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Systems Of Transversal Sections Near Critical Energy Levels Of Hamiltonian Systems In Mathbb R4
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Book Synopsis Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ by : Naiara V. de Paulo
Download or read book Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ written by Naiara V. de Paulo and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.
Book Synopsis Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups by : Olivier Frécon
Download or read book Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups written by Olivier Frécon and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.
Book Synopsis Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R4 by : Naiara V. De Paulo
Download or read book Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R4 written by Naiara V. De Paulo and published by . This book was released on 2018 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Space-Time Algebra by : David Hestenes
Download or read book Space-Time Algebra written by David Hestenes and published by Birkhäuser. This book was released on 2015-04-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible. There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future. From the Foreward by Anthony Lasenby
Book Synopsis Emerging Frontiers in Nonlinear Science by : Panayotis G. Kevrekidis
Download or read book Emerging Frontiers in Nonlinear Science written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on 2020-05-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.
Book Synopsis Geometric Mechanics and Symmetry by : James Montaldi
Download or read book Geometric Mechanics and Symmetry written by James Montaldi and published by Cambridge University Press. This book was released on 2005-05-05 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.
Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding
Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes
Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Book Synopsis The Turbulence Problem by : Michael Eckert
Download or read book The Turbulence Problem written by Michael Eckert and published by Springer Nature. This book was released on 2019-10-05 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the road toward a history of turbulence, this book focuses on what the actors in this research field have identified as the “turbulence problem”. Turbulent flow rose to prominence as one of the most persistent challenges in science. At different times and in different social and disciplinary settings, the nature of this problem has changed in response to changing research agendas. This book does not seek to provide a comprehensive account, but instead an exemplary exposition on the environments in which problems become the subjects of research agendas, with particular emphasis on the first half of the 20th century.
Book Synopsis Relativistic Classical Mechanics and Electrodynamics by : Martin Land
Download or read book Relativistic Classical Mechanics and Electrodynamics written by Martin Land and published by Springer Nature. This book was released on 2022-05-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the -evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five -dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at to an infinitesimally close 4D block universe defined at +. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.
Book Synopsis Computational Line Geometry by : Helmut Pottmann
Download or read book Computational Line Geometry written by Helmut Pottmann and published by Springer Science & Business Media. This book was released on 2001-06-20 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews
Book Synopsis Heart-life in Song by : Frances Harrison Marr
Download or read book Heart-life in Song written by Frances Harrison Marr and published by . This book was released on 1883 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Clifford (Geometric) Algebras and Applications by : Rafal Ablamowicz
Download or read book Lectures on Clifford (Geometric) Algebras and Applications written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
Book Synopsis Complex Semisimple Lie Algebras by : Jean-Pierre Serre
Download or read book Complex Semisimple Lie Algebras written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are a record of a course given in Algiers from lOth to 21st May, 1965. Their contents are as follows. The first two chapters are a summary, without proofs, of the general properties of nilpotent, solvable, and semisimple Lie algebras. These are well-known results, for which the reader can refer to, for example, Chapter I of Bourbaki or my Harvard notes. The theory of complex semisimple algebras occupies Chapters III and IV. The proofs of the main theorems are essentially complete; however, I have also found it useful to mention some complementary results without proof. These are indicated by an asterisk, and the proofs can be found in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. A final chapter shows, without proof, how to pass from Lie algebras to Lie groups (complex-and also compact). It is just an introduction, aimed at guiding the reader towards the topology of Lie groups and the theory of algebraic groups. I am happy to thank MM. Pierre Gigord and Daniel Lehmann, who wrote up a first draft of these notes, and also Mlle. Franr,:oise Pecha who was responsible for the typing of the manuscript.
Book Synopsis Advanced Modern Algebra by : Joseph J. Rotman
Download or read book Advanced Modern Algebra written by Joseph J. Rotman and published by American Mathematical Society. This book was released on 2023-02-22 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
Book Synopsis Categories, Allegories by : P.J. Freyd
Download or read book Categories, Allegories written by P.J. Freyd and published by Elsevier. This book was released on 1990-11-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.
Book Synopsis Nonlinear Parabolic Equations by : Lucio Boccardo
Download or read book Nonlinear Parabolic Equations written by Lucio Boccardo and published by Longman Publishing Group. This book was released on 1987 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
