Recent Developments in Integrable Systems and Riemann-Hilbert Problems
Recent Developments in Integrable Systems and Riemann-Hilbert Problems

Author: Kenneth T-R McLaughlin

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 198

ISBN-13: 0821832034

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This volume is a collection of papers presented at a special session on integrable systems and Riemann-Hilbert problems. The goal of the meeting was to foster new research by bringing together experts from different areas. Their contributions to the volume provide a useful portrait of the breadth and depth of integrable systems. Topics covered include discrete Painleve equations, integrable nonlinear partial differential equations, random matrix theory, Bose-Einstein condensation, spectral and inverse spectral theory, and last passage percolation models. In most of these articles, the Riemann-Hilbert problem approach plays a central role, which is powerful both analytically and algebraically. The book is intended for graduate students and researchers interested in integrable systems and its applications.

Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions

Author: Thomas Trogdon

Publisher: SIAM

Published: 2015-12-22

Total Pages: 370

ISBN-13: 1611974194

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Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.?

Current Trends in Scientific Computing
Current Trends in Scientific Computing

Author: Zhangxin Chen

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 386

ISBN-13: 0821832611

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This volume contains 36 research papers written by prominent researchers. The papers are based on a large satellite conference on scientific computing held at the International Congress of Mathematics (ICM) in Xi'an, China. Topics covered include a variety of subjects in modern scientific computing and its applications, such as numerical discretization methods, linear solvers, parallel computing, high performance computing, and applications to solid and fluid mechanics, energy, environment, and semiconductors. The book will serve as an excellent reference work for graduate students and researchers working with scientific computing for problems in science and engineering.

Inverse Problems: Theory and Applications
Inverse Problems: Theory and Applications

Author: Giovanni Alessandrini

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 228

ISBN-13: 0821833677

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This volume presents the proceedings of a workshop on Inverse Problems and Applications and a special session on Inverse Boundary Problems and Applications. Inverse problems arise in practical situations, such as medical imaging, exploration geophysics, and non-destructive evaluation where measurements made in the exterior of a body are used to deduce properties of the hidden interior. A large class of inverse problems arise from a physical situation modeled by partial differential equations. The inverse problem is to determine some coefficients of the equation given some information about solutions. Analysis of such problems is a fertile area for interaction between pure and applied mathematics. This interplay is well represented in this volume where several theoretical and applied aspects of inverse problems are considered. The book includes articles on a broad range of inverse problems including the inverse conductivity problem, inverse problems for Maxwell's equations, time reversal mirrors, ultrasound using elastic pressure waves, inverse problems arising in the environment, inverse scattering for the three-body problem, and optical tomography. Also included are several articles on unique continuation and on the study of propagation of singularities for hyperbolic equations in anisotropic media. This volume is suitable for graduate students and research mathematicians interested in inverse problems and applications.

Noncompact Problems at the Intersection of Geometry, Analysis, and Topology
Noncompact Problems at the Intersection of Geometry, Analysis, and Topology

Author: Abbas Bahri

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 266

ISBN-13: 0821836358

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This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Recent Developments in Integrable Systems and Related Topics of Mathematical Physics
Recent Developments in Integrable Systems and Related Topics of Mathematical Physics

Author: Victor M. Buchstaber

Publisher: Springer

Published: 2018-12-30

Total Pages: 226

ISBN-13: 3030048071

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This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.

Recent Advances in Riemannian and Lorentzian Geometries
Recent Advances in Riemannian and Lorentzian Geometries

Author: Krishan L. Duggal

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 214

ISBN-13: 0821833790

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This volume covers material presented by invited speakers at the AMS special session on Riemannian and Lorentzian geometries held at the annual Joint Mathematics Meetings in Baltimore. Topics covered include classification of curvature-related operators, curvature-homogeneous Einstein 4-manifolds, linear stability/instability singularity and hyperbolic operators of spacetimes, spectral geometry of holomorphic manifolds, cut loci of nilpotent Lie groups, conformal geometry of almost Hermitian manifolds, and also submanifolds of complex and contact spaces. This volume can serve as a good reference source and provide indications for further research. It is suitable for graduate students and research mathematicians interested in differential geometry.

Commutative Algebra
Commutative Algebra

Author: Luchezar L. Avramov

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 376

ISBN-13: 0821832336

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This volume contains 21 articles based on invited talks given at two international conferences held in France in 2001. Most of the papers are devoted to various problems of commutative algebra and their relation to properties of algebraic varieties. The book is suitable for graduate students and research mathematicians interested in commutative algebra and algebraic geometry.

The $p$-Harmonic Equation and Recent Advances in Analysis
The $p$-Harmonic Equation and Recent Advances in Analysis

Author: Pietro Poggi-Corradini

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 226

ISBN-13: 0821836102

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Comprised of papers from the IIIrd Prairie Analysis Seminar held at Kansas State University, this book reflects the many directions of current research in harmonic analysis and partial differential equations. Included is the work of the distinguished main speaker, Tadeusz Iwaniec, his invited guests John Lewis and Juan Manfredi, and many other leading researchers. The main topic is the so-called p-harmonic equation, which is a family of nonlinear partial differential equations generalizing the usual Laplace equation. This study of p-harmonic equations touches upon many areas of analysis with deep relations to functional analysis, potential theory, and calculus of variations. The material is suitable for graduate students and research mathematicians interested in harmonic analysis and partial differential equations.