Geometric Asymptotics

Author : Victor Guillemin,Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 500 pages
File Size : 43,5 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821816332

Get Book

Geometric Asymptotics by Victor Guillemin,Shlomo Sternberg Pdf

Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years--the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence.

Author : N.M. Ercolani,I.R. Gabitov,C.D. Levermore,D. Serre
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461524748

Get Book

Singular Limits of Dispersive Waves by N.M. Ercolani,I.R. Gabitov,C.D. Levermore,D. Serre Pdf

Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991

Author : Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Publisher : American Mathematical Society
Page : 645 pages
File Size : 51,6 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470463601

Get Book

Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman Pdf

This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.

Author : Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 45,7 Mb
Release : 2016-05-18
Category : Geometric analysis
ISBN : 9781470423131

Get Book

Geometric Analysis by Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum Pdf

This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Author : Sultan Catto,Alvany Rocha
Publisher : World Scientific
Page : 1228 pages
File Size : 41,9 Mb
Release : 1992-01-27
Category : Electronic
ISBN : 9789814555500

Get Book

Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) by Sultan Catto,Alvany Rocha Pdf

This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.

Author : Andrej Bóna,Michael A Slawinski
Publisher : World Scientific Publishing Company
Page : 295 pages
File Size : 55,9 Mb
Release : 2011-05-09
Category : Science
ISBN : 9789813107823

Get Book

Wavefronts and Rays as Characteristics and Asymptotics by Andrej Bóna,Michael A Slawinski Pdf

This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.

Author : Andrej Bona,Michael A Slawinski
Publisher : World Scientific
Page : 357 pages
File Size : 44,6 Mb
Release : 2020-09-24
Category : Science
ISBN : 9789811226489

Get Book

Wavefronts And Rays As Characteristics And Asymptotics (Third Edition) by Andrej Bona,Michael A Slawinski Pdf

Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.

Author : Andrej Bóna,Michael A Slawinski
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 46,8 Mb
Release : 2014-12-30
Category : Science
ISBN : 9789814651554

Get Book

Wavefronts and Rays as Characteristics and Asymptotics by Andrej Bóna,Michael A Slawinski Pdf

This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.

Author : Anonim
Publisher : Unknown
Page : 285 pages
File Size : 55,9 Mb
Release : 1962
Category : Differential equations, Nonlinear
ISBN : 0821821091

Get Book

Translations of Mathematical Monographs by Anonim Pdf

Author : Victor Ivrii
Publisher : Springer
Page : 244 pages
File Size : 42,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540389118

Get Book

Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds with Boundary by Victor Ivrii Pdf

a

Author : Pierre H. Berard
Publisher : Springer
Page : 284 pages
File Size : 44,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540409588

Get Book

Spectral Geometry by Pierre H. Berard Pdf

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 45,7 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

Get Book

Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

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.

Author : Eric Grinberg
Publisher : American Mathematical Soc.
Page : 167 pages
File Size : 46,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851531

Get Book

Geometric Analysis by Eric Grinberg Pdf

This volume contains the refereed proceedings of the Special Session on Geometric Analysis held at the AMS meeting in Philadelphia in October 1991. The term ``geometric analysis'' is being used with increasing frequency in the mathematical community, but its meaning is not entirely fixed. The papers in this collection should help to better define the notion of geometric analysis by illustrating emerging trends in the subject. The topics covered range over a broad spectrum: integral geometry, Radon transforms, geometric inequalities, microlocal analysis, harmonic analysis, analysis on Lie groups and symmetric spaces, and more. Containing articles varying from the expository to the technical, this book presents the latest results in a broad range of analytic and geometric topics.

Author : Reuven Segev
Publisher : Springer Nature
Page : 410 pages
File Size : 43,6 Mb
Release : 2023-10-31
Category : Mathematics
ISBN : 9783031356551

Get Book

Foundations of Geometric Continuum Mechanics by Reuven Segev Pdf

This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.

Author : N.E. Hurt
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 53,8 Mb
Release : 1982-12-31
Category : Mathematics
ISBN : 9027714266

Get Book

Geometric Quantization in Action by N.E. Hurt Pdf

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.