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: 1086

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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.
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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

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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.
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Lectures on Geometric Methods in Mathematical Physics

Author: Jerrold E. Marsden

Publisher: SIAM

ISBN: 0898711703

Category: Science

Page: 97

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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.
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Variational Problems in Topology

The Geometry of Length, Area and Volume

Author: A.T. Fomenko

Publisher: CRC Press

ISBN: 9782881247408

Category: Mathematics

Page: 226

View: 3198

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Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clean explanation of some of these problems (both solved and unsolved), using current methods and analytical topology. The author's skillful exposition gives an unusual motivation to the theory expounded, and his work is recommended reading for specialists and nonspecialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
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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: 5140

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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.
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Variational Methods in Lorentzian Geometry

Author: Antonio Masiello

Publisher: CRC Press

ISBN: 9780582237995

Category: Mathematics

Page: 200

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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.
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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: 1378

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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.
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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: 3300

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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.
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Modern Methods in Scientific Computing and Applications

Author: Gert Sabidussi

Publisher: Springer Science & Business Media

ISBN: 9781402007811

Category: Computers

Page: 492

View: 5635

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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.
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