -- 10.2 Taub NUT spacetime -- 11 Locally homogeneous models -- 11.1 n-dimensional compact manifolds -- 11.2 Compact 3-manifolds -- 12 Recent observations and conjectures -- VI: Local Cauchy problem -- 1 Introduction -- 2 Moving frame formulae -- 2.1 Frame and coframe -- 2.2 Metric -- 2.3 Connection -- 2.4 Curvature -- 3 n + 1 splitting adapted to space slices -- 3.1 Adapted frame and coframe -- 3.2 Structure coefficients -- 3.3 Splitting of the connection. -- 3.4 Extrinsic curvature -- 3.5 Splitting of the Riemann tensor -- 4 Constraints and evolution -- 4.1 Equations. Conservation of constraints -- 5 Hamiltonian and symplectic formulation -- 5.1 Hamilton equations -- 5.2 Symplectic formulation -- 6 Cauchy problem -- 6.1 Definitions -- 6.2 The analytic case -- 7 Wave gauges -- 7.1 Wave coordinates -- 7.2 Generalized wave coordinates -- 7.3 Damped wave coordinates -- 7.4 Globalization in space, ê wave gauges -- 7.5 Local in time existence in a wave gauge -- 8 Local existence for the full Einstein equations -- 8.1 Preservation of the wave gauges -- 8.2 Geometric local existence. 8.3 Geometric uniqueness -- 8.4 Causality -- 9 Constraints in a wave gauge -- 10 Einstein equations with field sources -- 10.1 Maxwell constraints -- 10.2 Lorentz gauge -- 10.3 Existence and uniqueness theorems -- 10.4 Wave equation for F -- VII: Constraints -- 1 Introduction -- 2 Linearization and stability -- 2.1 Linearization of the constraints map, adjoint map -- 2.2 Linearization stability -- 3 CF (Conformally Formulated) constraints -- 3.1 Hamiltonian constraint -- 3.2 Momentum constraint -- 3.3 Scaling of the sources -- 3.4 Summary of results -- 3.5 Conformal transformation of the CF constraints -- 3.6 The momentum constraint as an elliptic system -- 4 Case n = 2 -- 5 Solutions on compact manifolds -- 6 Solution of the momentum constraint -- 7 Lichnerowicz equation -- 7.1 The Yamabe classification -- 7.2 Non-existence and uniqueness -- 7.3 Existence theorems -- 8 System of constraints -- 8.1 Constant mean curvature & -- #915 -- sources with York-scaled momentum -- 8.2 Solutions with & -- #915 -- & -- #8802 -- constant or J[(0)] & -- #8802 -- 0 -- 9 Solutions on asymptotically Euclidean Manifolds -- 10 Momentum constraint -- 11 Solution of the Lichnerowicz equation -- 11.1 Uniqueness theorem -- 11.2 Generalized Brill-Cantor theorem -- 11.3 Existence theorems -- 12 Solutions of the system of constraints -- 12.1 Decoupled system -- 12.2 Coupled system -- 13 Gluing solutions of the constraint equations -- 13.1 Connected sum gluing -- 13.2 Exterior (Corvino-Schoen) gluing -- VIII: Other hyperbolic-elliptic well-posed systems -- 1 Introduction -- 2 Leray-Ohya non-hyperbolicity of [sup((4))] R[(ij)] = 0 -- 3 Wave equation for K -- 3.1 Hyperbolic system -- 3.2 Hyperbolic-elliptic system -- 4 Fourth-order non-strict and strict hyperbolic systems for g -- 5 First-order hyperbolic systems -- 5.1 FOSH systems -- 6 Bianchi-Einstein equations. 6.1 Wave equation for the Riemann tensor -- 6.2 Case n = 3, FOS system -- 6.3 Cauchy-adapted frame -- 6.4 FOSH system for u = (E, H, D, B, g, K, & -- #915 -- ) -- 6.5 Elliptic-hyperbolic system -- 7 Bel-Robinson tensor and energy -- 7.1 The Bel tensor -- 7.2 The Bel-Robinson tensor and energy -- 8 Bel-Robinson energy in a strip -- IX: Relativistic fluids -- 1 Introduction -- 2 Case of dust -- 2.1 Equations -- 2.2 Motion of isolated bodies (Choquet-Bruhat and Friedrichs 2006) -- 3 Charged dust -- 3.1 Equations -- 3.2 Existence and uniqueness theorem in wave and Lorentz gauges -- 3.3 Motion of isolated bodies -- 4 Perfect fluid, Euler equations -- 5 Energy properties -- 6 Particle number conservation -- 7 Thermodynamics -- 7.1 Definitions. Conservation of entropy -- 7.2 Equations of state -- 8 Wave fronts, propagation speeds, shocks -- 8.1 General definitions -- 8.2 Case of perfect fluids -- 8.3 Shocks -- 9 Stationary motion -- 