Mathematics

Harmonic Maps, Conservation Laws and Moving Frames

Author: Fr D Ric H Lein

Publisher: Cambridge University Press

ISBN: 9780521811606

Category: Mathematics

Page: 264

View: 6227

Accessible and pedagogical introduction to the theory of harmonic maps, covering recent results and applications.
Mathematics

Harmonic Maps, Conservation Laws and Moving Frames

Author: Fr D Ric H Lein

Publisher: Cambridge University Press

ISBN: 9780521811606

Category: Mathematics

Page: 264

View: 5854

Accessible and pedagogical introduction to the theory of harmonic maps, covering recent results and applications.
Mathematics

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

Author: Yuan Chiang

Publisher: Springer Science & Business Media

ISBN: 3034805349

Category: Mathematics

Page: 399

View: 4237

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.
Mathematics

Handbook of Global Analysis

Author: Demeter Krupka,David Saunders

Publisher: Elsevier

ISBN: 9780080556734

Category: Mathematics

Page: 1244

View: 9094

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents
Mathematics

Topics in Modern Regularity Theory

Author: Giuseppe Mingione

Publisher: Springer Science & Business Media

ISBN: 887642427X

Category: Mathematics

Page: 0

View: 5035

This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.
Mathematics

Numerical Methods for Nonlinear Partial Differential Equations

Author: Sören Bartels

Publisher: Springer

ISBN: 3319137972

Category: Mathematics

Page: 393

View: 4882

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Mathematics

The Lévy Laplacian

Author: M. N. Feller

Publisher: Cambridge University Press

ISBN: 9781139447966

Category: Mathematics

Page: N.A

View: 3375

The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Lévy–Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy–Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang–Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory.
Mathematics

Dynamics of Linear Operators

Author: Frédéric Bayart,Étienne Matheron

Publisher: Cambridge University Press

ISBN: 0521514967

Category: Mathematics

Page: 337

View: 4363

The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
Mathematics

Linear and Projective Representations of Symmetric Groups

Author: Alexander Kleshchev

Publisher: Cambridge University Press

ISBN: 9781139444064

Category: Mathematics

Page: N.A

View: 9081

The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.
Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1487

Computers

Harmonic Vector Fields

Variational Principles and Differential Geometry

Author: Sorin Dragomir,Domenico Perrone

Publisher: Elsevier

ISBN: 0124158269

Category: Computers

Page: 508

View: 5198

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector fields with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods
Science

An Introduction to Mechanics

Author: Daniel Kleppner,Robert Kolenkow

Publisher: Cambridge University Press

ISBN: 0521198119

Category: Science

Page: 566

View: 5794

This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.
Mathematics

Geometric Wave Equations

Author: Jalal M. Ihsan Shatah,Michael Struwe

Publisher: American Mathematical Soc.

ISBN: 0821827499

Category: Mathematics

Page: 137

View: 3571

This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Science

Structure and Interpretation of Classical Mechanics

Author: Gerald Jay Sussman,Jack Wisdom

Publisher: MIT Press

ISBN: 0262028964

Category: Science

Page: 584

View: 5850

The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation.
Science

Mathematical Analysis of Evolution, Information, and Complexity

Author: Wolfgang Arendt,Wolfgang P. Schleich

Publisher: John Wiley & Sons

ISBN: 3527628037

Category: Science

Page: 502

View: 8978

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.