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Refinar búsquedaAn Introduction to the Mathematical Theory of the Navier-Stokes Equations / Giovanni P. Galdi (2011)
Título : An Introduction to the Mathematical Theory of the Navier-Stokes Equations : Steady-State Problems Tipo de documento: documento electrónico Autores: Giovanni P. Galdi ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XIV, 1018 p. 4 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-09620-9 Idioma : Inglés (eng) Palabras clave: Mathematics Differential equations Partial differential Applied mathematics Engineering Fluid mechanics Equations Dynamics Applications of Ordinary Clasificación: 51 Matemáticas Resumen: The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated. An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists. Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations. Review of First Edition, First Volume: “The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995) Nota de contenido: Steady-State Solutions of the Navier–Stokes Equations: Statement of the Problem and Open Questions -- Basic Function Spaces and Related Inequalities -- The Function Spaces of Hydrodynamics -- Steady Stokes Flow in Bounded Domains -- Steady Stokes Flow in Exterior Domains -- Steady Stokes Flow in Domains with Unbounded Boundaries -- Steady Oseen Flow in Exterior Domains -- Steady Generalized Oseen Flow in Exterior Domains -- Steady Navier–Stokes Flow in Bounded Domains -- Steady Navier–Stokes Flow in Three-Dimensional Exterior Domains. Irrotational Case -- Steady Navier–Stokes Flow in Three-Dimensional Exterior Domains. Rotational Case -- Steady Navier–Stokes Flow in Two-Dimensional Exterior Domains -- Steady Navier–Stokes Flow in Domains with Unbounded Boundaries -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-387-09620-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33069 An Introduction to the Mathematical Theory of the Navier-Stokes Equations : Steady-State Problems [documento electrónico] / Giovanni P. Galdi ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XIV, 1018 p. 4 illus : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-0-387-09620-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential equations Partial differential Applied mathematics Engineering Fluid mechanics Equations Dynamics Applications of Ordinary Clasificación: 51 Matemáticas Resumen: The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated. An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists. Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations. Review of First Edition, First Volume: “The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995) Nota de contenido: Steady-State Solutions of the Navier–Stokes Equations: Statement of the Problem and Open Questions -- Basic Function Spaces and Related Inequalities -- The Function Spaces of Hydrodynamics -- Steady Stokes Flow in Bounded Domains -- Steady Stokes Flow in Exterior Domains -- Steady Stokes Flow in Domains with Unbounded Boundaries -- Steady Oseen Flow in Exterior Domains -- Steady Generalized Oseen Flow in Exterior Domains -- Steady Navier–Stokes Flow in Bounded Domains -- Steady Navier–Stokes Flow in Three-Dimensional Exterior Domains. Irrotational Case -- Steady Navier–Stokes Flow in Three-Dimensional Exterior Domains. Rotational Case -- Steady Navier–Stokes Flow in Two-Dimensional Exterior Domains -- Steady Navier–Stokes Flow in Domains with Unbounded Boundaries -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-387-09620-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33069 Ejemplares
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Título : Approximation Theory and Harmonic Analysis on Spheres and Balls Tipo de documento: documento electrónico Autores: Feng Dai ; SpringerLink (Online service) ; Yuan Xu Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XVIII, 440 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6660-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Fourier Special functions Approximations and Expansions Functions Clasificación: 51 Matemáticas Resumen: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area Nota de contenido: 1 Spherical Harmonics -- 2 Convolution and Spherical Harmonic Expansion -- 3 Littlewood-Paley Theory and Multiplier Theorem -- 4 Approximation on the Sphere -- 5 Weighted Polynomial Inequalities -- 6 Cubature Formulas on Spheres -- 7 Harmonic Analysis Associated to Reflection Groups -- 8 Boundedness of Projection Operator and Cesàro Means -- 9 Projection Operators and Cesàro Means in L^p Spaces -- 10 Weighted Best Approximation by Polynomials -- 11 Harmonic Analysis on the Unit Ball -- 12 Polynomial Approximation on the Unit Ball -- 13 Harmonic Analysis on the Simplex -- 14 Applications -- A Distance, Difference and Integral Formulas -- B Jacobi and Related Orthogonal Polynomials -- References -- Index -- Symbol Index En línea: http://dx.doi.org/10.1007/978-1-4614-6660-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32314 Approximation Theory and Harmonic Analysis on Spheres and Balls [documento electrónico] / Feng Dai ; SpringerLink (Online service) ; Yuan Xu . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XVIII, 440 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-4614-6660-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Fourier Special functions Approximations and Expansions Functions Clasificación: 51 Matemáticas Resumen: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area Nota de contenido: 1 Spherical Harmonics -- 2 Convolution and Spherical Harmonic Expansion -- 3 Littlewood-Paley Theory and Multiplier Theorem -- 4 Approximation on the Sphere -- 5 Weighted Polynomial Inequalities -- 6 Cubature Formulas on Spheres -- 7 Harmonic Analysis Associated to Reflection Groups -- 8 Boundedness of Projection Operator and Cesàro Means -- 9 Projection Operators and Cesàro Means in L^p Spaces -- 10 Weighted Best Approximation by Polynomials -- 11 Harmonic Analysis on the Unit Ball -- 12 Polynomial Approximation on the Unit Ball -- 13 Harmonic Analysis on the Simplex -- 14 Applications -- A Distance, Difference and Integral Formulas -- B Jacobi and Related Orthogonal Polynomials -- References -- Index -- Symbol Index En línea: http://dx.doi.org/10.1007/978-1-4614-6660-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32314 Ejemplares
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Título : Arithmetic of Quadratic Forms Tipo de documento: documento electrónico Autores: Shimura, Goro ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Otro editor: Imprint: Springer Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XII, 238 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-1732-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Number theory Theory General Algebraic Systems Clasificación: 51 Matemáticas Resumen: This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references Nota de contenido: The Quadratic Reciprocity Law -- Arithmetic in an Algebraic Number Field -- Various Basic Theorems -- Algebras Over a Field -- Quadratic Forms -- Deeper Arithmetic of Quadratic Forms -- Quadratic Diophantine Equations En línea: http://dx.doi.org/10.1007/978-1-4419-1732-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33606 Arithmetic of Quadratic Forms [documento electrónico] / Shimura, Goro ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2010 . - XII, 238 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-4419-1732-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Number theory Theory General Algebraic Systems Clasificación: 51 Matemáticas Resumen: This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references Nota de contenido: The Quadratic Reciprocity Law -- Arithmetic in an Algebraic Number Field -- Various Basic Theorems -- Algebras Over a Field -- Quadratic Forms -- Deeper Arithmetic of Quadratic Forms -- Quadratic Diophantine Equations En línea: http://dx.doi.org/10.1007/978-1-4419-1732-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33606 Ejemplares
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Título : Concrete Functional Calculus Tipo de documento: documento electrónico Autores: R. M. Dudley ; SpringerLink (Online service) ; Rimas Norvaisa Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XII, 671 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-6950-7 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Integral equations Operator theory Functions of real variables Analysis Equations Theory Real Clasificación: 51 Matemáticas Resumen: Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability Nota de contenido: Preface -- 1 Introduction and Overview -- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals -- 3 Phi-variation and p-variation; Inequalities for Integrals -- 4 Banach Algebras -- 5 Derivatives and Analyticity in Normed Spaces -- 6 Nemytskii Operators on Some Function Spaces -- 7 Nemytskii Oerators on Lp Spaces -- 8 Two-Function Composition -- 9 Product Integration -- 10 Nonlinear Differential and Integral Equations -- 11 Fourier Series -- 12 Stochastic Processes and Phi-Variation -- Appendix Nonatomic Measure Spaces -- References -- Subject Index -- Author Index -- Index of Notation En línea: http://dx.doi.org/10.1007/978-1-4419-6950-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33149 Concrete Functional Calculus [documento electrónico] / R. M. Dudley ; SpringerLink (Online service) ; Rimas Norvaisa . - New York, NY : Springer New York, 2011 . - XII, 671 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-4419-6950-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Integral equations Operator theory Functions of real variables Analysis Equations Theory Real Clasificación: 51 Matemáticas Resumen: Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability Nota de contenido: Preface -- 1 Introduction and Overview -- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals -- 3 Phi-variation and p-variation; Inequalities for Integrals -- 4 Banach Algebras -- 5 Derivatives and Analyticity in Normed Spaces -- 6 Nemytskii Operators on Some Function Spaces -- 7 Nemytskii Oerators on Lp Spaces -- 8 Two-Function Composition -- 9 Product Integration -- 10 Nonlinear Differential and Integral Equations -- 11 Fourier Series -- 12 Stochastic Processes and Phi-Variation -- Appendix Nonatomic Measure Spaces -- References -- Subject Index -- Author Index -- Index of Notation En línea: http://dx.doi.org/10.1007/978-1-4419-6950-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33149 Ejemplares
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Título : Discrete Integrable Systems : QRT Maps and Elliptic Surfaces Tipo de documento: documento electrónico Autores: J.J. Duistermaat ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XXII, 627 p. 116 illus Il.: online resource ISBN/ISSN/DL: 978-1-4419-9126-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Functions of complex variables Number theory Physics Geometry a Complex Variable Theoretical, Mathematical and Computational Theory Clasificación: 51 Matemáticas Resumen: The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the author’s insights and understanding of a birational transformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a complete treatment not only of the basic facts about QRT maps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodaira’s theory of elliptic surfaces and the collection of nontrivial applications presented here. While prerequisites for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able to become familiar with any selected interest in the book without having to make an extensive journey through the literature Nota de contenido: The QRT Map -- The Pencil of Biquadratic Curves in -- The QRT surface -- Cubic Curves in the Projective Plane -- The Action of the QRT Map on Homology -- Elliptic Surfaces -- Automorphisms of Elliptic Surfaces -- Elliptic Fibrations with a Real Structure -- Rational elliptic surfaces -- Symmetric QRT Maps -- Examples from the Literature -- Appendices En línea: http://dx.doi.org/10.1007/978-1-4419-9126-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33647 Discrete Integrable Systems : QRT Maps and Elliptic Surfaces [documento electrónico] / J.J. Duistermaat ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XXII, 627 p. 116 illus : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-4419-9126-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Functions of complex variables Number theory Physics Geometry a Complex Variable Theoretical, Mathematical and Computational Theory Clasificación: 51 Matemáticas Resumen: The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the author’s insights and understanding of a birational transformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a complete treatment not only of the basic facts about QRT maps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodaira’s theory of elliptic surfaces and the collection of nontrivial applications presented here. While prerequisites for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able to become familiar with any selected interest in the book without having to make an extensive journey through the literature Nota de contenido: The QRT Map -- The Pencil of Biquadratic Curves in -- The QRT surface -- Cubic Curves in the Projective Plane -- The Action of the QRT Map on Homology -- Elliptic Surfaces -- Automorphisms of Elliptic Surfaces -- Elliptic Fibrations with a Real Structure -- Rational elliptic surfaces -- Symmetric QRT Maps -- Examples from the Literature -- Appendices En línea: http://dx.doi.org/10.1007/978-1-4419-9126-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33647 Ejemplares
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