Bücher der Reihe Lecture Notes in Mathematics

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.

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.

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating -function.

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The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity;

The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. Drinfeld Shtukas (Lectures by G. Drinfeld modules and Elliptic Sheaves (Lectures by U.

The summer school on Mathematics inspired by Biology was held at Martina Franca, Apulia, Italy in 1997. But the type of structure ranges from spatial (hadeler and maini in the deterministic setting, Durrett in the stochastic setting) to physiological (Diekmann) and order (Smith).

The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images.

The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems.

This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process.

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits.

With a historical overview by Elvira Mascolo

The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Levy processes. The chapters cover the main aspects of the estimation of discretely observed Levy processes, when the observation scheme is regular, from an up-to-date viewpoint.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.

This book presents the state of the art in mathematical research on modelling the mechanics of biological systems - a science at the intersection between biology, mechanics and mathematics known as mechanobiology.

The new corrected and expanded edition adds a special appendix on Schensted Correspondence and Littelmann Paths. This appendix can be read independently of the rest of the volume and is an account of the Littelmann path model for the case gln.

Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory.