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Lecture Notes of the Unione Matematica Italiana
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Título : An Introduction to Navier'Stokes Equation and Oceanography Tipo de documento: documento electrónico Autores: Tartar, Luc ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 1 Número de páginas: XXVIII, 247 p Il.: online resource ISBN/ISSN/DL: 978-3-540-36545-7 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Continuum physics Differential Equations Classical Physics Clasificación: 51 Matemáticas Resumen: The Introduction to Navier-Stokes Equation and Oceanography corresponds to a graduate course in mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to the lecture notes distributed to the students, as well as short biographical information for all scientists mentioned in the text, the purpose being to show that the creation of scientific knowledge is an international enterprise, and who contributed to it, from where, and when. The goal of the course is to teach a critical point of view concerning the partial differential equations of continuum mechanics, and to show the need for developing new adapted mathematical tools Nota de contenido: Basic physical laws and units -- Radiation balance of atmosphere -- Conservations in ocean and atmosphere -- Sobolev spaces I -- Particles and continuum mechanics -- Conservation of mass and momentum -- Conservation of energy -- One-dimensional wave equation -- Nonlinear effects, shocks -- Sobolev spaces II -- Linearized elasticity -- Ellipticity conditions -- Sobolev spaces III -- Sobolev spaces IV -- Sobolev spaces V -- Sobolev embedding theorem -- Fixed point theorems -- Brouwer's topological degree -- Time-dependent solutions I -- Time-dependent solutions II -- Time-dependent solutions III -- Uniqueness in 2 dimensions -- Traces -- Using compactness -- Existence of smooth solutions -- Semilinear models -- Size of singular sets -- Local estimates, compensated integrability -- Coriolis force -- Equation for the vorticity -- Boundary conditions in linearized elasticity -- Turbulence, homogenization -- G-convergence and H-convergence -- One-dimensional homogenization, Young measures -- Nonlocal effects I -- Nonlocal effects II -- A model problem -- Compensated compactness I -- Compensated compactness II -- Differential forms -- The compensated compactness method -- H-measures and variants -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/3-540-36545-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34992 An Introduction to Navier'Stokes Equation and Oceanography [documento electrónico] / Tartar, Luc ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XXVIII, 247 p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 1) .
ISBN : 978-3-540-36545-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Continuum physics Differential Equations Classical Physics Clasificación: 51 Matemáticas Resumen: The Introduction to Navier-Stokes Equation and Oceanography corresponds to a graduate course in mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to the lecture notes distributed to the students, as well as short biographical information for all scientists mentioned in the text, the purpose being to show that the creation of scientific knowledge is an international enterprise, and who contributed to it, from where, and when. The goal of the course is to teach a critical point of view concerning the partial differential equations of continuum mechanics, and to show the need for developing new adapted mathematical tools Nota de contenido: Basic physical laws and units -- Radiation balance of atmosphere -- Conservations in ocean and atmosphere -- Sobolev spaces I -- Particles and continuum mechanics -- Conservation of mass and momentum -- Conservation of energy -- One-dimensional wave equation -- Nonlinear effects, shocks -- Sobolev spaces II -- Linearized elasticity -- Ellipticity conditions -- Sobolev spaces III -- Sobolev spaces IV -- Sobolev spaces V -- Sobolev embedding theorem -- Fixed point theorems -- Brouwer's topological degree -- Time-dependent solutions I -- Time-dependent solutions II -- Time-dependent solutions III -- Uniqueness in 2 dimensions -- Traces -- Using compactness -- Existence of smooth solutions -- Semilinear models -- Size of singular sets -- Local estimates, compensated integrability -- Coriolis force -- Equation for the vorticity -- Boundary conditions in linearized elasticity -- Turbulence, homogenization -- G-convergence and H-convergence -- One-dimensional homogenization, Young measures -- Nonlocal effects I -- Nonlocal effects II -- A model problem -- Compensated compactness I -- Compensated compactness II -- Differential forms -- The compensated compactness method -- H-measures and variants -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/3-540-36545-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34992 Ejemplares
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Título : An Introduction to Sobolev Spaces and Interpolation Spaces Tipo de documento: documento electrónico Autores: Tartar, Luc ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 3 Número de páginas: XXV, 219 p Il.: online resource ISBN/ISSN/DL: 978-3-540-71483-5 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience Nota de contenido: Historical Background -- The Lebesgue Measure, Convolution -- Smoothing by Convolution -- Truncation; Radon Measures; Distributions -- Sobolev Spaces; Multiplication by Smooth Functions -- Density of Tensor Products; Consequences -- Extending the Notion of Support -- Sobolev's Embedding Theorem, 1 ? En línea: http://dx.doi.org/10.1007/978-3-540-71483-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34661 An Introduction to Sobolev Spaces and Interpolation Spaces [documento electrónico] / Tartar, Luc ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XXV, 219 p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 3) .
ISBN : 978-3-540-71483-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience Nota de contenido: Historical Background -- The Lebesgue Measure, Convolution -- Smoothing by Convolution -- Truncation; Radon Measures; Distributions -- Sobolev Spaces; Multiplication by Smooth Functions -- Density of Tensor Products; Consequences -- Extending the Notion of Support -- Sobolev's Embedding Theorem, 1 ? En línea: http://dx.doi.org/10.1007/978-3-540-71483-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34661 Ejemplares
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Título : Convolution Operators on Groups Tipo de documento: documento electrónico Autores: Derighetti, Antoine ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 11 Número de páginas: XII, 171p Il.: online resource ISBN/ISSN/DL: 978-3-642-20656-6 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Abstract Analysis Clasificación: 51 Matemáticas Resumen: This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson Nota de contenido: 1 Elementary Results -- 2 An Approximation Theorem for CV2(G) -- 3 The Figa-Talamanca Herz Algebra -- 4 The Dual of Ap(G) -- 5 CVp(G) as a Module on Ap(G) -- 6 The Support of a Convolution Operator -- 7 Convolution Operators Supported by Subgroups -- 8 CVp(G) as a Subspace of CV2(G) En línea: http://dx.doi.org/10.1007/978-3-642-20656-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33426 Convolution Operators on Groups [documento electrónico] / Derighetti, Antoine ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - XII, 171p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 11) .
ISBN : 978-3-642-20656-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Abstract Analysis Clasificación: 51 Matemáticas Resumen: This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson Nota de contenido: 1 Elementary Results -- 2 An Approximation Theorem for CV2(G) -- 3 The Figa-Talamanca Herz Algebra -- 4 The Dual of Ap(G) -- 5 CVp(G) as a Module on Ap(G) -- 6 The Support of a Convolution Operator -- 7 Convolution Operators Supported by Subgroups -- 8 CVp(G) as a Subspace of CV2(G) En línea: http://dx.doi.org/10.1007/978-3-642-20656-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33426 Ejemplares
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Título : Factoring Ideals in Integral Domains Tipo de documento: documento electrónico Autores: Fontana, Marco ; SpringerLink (Online service) ; Houston, Evan ; Lucas, Thomas Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 14 Número de páginas: VIII, 164 p Il.: online resource ISBN/ISSN/DL: 978-3-642-31712-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Commutative algebra rings Number theory Rings and Algebras Geometry Theory Clasificación: 51 Matemáticas Resumen: This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well En línea: http://dx.doi.org/10.1007/978-3-642-31712-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32516 Factoring Ideals in Integral Domains [documento electrónico] / Fontana, Marco ; SpringerLink (Online service) ; Houston, Evan ; Lucas, Thomas . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - VIII, 164 p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 14) .
