Approximation Of Free Discontinuity Problems

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Approximation of Free-Discontinuity Problems

Andrea Braides
Approximation of Free Discontinuity Problems Book PDF

Author : Andrea Braides
Publisher : Springer
Page : 160 pages
File Size : 52,5 Mb
Release : 2006-11-13
Category : Mathematics
ISBN : 9783540687146

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Approximation of Free-Discontinuity Problems by Andrea Braides Pdf

Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.

Foundations of Computational Mathematics

Felipe Cucker,Michael Shub
Foundations of Computational Mathematics Book PDF

Author : Felipe Cucker,Michael Shub
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 48,8 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.

Gamma-Convergence for Beginners

Andrea Braides
Gamma Convergence for Beginners Book PDF

Author : Andrea Braides
Publisher : Clarendon Press
Page : 230 pages
File Size : 40,7 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9780191523199

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Gamma-Convergence for Beginners by Andrea Braides Pdf

The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.

Free Discontinuity Problems

Nicola Fusco,Aldo Pratelli
Free Discontinuity Problems Book PDF

Author : Nicola Fusco,Aldo Pratelli
Publisher : Springer
Page : 237 pages
File Size : 51,6 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.

European Congress of Mathematics

Antal Balog,D. Szasz,A. Recski,G.D.H. Katona
European Congress of Mathematics Book PDF

Author : Antal Balog,D. Szasz,A. Recski,G.D.H. Katona
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 43,8 Mb
Release : 1998-07-21
Category : Mathematics
ISBN : 3764354976

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European Congress of Mathematics by Antal Balog,D. Szasz,A. Recski,G.D.H. Katona Pdf

This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

Advances in Image and Video Segmentation

Zhang, Yu-Jin
Advances in Image and Video Segmentation Book PDF

Author : Zhang, Yu-Jin
Publisher : IGI Global
Page : 472 pages
File Size : 41,9 Mb
Release : 2006-05-31
Category : Technology & Engineering
ISBN : 9781591407553

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Advances in Image and Video Segmentation by Zhang, Yu-Jin Pdf

"This book attempts to bring together a selection of the latest results of state-of-the art research in image and video segmentation, one of the most critical tasks of image and video analysis that has the objective of extracting information (represented by data) from an image or a sequence of images (video)"--Provided by publisher.

Variational and Free Boundary Problems

Avner Friedman,Joel Spruck
Variational and Free Boundary Problems Book PDF

Author : Avner Friedman,Joel Spruck
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461383574

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Variational and Free Boundary Problems by Avner Friedman,Joel Spruck Pdf

This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.

Calculus of Variations and Partial Differential Equations

Luigi Ambrosio,Norman Dancer
Calculus of Variations and Partial Differential Equations Book PDF

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 46,6 Mb
Release : 2000-01-24
Category : Mathematics
ISBN : 3540648038

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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.

Topics on Concentration Phenomena and Problems with Multiple Scales

Andrea Braides,Valeria Chiadò Piat
Topics on Concentration Phenomena and Problems with Multiple Scales Book PDF

Author : Andrea Braides,Valeria Chiadò Piat
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 51,6 Mb
Release : 2006-11-22
Category : Mathematics
ISBN : 9783540365464

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Topics on Concentration Phenomena and Problems with Multiple Scales by Andrea Braides,Valeria Chiadò Piat Pdf

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

Handbook of Differential Equations: Stationary Partial Differential Equations

Michel Chipot,Pavol Quittner
Handbook of Differential Equations Stationary Partial Differential Equations Book PDF

Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 630 pages
File Size : 47,7 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

Scale Space and Variational Methods in Computer Vision

Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie
Scale Space and Variational Methods in Computer Vision Book PDF

Author : Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie
Publisher : Springer
Page : 870 pages
File Size : 53,9 Mb
Release : 2009-05-24
Category : Computers
ISBN : 9783642022562

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Scale Space and Variational Methods in Computer Vision by Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie Pdf

This book contains 71 original, scienti?c articles that address state-of-the-art researchrelatedto scale space and variationalmethods for image processing and computer vision. Topics covered in the book range from mathematical analysis of both established and new models, fast numerical methods, image analysis, segmentation, registration, surface and shape construction and processing, to real applications in medical imaging and computer vision. The ideas of scale spaceandvariationalmethodsrelatedtopartialdi?erentialequationsarecentral concepts. The papers re?ect the newest developments in these ?elds and also point to the latest literature. All the papers were submitted to the Second International Conference on Scale Space and Variational Methods in Computer Vision, which took place in Voss, Norway, during June 1–5, 2009. The papers underwent a peer review process similar to that of high-level journals in the ?eld. We thank the authors, the Scienti?c Committee, the Program Committee and the reviewers for their hard work and helpful collaboration. Their contribution has been crucial for the e?cient processing of this book, and for the success of the conference.

