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Refinar búsquedaAssociahedra, Tamari Lattices and Related Structures / SpringerLink (Online service) ; Müller-Hoissen, Folkert ; Pallo, Jean Marcel ; Stasheff, Jim (2012)
Título : Associahedra, Tamari Lattices and Related Structures : Tamari Memorial Festschrift Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Müller-Hoissen, Folkert ; Pallo, Jean Marcel ; Stasheff, Jim Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematics, ISSN 0743-1643 num. 299 Número de páginas: XX, 436 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0405-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Convex geometry Discrete Number theory Algebraic topology and Geometry Theory Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations En línea: http://dx.doi.org/10.1007/978-3-0348-0405-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32887 Associahedra, Tamari Lattices and Related Structures : Tamari Memorial Festschrift [documento electrónico] / SpringerLink (Online service) ; Müller-Hoissen, Folkert ; Pallo, Jean Marcel ; Stasheff, Jim . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - XX, 436 p : online resource. - (Progress in Mathematics, ISSN 0743-1643; 299) .
ISBN : 978-3-0348-0405-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Convex geometry Discrete Number theory Algebraic topology and Geometry Theory Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations En línea: http://dx.doi.org/10.1007/978-3-0348-0405-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32887 Ejemplares
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Título : Basic Algebra : Along with a companion volume Advanced Algebra Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Otro editor: Imprint: Birkhäuser Colección: Cornerstones Número de páginas: XXV, 735 p. 46 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4529-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Commutative algebra Field theory (Physics) Group Matrix Linear and Multilinear Algebras, Theory Algebras Generalizations Polynomials Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study *Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs Nota de contenido: Preliminaries about the Integers, Polynomials, and Matrices -- Vector Spaces over ?, ?, and ? -- Inner-Product Spaces -- Groups and Group Actions -- Theory of a Single Linear Transformation -- Multilinear Algebra -- Advanced Group Theory -- Commutative Rings and Their Modules -- Fields and Galois Theory -- Modules over Noncommutative Rings En línea: http://dx.doi.org/10.1007/978-0-8176-4529-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34882 Basic Algebra : Along with a companion volume Advanced Algebra [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2006 . - XXV, 735 p. 46 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4529-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Commutative algebra Field theory (Physics) Group Matrix Linear and Multilinear Algebras, Theory Algebras Generalizations Polynomials Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study *Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs Nota de contenido: Preliminaries about the Integers, Polynomials, and Matrices -- Vector Spaces over ?, ?, and ? -- Inner-Product Spaces -- Groups and Group Actions -- Theory of a Single Linear Transformation -- Multilinear Algebra -- Advanced Group Theory -- Commutative Rings and Their Modules -- Fields and Galois Theory -- Modules over Noncommutative Rings En línea: http://dx.doi.org/10.1007/978-0-8176-4529-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34882 Ejemplares
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Título : Bounded Noises in Physics, Biology, and Engineering Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Alberto D'Onofrio Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Modeling and Simulation in Science, Engineering and Technology, ISSN 2164-3679 Número de páginas: XVI, 285 p. 87 illus., 39 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-7385-5 Idioma : Inglés (eng) Palabras clave: Mathematics System theory Mathematical models Probabilities Biomathematics Physics Applied mathematics Engineering Modeling and Industrial Computational Biology Theoretical, Appl.Mathematics/Computational Methods of Probability Theory Stochastic Processes Complex Systems Clasificación: 51 Matemáticas Resumen: Since the parameters in dynamical systems of biological interest are inherently positive and bounded, bounded noises are a natural way to model the realistic stochastic fluctuations of a biological system that are caused by its interaction with the external world. Bounded Noises in Physics, Biology, and Engineering is the first contributed volume devoted to the modeling of bounded noises in theoretical and applied statistical mechanics, quantitative biology, and mathematical physics. It gives an overview of the current state-of-the-art and is intended to stimulate further research. The volume is organized in four parts. The first part presents the main kinds of bounded noises and their applications in theoretical physics. The theory of bounded stochastic processes is intimately linked to its applications to mathematical and statistical physics, and it would be difficult and unnatural to separate the theory from its physical applications. The second is devoted to framing bounded noises in the theory of random dynamical systems and random bifurcations, while the third is devoted to applications of bounded stochastic processes in biology, one of the major areas of potential applications of this subject. The final part concerns the application of bounded stochastic processes in mechanical and structural engineering, the area where the renewed interest for non-Gaussian bounded noises started. Pure mathematicians working on stochastic calculus will find here a rich source of problems that are challenging from the point of view of contemporary nonlinear analysis. Bounded Noises in Physics, Biology, and Engineering is intended for scientists working on stochastic processes with an interest in both fundamental issues and applications. It will appeal to a broad range of applied mathematicians, mathematical biologists, physicists, engineers, and researchers in other fields interested in complexity theory. It is accessible to anyone with a working knowledge of stochastic modeling, from advanced undergraduates to senior researchers Nota de contenido: Introduction -- Part I : Modeling of Bounded Noises and Their Applications in Physics -- On Bounded Stochastic Processes -- Dynamics of Systems With Randomly Disordered Periodic Excitations -- Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics -- Dynamical Systems Driven by Dichotomous Noise -- Stochastic Oscillator : Brownian Motion With Adhesion -- Numerical Study of Energetic Stability For Harmonic Oscillator With Fluctuating Damping Parameter -- A Moment-Based Approach to Bounded Non-Gaussian Colored Noise -- Spatiotemporal Bounded Noises, and Their Application to the Ginzburg-Landau Equation -- Part II: Bounded Noises in the Framework of Discrete and Continuous Random Dynamical Systems -- Bifurcations of Random Differential Equations With Bounded Noise -- Effects of Bounded Random Perturbations on Discrete Dynamical Systems -- Part III: Bounded Stochastic Fluctuations in Biology -- Bounded Stochastic Perturbations May Induce Non-Genetic Resistance to Anti-Tumor Chemotherapy -- Interplay Between Cross Correlation and Delays in the Sine-Wienernoise-Induced Transitions -- Bounded Extrinsic Noises Affecting Biochemical Networks With Low Molecule Numbers -- Part IV: Bounded Noises: Applications in Engineering -- Almost Sure Stability of Fractional Viscoelastic Systems Driven By Bounded Noises -- Model Selection for Random Functions With Bounded Range. Applications in Science and Engineering -- From Model-Based to Data-Driven Filter Design En línea: http://dx.doi.org/10.1007/978-1-4614-7385-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32353 Bounded Noises in Physics, Biology, and Engineering [documento electrónico] / SpringerLink (Online service) ; Alberto D'Onofrio . - New York, NY : Springer New York : Imprint: Birkhäuser, 2013 . - XVI, 285 p. 87 illus., 39 illus. in color : online resource. - (Modeling and Simulation in Science, Engineering and Technology, ISSN 2164-3679) .
ISBN : 978-1-4614-7385-5
Idioma : Inglés (eng)
Palabras clave: Mathematics System theory Mathematical models Probabilities Biomathematics Physics Applied mathematics Engineering Modeling and Industrial Computational Biology Theoretical, Appl.Mathematics/Computational Methods of Probability Theory Stochastic Processes Complex Systems Clasificación: 51 Matemáticas Resumen: Since the parameters in dynamical systems of biological interest are inherently positive and bounded, bounded noises are a natural way to model the realistic stochastic fluctuations of a biological system that are caused by its interaction with the external world. Bounded Noises in Physics, Biology, and Engineering is the first contributed volume devoted to the modeling of bounded noises in theoretical and applied statistical mechanics, quantitative biology, and mathematical physics. It gives an overview of the current state-of-the-art and is intended to stimulate further research. The volume is organized in four parts. The first part presents the main kinds of bounded noises and their applications in theoretical physics. The theory of bounded stochastic processes is intimately linked to its applications to mathematical and statistical physics, and it would be difficult and unnatural to separate the theory from its physical applications. The second is devoted to framing bounded noises in the theory of random dynamical systems and random bifurcations, while the third is devoted to applications of bounded stochastic processes in biology, one of the major areas of potential applications of this subject. The final part concerns the application of bounded stochastic processes in mechanical and structural engineering, the area where the renewed interest for non-Gaussian bounded noises started. Pure mathematicians working on stochastic calculus will find here a rich source of problems that are challenging from the point of view of contemporary nonlinear analysis. Bounded Noises in Physics, Biology, and Engineering is intended for scientists working on stochastic processes with an interest in both fundamental issues and applications. It will appeal to a broad range of applied mathematicians, mathematical biologists, physicists, engineers, and researchers in other fields interested in complexity theory. It is accessible to anyone with a working knowledge of stochastic modeling, from advanced undergraduates to senior researchers Nota de contenido: Introduction -- Part I : Modeling of Bounded Noises and Their Applications in Physics -- On Bounded Stochastic Processes -- Dynamics of Systems With Randomly Disordered Periodic Excitations -- Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics -- Dynamical Systems Driven by Dichotomous Noise -- Stochastic Oscillator : Brownian Motion With Adhesion -- Numerical Study of Energetic Stability For Harmonic Oscillator With Fluctuating Damping Parameter -- A Moment-Based Approach to Bounded Non-Gaussian Colored Noise -- Spatiotemporal Bounded Noises, and Their Application to the Ginzburg-Landau Equation -- Part II: Bounded Noises in the Framework of Discrete and Continuous Random Dynamical Systems -- Bifurcations of Random Differential Equations With Bounded Noise -- Effects of Bounded Random Perturbations on Discrete Dynamical Systems -- Part III: Bounded Stochastic Fluctuations in Biology -- Bounded Stochastic Perturbations May Induce Non-Genetic Resistance to Anti-Tumor Chemotherapy -- Interplay Between Cross Correlation and Delays in the Sine-Wienernoise-Induced Transitions -- Bounded Extrinsic Noises Affecting Biochemical Networks With Low Molecule Numbers -- Part IV: Bounded Noises: Applications in Engineering -- Almost Sure Stability of Fractional Viscoelastic Systems Driven By Bounded Noises -- Model Selection for Random Functions With Bounded Range. Applications in Science and Engineering -- From Model-Based to Data-Driven Filter Design En línea: http://dx.doi.org/10.1007/978-1-4614-7385-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32353 Ejemplares
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Título : Chaos : Poincaré Seminar 2010 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Duplantier, Bertrand ; Nonnenmacher, Stéphane ; Rivasseau, Vincent Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematical Physics, ISSN 1544-9998 num. 66 Número de páginas: XII, 270 p. 100 illus., 61 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0697-8 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Number Quantum field String Statistical physics Dynamical systems Systems and Theory Field Theories, Physics, Complexity Clasificación: 51 Matemáticas Resumen: This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ?-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ?-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S. Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians Nota de contenido: Foreword -- 1 Étienne Ghys, The Lorenz Attractor, a Paradigm for Chaos -- 2 Stéphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows -- 3 Uzy Smilansky, Discrete Graphs - A Paradigm Model for Quantum Chaos -- 4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann ?-function -- 5 Hans-Jürgen Stöckmann, Chaos in Microwave Resonators -- 6 Stéphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates -- 7 Jacques Laskar, Is the Solar System Stable? En línea: http://dx.doi.org/10.1007/978-3-0348-0697-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32448 Chaos : Poincaré Seminar 2010 [documento electrónico] / SpringerLink (Online service) ; Duplantier, Bertrand ; Nonnenmacher, Stéphane ; Rivasseau, Vincent . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XII, 270 p. 100 illus., 61 illus. in color : online resource. - (Progress in Mathematical Physics, ISSN 1544-9998; 66) .
ISBN : 978-3-0348-0697-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Number Quantum field String Statistical physics Dynamical systems Systems and Theory Field Theories, Physics, Complexity Clasificación: 51 Matemáticas Resumen: This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ?-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ?-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S. Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians Nota de contenido: Foreword -- 1 Étienne Ghys, The Lorenz Attractor, a Paradigm for Chaos -- 2 Stéphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows -- 3 Uzy Smilansky, Discrete Graphs - A Paradigm Model for Quantum Chaos -- 4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann ?-function -- 5 Hans-Jürgen Stöckmann, Chaos in Microwave Resonators -- 6 Stéphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates -- 7 Jacques Laskar, Is the Solar System Stable? En línea: http://dx.doi.org/10.1007/978-3-0348-0697-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32448 Ejemplares
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Título : Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Third Edition Tipo de documento: documento electrónico Autores: Walter Benz ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Número de páginas: XVIII, 310 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0420-2 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Möbius and Lie as well as geometries where Lorentz transformations play the key role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts Nota de contenido: Preface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 d–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0420-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32891 Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces Third Edition [documento electrónico] / Walter Benz ; SpringerLink (Online service) . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - XVIII, 310 p : online resource.
ISBN : 978-3-0348-0420-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Physics Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Möbius and Lie as well as geometries where Lorentz transformations play the key role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts Nota de contenido: Preface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 d–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0420-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32891 Ejemplares
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