Bøger i Lecture Notes in Mathematics serien

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients.

They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra.

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics withinthe field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Featuring updated versions of two research courses held at the Centre Emile Borel in Paris in 2001, this book describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields.

The main ideas are illustrated in the context of three different physical problems:(i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous.

This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006

This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems.

Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jurgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Alvarez Montaner.

Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control.

Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years.

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.

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force.

This volume presents a review of advanced technological problems in the glass industry and of the mathematics involved.

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics.

Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics.

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections.

This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer's eye.

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments.

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations.

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge¿Ampère and linearized Monge¿Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge¿Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton¿Jacobi equations, which have received much attention in the last two decades, and a newapproach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton¿Jacobi equations.

This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximationtheory, mathematical physics.