Download or read book Time Varying Vector Fields and Their Flows written by Saber Jafarpour and published by Springer. This book was released on 2014-10-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic. The presentation of this material in the real analytic setting is new, as is the manner in which the various hypotheses are unified using functional analysis. Indeed, a major contribution of the book is the coherent development of locally convex topologies for the space of real analytic sections of a vector bundle, and the development of this in a manner that relates easily to classically known topologies in, for example, the finitely differentiable and smooth cases. The tools used in this development will be of use to researchers in the area of geometric functional analysis.
Download or read book Time Varying Vector Fields and Their Flows written by Saber Jafarpour and published by Springer. This book was released on 2014-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic. The presentation of this material in the real analytic setting is new, as is the manner in which the various hypotheses are unified using functional analysis. Indeed, a major contribution of the book is the coherent development of locally convex topologies for the space of real analytic sections of a vector bundle, and the development of this in a manner that relates easily to classically known topologies in, for example, the finitely differentiable and smooth cases. The tools used in this development will be of use to researchers in the area of geometric functional analysis.
Download or read book Topology Based Methods in Visualization II written by Hans-Christian Hege and published by Springer Science & Business Media. This book was released on 2009-02-07 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto newconceptsandsuccessfulapplications. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4–6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopology-basedanalysisandvisualizationof ?uid?owsimulations;twopapersconcernmoregeneraltopologicalalgorithms, while the remaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Download or read book Differential Geometry Manifolds Curves and Surfaces written by Marcel Berger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.
Download or read book Differential Equations Theory and Applications written by David Betounes and published by Springer Science & Business Media. This book was released on 2009-10-31 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.
Download or read book High Performance Visualization written by E. Wes Bethel and published by CRC Press. This book was released on 2012-10-25 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visualization and analysis tools, techniques, and algorithms have undergone a rapid evolution in recent decades to accommodate explosive growth in data size and complexity and to exploit emerging multi- and many-core computational platforms. High Performance Visualization: Enabling Extreme-Scale Scientific Insight focuses on the subset of scientifi
Download or read book Introduction to Smooth Manifolds written by John Lee and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
Download or read book Transport Barriers and Coherent Structures in Flow Data written by George Haller and published by Cambridge University Press. This book was released on 2023-02-28 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore a wealth of proven mathematical methods for uncovering transport barriers in numerical, experimental and observational flow data.
Download or read book Nonlinear and Optimal Control Theory written by and published by Springer Science & Business Media. This book was released on 2008 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book In Situ Visualization for Computational Science written by Hank Childs and published by Springer Nature. This book was released on 2022-05-04 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the emerging field of in situ visualization, i.e. visualizing simulation data as it is generated. In situ visualization is a processing paradigm in response to recent trends in the development of high-performance computers. It has great promise in its ability to access increased temporal resolution and leverage extensive computational power. However, the paradigm also is widely viewed as limiting when it comes to exploration-oriented use cases. Furthermore, it will require visualization systems to become increasingly complex and constrained in usage. As research efforts on in situ visualization are growing, the state of the art and best practices are rapidly maturing. Specifically, this book contains chapters that reflect state-of-the-art research results and best practices in the area of in situ visualization. Our target audience are researchers and practitioners from the areas of mathematics computational science, high-performance computing, and computer science that work on or with in situ techniques, or desire to do so in future.
Download or read book Structural Syntactic and Statistical Pattern Recognition written by Niels da Vitoria Lobo and published by Springer Science & Business Media. This book was released on 2008-11-24 with total page 1029 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Workshop on Structural and Syntactic Pattern Recognition, SSPR 2008 and the 7th International Workshop on Statistical Techniques in Pattern Recognition, SPR 2008, held jointly in Orlando, FL, USA, in December 2008 as a satellite event of the 19th International Conference of Pattern Recognition, ICPR 2008. The 56 revised full papers and 42 revised poster papers presented together with the abstracts of 4 invited papers were carefully reviewed and selected from 175 submissions. The papers are organized in topical sections on graph-based methods, probabilistic and stochastic structural models for PR, image and video analysis, shape analysis, kernel methods, recognition and classification, applications, ensemble methods, feature selection, density estimation and clustering, computer vision and biometrics, pattern recognition and applications, pattern recognition, as well as feature selection and clustering.
Download or read book Topological and Statistical Methods for Complex Data written by Janine Bennett and published by Springer. This book was released on 2014-11-19 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
Download or read book The Geometry of Physics written by Frankel Theodore and published by 清华大学出版社有限公司. This book was released on 2005 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometrical Dynamics of Complex Systems written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical Dynamics of Complex Systems is a graduate?level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By?complexsystems?,inthis book are meant high?dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:engineering,physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi?input multi?output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular ?soft complexity philosophy?, we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high?dimensional nonlinear systems and processes of ?real life? can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well?known that linear systems, which are completely predictable and controllable by de?nition ? live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
Download or read book The Geometry of Physics written by Theodore Frankel and published by Cambridge University Press. This book was released on 2011-11-03 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
