Real Methods In Complex And Cr Geometry
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| Author | : Marco Abate |
| Publisher | : Springer |
| Total Pages | : 224 |
| Release | : 2004-08-30 |
| Genre | : Mathematics |
| ISBN | : 3540444874 |
The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.
| Author | : Torsten Linß |
| Publisher | : Springer |
| Total Pages | : 331 |
| Release | : 2009-11-21 |
| Genre | : Mathematics |
| ISBN | : 3642051340 |
This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
| Author | : Vicent Caselles |
| Publisher | : Springer |
| Total Pages | : 200 |
| Release | : 2009-12-24 |
| Genre | : Computers |
| ISBN | : 3642046118 |
This book discusses the basic geometric contents of an image and presents a treedatastructuretohandleite?ciently.Itanalyzesalsosomemorphological operators that simplify this geometric contents and their implementation in termsofthe datastructuresintroduced.It?nallyreviewsseveralapplications to image comparison and registration, to edge and corner computation, and the selection of features associated to a given scale in images. Let us ?rst say that, to avoid a long list, we shall not give references in this summary; they are obviously contained in this monograph. A gray level image is usually modeled as a function de?ned in a bounded N domain D? R (typically N = 2 for usual snapshots, N=3formedical images or movies) with values in R. The sensors of a camera or a CCD array transform the continuum of light energies to a ?nite interval of values by means of a nonlinear function g. The contrast change g depends on the pr- ertiesofthesensors,butalsoontheilluminationconditionsandthere?ection propertiesofthe objects,andthoseconditionsaregenerallyunknown.Images are thus observed modulo an arbitrary and unknown contrast change.
| Author | : Habib Ammari |
| Publisher | : Springer |
| Total Pages | : 244 |
| Release | : 2009-09-18 |
| Genre | : Mathematics |
| ISBN | : 3642034446 |
This volume details promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
| Author | : Nicolas Ginoux |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 168 |
| Release | : 2009-06-11 |
| Genre | : Mathematics |
| ISBN | : 3642015697 |
This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.
| Author | : Matthew J. Gursky |
| Publisher | : Springer |
| Total Pages | : 296 |
| Release | : 2009-07-31 |
| Genre | : Mathematics |
| ISBN | : 364201674X |
This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
| Author | : Maria Chlouveraki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 173 |
| Release | : 2009-09-14 |
| Genre | : Mathematics |
| ISBN | : 3642030637 |
The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.
| Author | : Nicolas Privault |
| Publisher | : Springer |
| Total Pages | : 322 |
| Release | : 2009-07-14 |
| Genre | : Mathematics |
| ISBN | : 3642023800 |
This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.
| Author | : Kazuaki Taira |
| Publisher | : Springer |
| Total Pages | : 196 |
| Release | : 2009-06-17 |
| Genre | : Mathematics |
| ISBN | : 3642016774 |
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.
| Author | : Krzysztof Bogdan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 200 |
| Release | : 2009-07-14 |
| Genre | : Mathematics |
| ISBN | : 3642021417 |
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.
