Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms
Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms

Author: John Neuberger

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 298

ISBN-13: 0821833391

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This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.

Recent Advances in Operator-Related Function Theory
Recent Advances in Operator-Related Function Theory

Author: Alec L. Matheson

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 230

ISBN-13: 082183925X

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The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.

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.

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.

Groups, Languages, Algorithms
Groups, Languages, Algorithms

Author: Alexandre Borovik

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 360

ISBN-13: 0821836188

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Since the pioneering works of Novikov and Maltsev, group theory has been a testing ground for mathematical logic in its many manifestations, from the theory of algorithms to model theory. The interaction between logic and group theory led to many prominent results which enriched both disciplines. This volume reflects the major themes of the American Mathematical Society/Association for Symbolic Logic Joint Special Session (Baltimore, MD), Interactions between Logic, Group Theory and Computer Science. Included are papers devoted to the development of techniques used for the interaction of group theory and logic. It is suitable for graduate students and researchers interested in algorithmic and combinatorial group theory. A complement to this work is Volume 349 in the AMS series, Contemporary Mathematics, Computational and Experimental Group Theory, which arose from the same meeting and concentrates on the interaction of group theory and computer science.

Geometric Methods in Group Theory
Geometric Methods in Group Theory

Author: José Burillo

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 242

ISBN-13: 0821833626

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This volume presents articles by speakers and participants in two AMS special sessions, Geometric Group Theory and Geometric Methods in Group Theory, held respectively at Northeastern University (Boston, MA) and at Universidad de Sevilla (Spain). The expository and survey articles in the book cover a wide range of topics, making it suitable for researchers and graduate students interested in group theory.

BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS
BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS

Author: Goong Chen

Publisher: Springer Science & Business Media

Published: 2010-09-01

Total Pages: 733

ISBN-13: 9491216279

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Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.

Analyzable Functions and Applications
Analyzable Functions and Applications

Author: Ovidiu Costin

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 384

ISBN-13: 0821834193

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The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle. Similar techniques and conceptsin analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. Thisvolume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.

Integer Points in Polyhedra -- Geometry, Number Theory, Algebra, Optimization
Integer Points in Polyhedra -- Geometry, Number Theory, Algebra, Optimization

Author: Alexander Barvinok

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 210

ISBN-13: 0821834592

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The AMS-IMS-SIAM Summer Research Conference on Integer Points in Polyhedra took place in Snowbird (UT). This proceedings volume contains original research and survey articles stemming from that event. Topics covered include commutative algebra, optimization, discrete geometry, statistics, representation theory, and symplectic geometry. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.

In the Tradition of Ahlfors and Bers, III
In the Tradition of Ahlfors and Bers, III

Author: William Abikoff

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 364

ISBN-13: 0821836072

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Contains proceedings that reflects the 2001 Ahlfors-Bers Colloquium held at the University of Connecticut (Storrs). This book is suitable for graduate students and researchers interested in complex analysis.