Download or read book Stable Approximate Evaluation of Unbounded Operators written by C. W. Groetsch and published by Springer Science & Business Media. This book was released on 2007 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Download or read book Eigenvalues Embeddings and Generalised Trigonometric Functions written by Jan Lang and published by Springer. This book was released on 2011-03-17 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.
Download or read book Random Perturbation of PDEs and Fluid Dynamic Models written by Franco Flandoli and published by Springer. This book was released on 2011-03-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.
Download or read book Computational Approach to Riemann Surfaces written by Alexander I. Bobenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
Download or read book Fatou Julia Montel written by Michèle Audin and published by Springer. This book was released on 2011-01-29 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)
Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer. This book was released on 2011-01-05 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
Download or read book Affine Density in Wavelet Analysis written by Gitta Kutyniok and published by Springer Science & Business Media. This book was released on 2007-06-07 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a thorough and comprehensive treatment of irregular wavelet frames. It introduces and employs a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Coverage includes non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Download or read book Spin Glasses written by Erwin Bolthausen and published by Springer. This book was released on 2007-01-11 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Download or read book Iterative Regularization Methods for Nonlinear Ill Posed Problems written by Barbara Kaltenbacher and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Download or read book Calculus of Variations and Nonlinear Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a historical overview by Elvira Mascolo
Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Download or read book Generalized Bessel Functions of the First Kind written by Árpád Baricz and published by Springer Science & Business Media. This book was released on 2010-05-25 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.
Download or read book Representation Theory and Complex Analysis written by Michael Cowling and published by Springer Science & Business Media. This book was released on 2008-02-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Download or read book Quantum Potential Theory written by Philippe Biane and published by Springer Science & Business Media. This book was released on 2008-09-23 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Download or read book Stability of Queueing Networks written by Maury Bramson and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen.
Download or read book Laplacian Eigenvectors of Graphs written by Türker Biyikoglu and published by Springer. This book was released on 2007-07-07 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.
Download or read book S minaire de Probabilit s XL written by Catherine Donati-Martin and published by Springer. This book was released on 2007-07-25 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who could have predicted that the S ́ eminaire de Probabilit ́ es would reach the age of 40? This long life is ?rst due to the vitality of the French probabil- tic school, for which the S ́ eminaire remains one of the most speci?c media of exchange. Another factor is the amount of enthusiasm, energy and time invested year after year by the R ́ edacteurs: Michel Ledoux dedicated himself tothistaskuptoVolumeXXXVIII,andMarcYormadehisnameinseparable from the S ́ eminaire by devoting himself to it during a quarter of a century. Browsing among the past volumes can only give a faint glimpse of how much is owed to them; keeping up with the standard they have set is a challenge to the new R ́ edaction. In a changing world where the status of paper and ink is questioned and where, alas, pressure for publishing is increasing, in particular among young mathematicians, we shall try and keep the same direction. Although most contributions are anonymously refereed, the S ́ eminaire is not a mathema- cal journal; our ?rst criterion is not mathematical depth, but usefulness to the French and international probabilistic community. We do not insist that everything published in these volumes should have reached its ?nal form or be original, and acceptance–rejection may not be decided on purely scienti?c grounds.