10 Dynamic velocity for barotropic fluids -- 10.1 Fluid index and equations -- 10.2 Vorticity tensor and Helmholtz equations -- 10.3 Irrotational flows -- 11 General perfect fluids -- 12 Hyperbolic Leray system -- 12.1 Hyperbolicity of the Euler equations. -- 12.2 Reduced Einstein-Euler entropy system -- 12.3 Cauchy problem for the Einstein-Euler entropy system -- 12.4 Motion of isolated bodies -- 13 First-order symmetric hyperbolic system -- 14 Equations in a flow adapted frame -- 14.1 n + 1 splitting in a time adapted frame -- 14.2 Bianchi equations (case n = 3) -- 14.3 Vacuum case -- 14.4 Perfect fluid -- 14.5 Conclusion -- 15 Charged fluids -- 15.1 Equations -- 15.2 Fluids with zero conductivity -- 16 Fluids with finite conductivity -- 17 Magnetohydrodynamics -- 17.1 Equations -- 17.2 Wave fronts -- 18 Yang-Mills fluids -- 19 Dissipative fluids -- 19.1 Viscous fluids -- 19.2 The heat equation. X: Relativistic kinetic theory. |
| Record Nr. | UNINA-9910815087203321 |
|
Choquet-Bruhat Yvonne
|
||
| Oxford ; ; New York, : Oxford University Press, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple
| Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple |
| Autore | Groah Jeff |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (98 p.) |
| Disciplina | 531/.1133 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conservation laws (Physics)
Einstein field equations Shock waves Singularities (Mathematics) General relativity (Physics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0414-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""1 Introduction""; ""1.1 The Proof Strategy""; ""1.2 A Locally Inertial Glimm Scheme""; ""1.3 The Smoothness Class of the Metric""; ""2 Preliminaries""; ""3 The Fractional Step Scheme""; ""4 The Riemann Problem Step""; ""5 The ODE Step""; ""6 Estimates for the ODE step""; ""7 Analysis of the Approximate Solutions""; ""8 The Elimination of Assumptions""; ""9 Convergence"" |
| Record Nr. | UNINA-9910480883003321 |
|
Groah Jeff
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple
| Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple |
| Autore | Groah Jeff |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (98 p.) |
| Disciplina | 531/.1133 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conservation laws (Physics)
Einstein field equations Shock waves Singularities (Mathematics) General relativity (Physics) |
| ISBN | 1-4704-0414-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""1 Introduction""; ""1.1 The Proof Strategy""; ""1.2 A Locally Inertial Glimm Scheme""; ""1.3 The Smoothness Class of the Metric""; ""2 Preliminaries""; ""3 The Fractional Step Scheme""; ""4 The Riemann Problem Step""; ""5 The ODE Step""; ""6 Estimates for the ODE step""; ""7 Analysis of the Approximate Solutions""; ""8 The Elimination of Assumptions""; ""9 Convergence"" |
| Record Nr. | UNINA-9910788748003321 |
|
Groah Jeff
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple
| Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / / Jeff Groah, Blake Temple |
| Autore | Groah Jeff |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (98 p.) |
| Disciplina | 531/.1133 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conservation laws (Physics)
Einstein field equations Shock waves Singularities (Mathematics) General relativity (Physics) |
| ISBN | 1-4704-0414-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""1 Introduction""; ""1.1 The Proof Strategy""; ""1.2 A Locally Inertial Glimm Scheme""; ""1.3 The Smoothness Class of the Metric""; ""2 Preliminaries""; ""3 The Fractional Step Scheme""; ""4 The Riemann Problem Step""; ""5 The ODE Step""; ""6 Estimates for the ODE step""; ""7 Analysis of the Approximate Solutions""; ""8 The Elimination of Assumptions""; ""9 Convergence"" |
| Record Nr. | UNINA-9910818016103321 |
|
Groah Jeff
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