Geodesy for Planet Earth

Steve Kenyon,Maria Christina Pacino,Urs Marti
Geodesy for Planet Earth Book PDF

Author : Steve Kenyon,Maria Christina Pacino,Urs Marti
Publisher : Springer Science & Business Media
Page : 992 pages
File Size : 47,7 Mb
Release : 2012-01-26
Category : Science
ISBN : 9783642203381

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Geodesy for Planet Earth by Steve Kenyon,Maria Christina Pacino,Urs Marti Pdf

These proceedings include the written version of 130 papers presented at the International Association of Geodesy IAG2009 "Geodesy for Planet Earth" Scientific Assembly. It was held 31 August to 4 September 2009 in Buenos Aires, Argentina. The theme "Geodesy for Planet Earth" was selected to follow the International Year of Planet Earth 2007-2009 goals of utilizing the knowledge of the world’s geoscientists to improve society for current and future generations. The International Year started in January 2007 and ran thru 2009 which coincided with the IAG2009 Scientific Assembly, one of the largest and most significant meetings of the Geodesy community held every 4 years. The IAG2009 Scientific Assembly was organized into eight Sessions. Four of the Sessions of IAG2009 were based on the IAG Structure (i.e. one per Commission) and covered Reference Frames, Gravity Field, Earth Rotation and Geodynamics, and Positioning and Applications. Since IAG2009 was taking place in the great Argentine city of Buenos Aires, a Session was devoted to the Geodesy of Latin America. A Session dedicated to the IAG’s Global Geodetic Observing System (GGOS), the primary observing system focused on the multidisciplinary research being done in Geodesy that contributes to important societal issues such as monitoring global climate change and the environment. A Session on the IAG Services was also part of the Assembly detailing the important role they play in providing geodetic data, products, and analysis to the scientific community. A final Session devoted to the organizations ION, FIG, and ISPRS and their significant work in navigation and earth observation that complements the IAG.

Topics in Applied Analysis and Optimisation

Michael Hintermüller,José Francisco Rodrigues
Topics in Applied Analysis and Optimisation Book PDF

Author : Michael Hintermüller,José Francisco Rodrigues
Publisher : Springer Nature
Page : 396 pages
File Size : 45,9 Mb
Release : 2019-11-27
Category : Mathematics
ISBN : 9783030331160

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Topics in Applied Analysis and Optimisation by Michael Hintermüller,José Francisco Rodrigues Pdf

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.

Computational Methods of Multi-Physics Problems

Timon Rabczuk
Computational Methods of Multi Physics Problems Book PDF

Author : Timon Rabczuk
Publisher : MDPI
Page : 128 pages
File Size : 49,7 Mb
Release : 2019-08-20
Category : Technology & Engineering
ISBN : 9783039214174

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Computational Methods of Multi-Physics Problems by Timon Rabczuk Pdf

This book offers a collection of six papers addressing problems associated with the computational modeling of multi-field problems. Some of the proposed contributions present novel computational techniques, while other topics focus on applying state-of-the-art techniques in order to solve coupled problems in various areas including the prediction of material failure during the lithiation process, which is of major importance in batteries; efficient models for flexoelectricity, which require higher-order continuity; the prediction of composite pipes under thermomechanical conditions; material failure in rock; and computational materials design. The latter exploits nano-scale modeling in order to predict various material properties for two-dimensional materials with applications in, for example, semiconductors. In summary, this book provides a good overview of the computational modeling of different multi-field problems.

VII Hotine-Marussi Symposium on Mathematical Geodesy

Nico Sneeuw,Pavel Novák,Mattia Crespi,Fernando Sansò
VII Hotine Marussi Symposium on Mathematical Geodesy Book PDF

Author : Nico Sneeuw,Pavel Novák,Mattia Crespi,Fernando Sansò
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 51,9 Mb
Release : 2012-02-02
Category : Science
ISBN : 9783642220784

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VII Hotine-Marussi Symposium on Mathematical Geodesy by Nico Sneeuw,Pavel Novák,Mattia Crespi,Fernando Sansò Pdf

The Hotine-Marussi Symposium is the core meeting of a “think thank”, a group scientists in the geodetic environment working on theoretical and methodological subjects, while maintaining the foundations of geodesy to the proper level by corresponding to the strong advancements improved by technological development in the field of ICT, electronic computing, space technology, new measurement devices etc. The proceedings of the symposium cover a broad area of arguments which integrate the foundations of geodesy as a science. The common feature of the papers therefore is not on the object, but rather in the high mathematical standards with which subjects are treated.