Download or read book Sobolev Maps to the Circle written by Haim Brezis and published by Springer Nature. This book was released on 2022-01-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The “Complements and Open Problems” sections provide short introductions to various subsequent developments or related topics, and suggest newdirections of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Download or read book Perspectives in Nonlinear Partial Differential Equations written by Henri Berestycki and published by American Mathematical Soc.. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.
Download or read book Language Mapping written by Jürgen Erich Schmidt and published by Walter de Gruyter. This book was released on 2011-03-30 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Language Mapping aims to explore the core methodological and theoretical approaches of linguistic cartography. In both empirical and theoretical linguistics, the spatial variation of language is of increasing interest and the visualization of language in space is therefore also of growing significance. It is the precondition for correct data interpretation. But how does it work? What has to be considered when drawing a map? And how has the problem been tackled so far? This book provides answers to such questions by taking a closer look at the theoretical issues surrounding cartography and at the concrete practice of mapping. The fundamental issues raised are addressed particularly well, since linguistic geography is not only one of the domains with a lengthy tradition, it is also one of the most progressive fields in linguistics. At the same time, because of their visual primacy, linguistic maps directly confront the challenges of human perception and aesthetics. In this context, envisioning the fruits of language mapping is a fascinating and inspiring endeavor, not just for experts. With its accessible texts and wealth of full-color images, the handbook not only represents a comprehensive manual serving the interests of a variety of readers, it also fills a gap in the ongoing linguistic discourse.
Download or read book Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps written by Viviane Baladi and published by Springer. This book was released on 2018-05-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
Download or read book Homotopy Methods in Topological Fixed and Periodic Points Theory written by Jerzy Jezierski and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.
Download or read book Spectral Theory and Geometric Analysis written by Mikhail Aleksandrovich Shubin and published by American Mathematical Soc.. This book was released on 2011-02-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Spaces and Partial Differential Equations written by Ali Taheri and published by OUP Oxford. This book was released on 2015-07-30 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
Download or read book Annales written by and published by . This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Current Research in Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-18 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader’s understanding of theories, methods, and techniques utilized to solve significant problems. Topics include: Sobolev Spaces Maximal monotone operators A theorem of Brezis-Nirenberg Operator-norm convergence of the Trotter product formula Elliptic operators with infinitely many variables Pseudo-and quasiconvexities for nonsmooth function Anisotropic surface measures Eulerian and Lagrangian variables Multiple periodic solutions of Lagrangian systems Porous medium equation Nondiscrete Lassonde-Revalski principle Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg’s fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.
Download or read book Annales Academiae Scientiarum Fennicae written by and published by . This book was released on 1995 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavelet written by Carmen Hurley & and published by Scientific e-Resources. This book was released on 2018-11-11 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of "e;ondelettes"e; or "e;wavelets"e; started from the investigation of time-frequency signal analysis, wave engendering, and examining hypothesis. One of the principle explanations behind the disclosure of wavelets and wavelet changes is that the Fourier change analysis does not contain the neighborhood data of signals. So the Fourier change can't be utilized for examining signals in a joint time and frequency area. In 1982, Jean MorIet, in a joint effort with a gathering of French designers, first presented the possibility of wavelets as a group of capacities built by utilizing interpretation and expansion of a solitary capacity, called the mother wavelet, for the analysis of nonstationary signals. Wavelet analysis is an energizing new technique for taking care of troublesome issues in science, material science, and building, with present day applications as various as wave spread, information pressure, picture preparing, design acknowledgment, PC illustrations, the location of air ship and submarines, and change in CAT filters and other restorative picture innovation. Wavelets permit complex data, for example, music, discourse, pictures, and examples to be deteriorated into basic structures, called the central building hinders, at various positions and scales and in this manner remade with high accuracy.
Download or read book Mathematical Quantum Field Theory and Related Topics written by Joel S. Feldman and published by American Mathematical Soc.. This book was released on 1988 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for researchers and advanced graduate students in mathematical physics, this book constitutes the proceedings of a conference on mathematical quantum field theory and related topics. The conference was held at the Centre de Recherches Matheematiques of the Universite de Montreal in September 1987.
Download or read book Conformal Geometry written by Miao Jin and published by Springer. This book was released on 2018-04-10 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text. The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science, applied mathematics, and engineering.
Download or read book Ginzburg Landau Vortices written by Fabrice Bethuel and published by Birkhäuser. This book was released on 2017-09-21 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
Download or read book Hyperspatial Dynamics written by Dr. Marco Bitetto and published by Dr. Marco A. V. Bitetto. This book was released on 2020-02-14 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation has as its central focus the study of hyperspatial dynamics and as such makes use of mathematics in such an understanding and also the MAXYMA artificial intelligence computer simulation and programming language. As such, it will both discuss the use of MAXYMA in the understanding of hyperspatial dynamics and also include MAXYMA programs as well. This dissertation will conclude with a discussion of hyperspace and how one can travel through hyperspace and why one would want to travel through hyperspace.
