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: 9121

Continue Reading →

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: 4226

Continue Reading →

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: 1379

Continue Reading →

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: 5582

Continue Reading →

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: 4315

Continue Reading →

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: 2692

Continue Reading →

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: 674

Continue Reading →

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: 4190

Continue Reading →

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: 6806

Continue Reading →

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: 6390

Continue Reading →

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: 9830

Continue Reading →

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: 8813

Continue Reading →

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: 1461200490
Category: Mathematics
Page: 471
View: 620

Continue Reading →

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: 2221

Continue Reading →

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.

Variational Problems in Differential Geometry


Author: Roger Bielawski,Kevin Houston,Martin Speight
Publisher: Cambridge University Press
ISBN: 1139504118
Category: Mathematics
Page: N.A
View: 588

Continue Reading →

The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kähler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduate students and postdoctoral researchers.

Boundary Value Problems and Markov Processes


Author: Kazuaki Taira
Publisher: Springer Science & Business Media
ISBN: 3642016766
Category: Mathematics
Page: 192
View: 5471

Continue Reading →

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: 4772

Continue Reading →

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

Mathematical Methods in Computer Vision


Author: Peter J. Olver,Allen Tannenbaum
Publisher: Springer Science & Business Media
ISBN: 9780387004976
Category: Business & Economics
Page: 153
View: 1571

Continue Reading →

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.

Variational Analysis and Aerospace Engineering

Mathematical Challenges for the Aerospace of the Future
Author: Aldo Frediani,Bijan Mohammadi,Olivier Pironneau,Vittorio Cipolla
Publisher: Springer
ISBN: 3319456806
Category: Mathematics
Page: 524
View: 2435

Continue Reading →

This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

Variational Methods in Imaging


Author: Otmar Scherzer,Markus Grasmair,Harald Grossauer,Markus Haltmeier,Frank Lenzen
Publisher: Springer Science & Business Media
ISBN: 0387692770
Category: Mathematics
Page: 320
View: 1726

Continue Reading →

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.