Singular Sets Of Minimizers For The Mumford Shah Functional

Author : Guy David
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 43,5 Mb
Release : 2006-03-10
Category : Mathematics
ISBN : 9783764373023

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Singular Sets of Minimizers for the Mumford-Shah Functional by Guy David Pdf

The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. It is largely self-contained, and should be accessible to graduate students in analysis. The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

Author : Felipe Cucker,Michael Shub
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642605390

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Foundations of Computational Mathematics by Felipe Cucker,Michael Shub Pdf

This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics conference held at IMPA in Rio de Janeiro in January 1997. Some ofthe others are published in the December 1996 issue of the Journal of Complexity. Both of these publications were available and distributed at the meeting. Even in this aspect we hope to have achieved a synthesis of the mathematics and computer science cultures as well as of the disciplines. The reaction to the Park City meeting on Mathematics of Numerical Analy sis: Real Number Algorithms which was chaired by Steve Smale and had around 275 participants, was very enthusiastic. At the suggestion of Narendra Karmar mar a lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale decided to try to hold a periodic meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting. This is then the first edition of FoCM as such. It has been organized around a small collection of workshops, namely - Systems of algebraic equations and computational algebraic geometry - Homotopy methods and real machines - Information-based complexity - Numerical linear algebra - Approximation and PDEs - Optimization - Differential equations and dynamical systems - Relations to computer science - Vision and related computational tools There were also twelve plenary speakers.

Author : Pertti Mattila
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,6 Mb
Release : 1999-02-25
Category : Mathematics
ISBN : 9781316583692

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Geometry of Sets and Measures in Euclidean Spaces by Pertti Mattila Pdf

Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

Author : Jürgen Beyerer,Marco Huber
Publisher : KIT Scientific Publishing
Page : 258 pages
File Size : 48,7 Mb
Release : 2014-10-16
Category : Computers
ISBN : 9783866444690

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Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory by Jürgen Beyerer,Marco Huber Pdf

The joint workshop of the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, and the Vision and Fusion Laboratory (Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)), is organized annually since 2005 with the aim to report on the latest research and development findings of the doctoral students of both institutions. This book provides a collection of 16 technical reports on the research results presented on the 2009 workshop.

Author : Pertti Mattila
Publisher : Cambridge University Press
Page : 182 pages
File Size : 52,9 Mb
Release : 2023-01-12
Category : Mathematics
ISBN : 9781009288095

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Rectifiability by Pertti Mattila Pdf

Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside.

Author : Anonim
Publisher : Unknown
Page : 538 pages
File Size : 45,8 Mb
Release : 1995
Category : Aeronautics
ISBN : MINN:31951D01402122V

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Scientific and Technical Aerospace Reports by Anonim Pdf

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Author : Michael Benedicks,Peter Jones,Stanislav Smirnov
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 47,7 Mb
Release : 2006-06-01
Category : Mathematics
ISBN : 9783540304340

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Perspectives in Analysis by Michael Benedicks,Peter Jones,Stanislav Smirnov Pdf

The Conference “Perspectives in Analysis” was held during May 26–28, 2003 at the Royal Institute of Technology in Stockholm, Sweden. The purpose of the conference was to consider the future of analysis along with its relations to other areas of mathematics and physics, and to celebrate the seventy-?fth birthday of Lennart Carleson. The scienti?c theme was one with which the name of Lennart Carleson has been associated for over ?fty years. His modus operandi has long been to carry out a twofold approach to the selection of research problems. First one should look for promising new areas of ana- sis, especially those having close contact with physically oriented problems of geometric character. The second step is to select a core set of problems that require new techniques for their resolutions. After making a central contri- tion, Lennart would usually move on to a new area, though he might return to the topic of his previous work if new techniques were developed that could break old mathematical log jams. Lennart’s operating approach is based on fundamental realities of modern mathematics as well as his own inner c- victions. Here we ?rst refer to an empirical fact of mathematical research: All topics have a ?nite half-life, with ?fteen years being an upper bound for most areas. After that time it is usually a good idea to move on to so- thing new.

Author : Antonio Ambrosetti,Andrea Malchiodi
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 47,7 Mb
Release : 2005-11-18
Category : Mathematics
ISBN : 3764373210

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Perturbation Methods and Semilinear Elliptic Problems on R^n by Antonio Ambrosetti,Andrea Malchiodi Pdf

Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.

Author : José Seade
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,8 Mb
Release : 2005-11-18
Category : Mathematics
ISBN : 3764373229

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On the Topology of Isolated Singularities in Analytic Spaces by José Seade Pdf

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.

Author : Hiromichi Itou,Shiro Hirano,Masato Kimura,Victor A. Kovtunenko,Alexandr M. Khludnev
Publisher : Springer Nature
Page : 199 pages
File Size : 42,8 Mb
Release : 2020-08-29
Category : Science
ISBN : 9789811560620

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Mathematical Analysis of Continuum Mechanics and Industrial Applications III by Hiromichi Itou,Shiro Hirano,Masato Kimura,Victor A. Kovtunenko,Alexandr M. Khludnev Pdf

This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

Author : John J. Benedetto
Publisher : CRC Press
Page : 668 pages
File Size : 51,5 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781000674156

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Journal of Fourier Analysis and Applications Special Issue by John J. Benedetto Pdf

The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.

Author : Nicola Fusco,Aldo Pratelli
Publisher : Springer
Page : 237 pages
File Size : 55,5 Mb
Release : 2017-02-02
Category : Mathematics
ISBN : 9788876425936

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Free Discontinuity Problems by Nicola Fusco,Aldo Pratelli Pdf

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Author : Kossuth Lajos Tudományegyetem. Matematikai Intézet
Publisher : Unknown
Page : 536 pages
File Size : 44,6 Mb
Release : 2006
Category : Mathematics
ISBN : UCBK:C078318500

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Publicationes mathematicae by Kossuth Lajos Tudományegyetem. Matematikai Intézet Pdf

Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 630 pages
File Size : 55,6 Mb
Release : 2006-08-08
Category : Mathematics
ISBN : 0080463827

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Handbook of Differential Equations: Stationary Partial Differential Equations by Michel Chipot,Pavol Quittner Pdf

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics