Geometrical Methods in Variational Problems

Author: N.A. Bobylov,S.V. Emel'yanov,S. Korovin

Publisher: Springer Science & Business Media

ISBN: 9401146292

Category: Mathematics

Page: 543

View: 8003

This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods. Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.

Differential Geometric Methods in Mathematical Physics

Proceedings of an International Conference Held at the Technical University of Clausthal, FRG, August 30 - September 2, 1983

Author: Heinz-Dietrich Doebner,Jörg-Dieter Hennig

Publisher: Springer

ISBN: 3540395857

Category: Mathematics

Page: 344

View: 2852


Nonlinear Analysis and Variational Problems

In Honor of George Isac

Author: Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan

Publisher: Springer Science & Business Media

ISBN: 1441901582

Category: Business & Economics

Page: 490

View: 6286

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

Author: Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik

Publisher: Springer Science & Business Media

ISBN: 9783540207283

Category: Mathematics

Page: 190

View: 5140

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties. Most of the material appears here for the first time in print. The intended audience consists of research mathematicians at the graduate or post-graduate level.

Lectures on Geometric Methods in Mathematical Physics

Author: Jerrold E. Marsden

Publisher: SIAM

ISBN: 0898711703

Category: Science

Page: 97

View: 5096

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Variational Methods in Lorentzian Geometry

Author: Antonio Masiello

Publisher: CRC Press

ISBN: 9780582237995

Category: Mathematics

Page: 200

View: 3735

Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.

Geometric Level Set Methods in Imaging, Vision, and Graphics

Author: Stanley Osher,Nikos Paragios

Publisher: Springer Science & Business Media

ISBN: 0387954880

Category: Computers

Page: 513

View: 2690

Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.

Modern Methods in Scientific Computing and Applications

Author: Gert Sabidussi

Publisher: Springer Science & Business Media

ISBN: 9781402007811

Category: Computers

Page: 492

View: 1157

The influence of scientific computing has become very wide over the last few decades: almost every area of science and engineering is greatly influenced by simulations - image processing, thin films, mathematical finance, electrical engineering, moving interfaces and combustion, to name but a few. One half of this book focuses on the techniques of scientific computing: domain decomposition, the absorption of boundary conditions and one-way operators, convergence analysis of multi-grid methods and other multi-grid techniques, dynamical systems, and matrix analysis. The remainder of the book is concerned with combining techniques with concrete applications: stochastic differential equations, image processing, thin films, and asymptotic analysis for combustion problems.

Variational, Geometric, and Level Set Methods in Computer Vision

Third International Workshop, VLSM 2005, Beijing, China, October 16, 2005, Proceedings

Author: Nikos Paragios,Olivier Faugeras,Tony Chan,Christoph Schnoerr

Publisher: Springer Science & Business Media

ISBN: 9783540293484

Category: Computers

Page: 367

View: 9155

This book constitutes the refereed proceedings of the Third International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2005, held in Beijing, China in October 2005 within the scope of ICCV 2005, the International Conference on Computer Vision. The 30 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections and sub-sections as follows: image filtering and reconstruction - image enhancement, inpainting and compression; segmentation and grouping - model-free and model-based segmentation; registration and motion analysis - registration of curves and images, multi-frame segmentation; 3D and reconstruction - computational processes in manifolds, shape from shading, calibration and stereo reconstruction.

