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Título : Potential Theory Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; M. Brelot Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: C.I.M.E. Summer Schools num. 49 Número de páginas: IV, 252 p Il.: online resource ISBN/ISSN/DL: 978-3-642-11084-9 Idioma : Inglés (eng) Palabras clave: Mathematics Potential theory (Mathematics) Theory Clasificación: 51 Matemáticas Resumen: M. Brelot: Historical introduction.- H. Bauer: Harmonic spaces and associated Markov processes.- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel.- J. Deny: Méthodes hilbertiennes en theory du potentiel.- J.L. Doob: Martingale theory – Potential theory.- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés Nota de contenido: M. Brelot: Historical introduction -- H. Bauer: Harmonic spaces and associated Markov processes -- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel -- J. Deny: Méthodes hilbertiennes en theory du potentiel -- J.L. Doob: Martingale theory – Potential theory -- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés En línea: http://dx.doi.org/10.1007/978-3-642-11084-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33344 Potential Theory [documento electrónico] / SpringerLink (Online service) ; M. Brelot . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - IV, 252 p : online resource. - (C.I.M.E. Summer Schools; 49) .
ISBN : 978-3-642-11084-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Potential theory (Mathematics) Theory Clasificación: 51 Matemáticas Resumen: M. Brelot: Historical introduction.- H. Bauer: Harmonic spaces and associated Markov processes.- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel.- J. Deny: Méthodes hilbertiennes en theory du potentiel.- J.L. Doob: Martingale theory – Potential theory.- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés Nota de contenido: M. Brelot: Historical introduction -- H. Bauer: Harmonic spaces and associated Markov processes -- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel -- J. Deny: Méthodes hilbertiennes en theory du potentiel -- J.L. Doob: Martingale theory – Potential theory -- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés En línea: http://dx.doi.org/10.1007/978-3-642-11084-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33344 Ejemplares
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Título : Potential Theory Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Lester L. Helms Editorial: London : Springer London Fecha de publicación: 2009 Colección: Universitext, ISSN 0172-5939 Número de páginas: XI, 441 p. 2 illus Il.: online resource ISBN/ISSN/DL: 978-1-84882-319-8 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Potential theory (Mathematics) Applied mathematics Engineering Physics Theory Mathematical Methods in Engineering, general Differential Equations Applications of Clasificación: 51 Matemáticas Resumen: Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem of the calculus, the author develops methods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic partial differential equations involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary Nota de contenido: Preliminaries -- Laplace's Equation -- The Dirichlet Problem -- Green Functions -- Negligible Sets -- Dirichlet Problem for Unbounded Regions -- Energy -- Interpolation and Monotonicity -- Newtonian Potential -- Elliptic Operators -- Apriori Bounds -- Oblique Derivative Problem En línea: http://dx.doi.org/10.1007/978-1-84882-319-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33985 Potential Theory [documento electrónico] / SpringerLink (Online service) ; Lester L. Helms . - London : Springer London, 2009 . - XI, 441 p. 2 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-84882-319-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Potential theory (Mathematics) Applied mathematics Engineering Physics Theory Mathematical Methods in Engineering, general Differential Equations Applications of Clasificación: 51 Matemáticas Resumen: Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem of the calculus, the author develops methods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic partial differential equations involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary Nota de contenido: Preliminaries -- Laplace's Equation -- The Dirichlet Problem -- Green Functions -- Negligible Sets -- Dirichlet Problem for Unbounded Regions -- Energy -- Interpolation and Monotonicity -- Newtonian Potential -- Elliptic Operators -- Apriori Bounds -- Oblique Derivative Problem En línea: http://dx.doi.org/10.1007/978-1-84882-319-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33985 Ejemplares
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Título : Conformal and Potential Analysis in Hele-Shaw Cell Tipo de documento: documento electrónico Autores: Björn Gustafsson ; SpringerLink (Online service) ; Alexander Vasil’ev Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Advances in Mathematical Fluid Mechanics Número de páginas: X, 234 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7704-5 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Potential theory (Mathematics) Continuum physics Differential Equations Theory Classical Physics Clasificación: 51 Matemáticas Nota de contenido: and Background -- Explicit Strong Solutions -- Weak Solutions and Balayage -- Geometric Properties -- Capacities and Isoperimetric Inequalities -- General Evolution Equations -- Hele-Shaw Evolution and Strings En línea: http://dx.doi.org/10.1007/3-7643-7704-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35033 Conformal and Potential Analysis in Hele-Shaw Cell [documento electrónico] / Björn Gustafsson ; SpringerLink (Online service) ; Alexander Vasil’ev . - Basel : Birkhäuser Basel, 2006 . - X, 234 p : online resource. - (Advances in Mathematical Fluid Mechanics) .