ISBN : 978-3-642-31712-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Commutative algebra rings Number theory Rings and Algebras Geometry Theory Clasificación: 51 Matemáticas Resumen: This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well En línea: http://dx.doi.org/10.1007/978-3-642-31712-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32516 Ejemplares
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Título : From Hyperbolic Systems to Kinetic Theory : A Personalized Quest Tipo de documento: documento electrónico Autores: Tartar, Luc ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 6 Número de páginas: XXVIII, 282 p Il.: online resource ISBN/ISSN/DL: 978-3-540-77562-1 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Physics Continuum physics Differential Equations Classical Mathematical Methods in Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity! Nota de contenido: Historical Perspective -- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves -- Hyperbolic Systems: Contact Discontinuities, Shocks -- The Burgers Equation and the 1-D Scalar Case -- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik -- Hopf's Formulation of the E-Condition of Oleinik -- The Burgers Equation: Special Solutions -- The Burgers Equation: Small Perturbations; the Heat Equation -- Fourier Transform; the Asymptotic Behaviour for the Heat Equation -- Radon Measures; the Law of Large Numbers -- A 1-D Model with Characteristic Speed 1/? -- A 2-D Generalization; the Perron–Frobenius Theory -- A General Finite-Dimensional Model with Characteristic Speed 1/? -- Discrete Velocity Models -- The Mimura–Nishida and the Crandall–Tartar Existence Theorems -- Systems Satisfying My Condition (S) -- Asymptotic Estimates for the Broadwell and the Carleman Models -- Oscillating Solutions; the 2-D Broadwell Model -- Oscillating Solutions: the Carleman Model -- The Carleman Model: Asymptotic Behaviour -- Oscillating Solutions: the Broadwell Model -- Generalized Invariant Regions; the Varadhan Estimate -- Questioning Physics; from Classical Particles to Balance Laws -- Balance Laws; What Are Forces? -- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation -- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity -- The Two-Body Problem -- The Boltzmann Equation -- The Illner–Shinbrot and the Hamdache Existence Theorems -- The Hilbert Expansion -- Compactness by Integration -- Wave Front Sets; H-Measures -- H-Measures and “Idealized Particles” -- Variants of H-Measures -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/978-3-540-77562-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34371 From Hyperbolic Systems to Kinetic Theory : A Personalized Quest [documento electrónico] / Tartar, Luc ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - XXVIII, 282 p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 6) .
ISBN : 978-3-540-77562-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Physics Continuum physics Differential Equations Classical Mathematical Methods in Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity! Nota de contenido: Historical Perspective -- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves -- Hyperbolic Systems: Contact Discontinuities, Shocks -- The Burgers Equation and the 1-D Scalar Case -- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik -- Hopf's Formulation of the E-Condition of Oleinik -- The Burgers Equation: Special Solutions -- The Burgers Equation: Small Perturbations; the Heat Equation -- Fourier Transform; the Asymptotic Behaviour for the Heat Equation -- Radon Measures; the Law of Large Numbers -- A 1-D Model with Characteristic Speed 1/? -- A 2-D Generalization; the Perron–Frobenius Theory -- A General Finite-Dimensional Model with Characteristic Speed 1/? -- Discrete Velocity Models -- The Mimura–Nishida and the Crandall–Tartar Existence Theorems -- Systems Satisfying My Condition (S) -- Asymptotic Estimates for the Broadwell and the Carleman Models -- Oscillating Solutions; the 2-D Broadwell Model -- Oscillating Solutions: the Carleman Model -- The Carleman Model: Asymptotic Behaviour -- Oscillating Solutions: the Broadwell Model -- Generalized Invariant Regions; the Varadhan Estimate -- Questioning Physics; from Classical Particles to Balance Laws -- Balance Laws; What Are Forces? -- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation -- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity -- The Two-Body Problem -- The Boltzmann Equation -- The Illner–Shinbrot and the Hamdache Existence Theorems -- The Hilbert Expansion -- Compactness by Integration -- Wave Front Sets; H-Measures -- H-Measures and “Idealized Particles” -- Variants of H-Measures -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/978-3-540-77562-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34371 Ejemplares
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