Mathematical Methods in Science and Engineering

Author: Selcuk S. Bayin

Publisher: John Wiley & Sons

ISBN: 0470047410

Category: Mathematics

Page: 704

View: 5204

An innovative treatment of mathematical methods for a multidisciplinary audience Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper-level mathematical techniques. This book succeeds in not only being tuned in to the existing practical needs of this multidisciplinary audience, but also plays a role in the development of new interdisciplinary science by introducing new techniques to students and researchers. Mathematical Methods in Science and Engineering's modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. Each chapter serves as a review of its subject and can be read independently, thus it also serves as a valuable reference and refresher for scientists and beginning researchers. There are a growing number of research areas in applied sciences, such as earthquakes, rupture, financial markets, and crashes, that employ the techniques of fractional calculus and path integrals. The book's two unique chapters on these subjects, written in a style that makes these advanced techniques accessible to a multidisciplinary audience, are an indispensable tool for researchers and instructors who want to add something new to their compulsory courses. Mathematical Methods in Science and Engineering includes: * Comprehensive chapters on coordinates and tensors and on continuous groups and their representations * An emphasis on physical motivation and the multidisciplinary nature of the methods discussed * A coherent treatment of carefully selected topics in a style that makes advanced mathematical tools accessible to a multidisciplinary audience * Exercises at the end of every chapter and plentiful examples throughout the book Mathematical Methods in Science and Engineering is not only appropriate as a text for advanced undergraduate and graduate physics programs, but is also appropriate for engineering science and mechanical engineering departments due to its unique chapter coverage and easily accessible style. Readers are expected to be familiar with topics typically covered in the first three years of science and engineering undergraduate programs. Thoroughly class-tested, this book has been used in classes by more than 1,000 students over the past eighteen years.

Variational, Topological, and Partial Order Methods with Their Applications

Author: Zhitao Zhang

Publisher: Springer Science & Business Media

ISBN: 3642307086

Category: Mathematics

Page: 332

View: 4245

Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.

Variational Methods for Eigenvalue Approximation

Author: H. F. Weinberger

Publisher: SIAM

ISBN: 089871012X

Category: Mathematics

Page: 160

View: 675

Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships.

Mathematical Methods in Physics

Distributions, Hilbert Space Operators, and Variational Methods

Author: Philippe Blanchard,Erwin Bruening

Publisher: Springer Science & Business Media

ISBN: 9780817642280

Category: Mathematics

Page: 471

View: 8408

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Variational Problems in Riemannian Geometry

Bubbles, Scans and Geometric Flows

Author: Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui

Publisher: Springer Science & Business Media

ISBN: 9783764324322

Category: Mathematics

Page: 150

View: 5892

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. The articles provide a balance between introductory surveys and the most recent research, with a unique perspective on singular phenomena. Notions such as scans and the study of the evolution by curvature of networks of curves are completely new and lead the reader to the frontiers of the domain. The intended readership are postgraduate students and researchers in the fields of elliptic and parabolic partial differential equations that arise from variational problems, as well as researchers in related fields such as particle physics and optimization.

Duality Principles in Nonconvex Systems

Theory, Methods and Applications

Author: David Yang Gao

Publisher: Springer Science & Business Media

ISBN: 9780792361459

Category: Mathematics

Page: 454

View: 2278

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Recent Developments and Innovative Applications in Computational Mechanics

Author: Dana Mueller-Hoeppe,Stefan Loehnert,Stefanie Reese

Publisher: Springer Science & Business Media

ISBN: 9783642174841

Category: Technology & Engineering

Page: 340

View: 5549

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 60th birthday. It contains contributions from friends and collaborators as well as current and former PhD students from almost all continents. As a very diverse group of people, the authors cover a wide range of topics from fundamental research to industrial applications: contact mechanics, finite element technology, micromechanics, multiscale approaches, particle methods, isogeometric analysis, stochastic methods and further research interests. In summary, the volume presents an overview of the international state of the art in computational mechanics, both in academia and industry.

Boundary Value Problems and Markov Processes

Author: Kazuaki Taira

Publisher: Springer Science & Business Media

ISBN: 3642016766

Category: Mathematics

Page: 192

View: 5885

This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.

Variational Principles in Mathematical Physics, Geometry, and Economics

Qualitative Analysis of Nonlinear Equations and Unilateral Problems

Author: Alexandru Kristály,Vicenţiu D. Rădulescu,Csaba Varga

Publisher: Cambridge University Press

ISBN: 0521117828

Category: Mathematics

Page: 368

View: 3521

A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Singularities in PDE and the Calculus of Variations

Author: Stanley Alama,Lia Bronsard,Peter J. Sternberg

Publisher: American Mathematical Soc.

ISBN: 9780821873311

Category: Mathematics

Page: 267

View: 3213

This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.

Mathematical Methods in Computer Vision

Author: Peter J. Olver,Allen Tannenbaum

Publisher: Springer Science & Business Media

ISBN: 9780387004976

Category: Business & Economics

Page: 153

View: 8954

This volume contains papers presented at two successful workshops integral to the IMA annual program on Mathematics in Multimedia, 2000- 2001: Image Processing and Low Level Vision, and Image Analysis and High Level Vision.