ISBN : 978-3-7643-7704-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Potential theory (Mathematics) Continuum physics Differential Equations Theory Classical Physics Clasificación: 51 Matemáticas Nota de contenido: and Background -- Explicit Strong Solutions -- Weak Solutions and Balayage -- Geometric Properties -- Capacities and Isoperimetric Inequalities -- General Evolution Equations -- Hele-Shaw Evolution and Strings En línea: http://dx.doi.org/10.1007/3-7643-7704-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35033 Ejemplares
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Título : Stratified Lie Groups and Potential Theory for their Sub-Laplacians Tipo de documento: documento electrónico Autores: A. Bonfiglioli ; SpringerLink (Online service) ; E. Lanconelli ; F. Uguzzoni Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XXVI, 802 p Il.: online resource ISBN/ISSN/DL: 978-3-540-71897-0 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Topological groups Lie Partial differential equations Potential theory (Mathematics) Differential Equations Theory Groups, Groups Clasificación: 51 Matemáticas Resumen: The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator. This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerable attention due to their special role in the theory of linear second-order PDE's with semidefinite characteristic form. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups Nota de contenido: Elements of Analysis of Stratified Groups -- Stratified Groups and Sub-Laplacians -- Abstract Lie Groups and Carnot Groups -- Carnot Groups of Step Two -- Examples of Carnot Groups -- The Fundamental Solution for a Sub-Laplacian and Applications -- Elements of Potential Theory for Sub-Laplacians -- Abstract Harmonic Spaces -- The ?-harmonic Space -- ?-subharmonic Functions -- Representation Theorems -- Maximum Principle on Unbounded Domains -- ?-capacity, ?-polar Sets and Applications -- ?-thinness and ?-fine Topology -- d-Hausdorff Measure and ?-capacity -- Further Topics on Carnot Groups -- Some Remarks on Free Lie Algebras -- More on the Campbell–Hausdorff Formula -- Families of Diffeomorphic Sub-Laplacians -- Lifting of Carnot Groups -- Groups of Heisenberg Type -- The Carathéodory–Chow–Rashevsky Theorem -- Taylor Formula on Homogeneous Carnot Groups En línea: http://dx.doi.org/10.1007/978-3-540-71897-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34664 Stratified Lie Groups and Potential Theory for their Sub-Laplacians [documento electrónico] / A. Bonfiglioli ; SpringerLink (Online service) ; E. Lanconelli ; F. Uguzzoni . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XXVI, 802 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-3-540-71897-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Topological groups Lie Partial differential equations Potential theory (Mathematics) Differential Equations Theory Groups, Groups Clasificación: 51 Matemáticas Resumen: The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator. This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerable attention due to their special role in the theory of linear second-order PDE's with semidefinite characteristic form. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups Nota de contenido: Elements of Analysis of Stratified Groups -- Stratified Groups and Sub-Laplacians -- Abstract Lie Groups and Carnot Groups -- Carnot Groups of Step Two -- Examples of Carnot Groups -- The Fundamental Solution for a Sub-Laplacian and Applications -- Elements of Potential Theory for Sub-Laplacians -- Abstract Harmonic Spaces -- The ?-harmonic Space -- ?-subharmonic Functions -- Representation Theorems -- Maximum Principle on Unbounded Domains -- ?-capacity, ?-polar Sets and Applications -- ?-thinness and ?-fine Topology -- d-Hausdorff Measure and ?-capacity -- Further Topics on Carnot Groups -- Some Remarks on Free Lie Algebras -- More on the Campbell–Hausdorff Formula -- Families of Diffeomorphic Sub-Laplacians -- Lifting of Carnot Groups -- Groups of Heisenberg Type -- The Carathéodory–Chow–Rashevsky Theorem -- Taylor Formula on Homogeneous Carnot Groups En línea: http://dx.doi.org/10.1007/978-3-540-71897-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34664 Ejemplares
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Título : An Introduction to Mathematics of Emerging Biomedical Imaging Tipo de documento: documento electrónico Autores: Habib Ammari ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Mathématiques & Applications, ISSN 1154-483X num. 62 Número de páginas: X, 198 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-79553-7 Idioma : Inglés (eng) Palabras clave: Medicine Internal medicine Differential equations Partial differential Potential theory (Mathematics) Biomathematics & Public Health Mathematical and Computational Biology Theory Equations Ordinary Clasificación: 51 Matemáticas Resumen: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging Nota de contenido: Mathematical Tools -- Biomedical Imaging Modalities -- Preliminaries -- Layer Potential Techniques -- General Reconstruction Algorithms -- Tomographic Imaging with Non-Diffracting Sources -- Tomographic Imaging with Diffracting Sources -- Biomagnetic Source Imaging -- Anomaly Detection Algorithms -- Small Volume Expansions -- Imaging Techniques -- Hybrid Imaging Techniques -- Magnetic Resonance Electrical Impedance Tomography -- Impediography -- Magnetic Resonance Elastography En línea: http://dx.doi.org/10.1007/978-3-540-79553-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34380 An Introduction to Mathematics of Emerging Biomedical Imaging [documento electrónico] / Habib Ammari ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - X, 198 p. 16 illus : online resource. - (Mathématiques & Applications, ISSN 1154-483X; 62) .
ISBN : 978-3-540-79553-7
Idioma : Inglés (eng)
Palabras clave: Medicine Internal medicine Differential equations Partial differential Potential theory (Mathematics) Biomathematics & Public Health Mathematical and Computational Biology Theory Equations Ordinary Clasificación: 51 Matemáticas Resumen: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging Nota de contenido: Mathematical Tools -- Biomedical Imaging Modalities -- Preliminaries -- Layer Potential Techniques -- General Reconstruction Algorithms -- Tomographic Imaging with Non-Diffracting Sources -- Tomographic Imaging with Diffracting Sources -- Biomagnetic Source Imaging -- Anomaly Detection Algorithms -- Small Volume Expansions -- Imaging Techniques -- Hybrid Imaging Techniques -- Magnetic Resonance Electrical Impedance Tomography -- Impediography -- Magnetic Resonance Elastography En línea: http://dx.doi.org/10.1007/978-3-540-79553-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34380 Ejemplares
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