Mathematics and Science

Efficient transfer between science and society is crucial for their future development.

Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type.

This volume contains 19 contributions to various subjects in the theory of (commutative and non-commutative) stochastic processes.

The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension.

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This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds.

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory.

The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material.

Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems.

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action?

Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph.

The aim of this work is the definition of the polyhedral compactification of the Bruhat-Tits building of a reductive group over a local field.

This volume includes the five lecture courses given at the CIME-EMS School on "e;Stochastic Methods in Finance"e; held in Bressanone/Brixen, Italy 2003.

Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra.

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Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "e;shape"e; of some region.

Bond markets differ in one fundamental aspect from standard stock markets.

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmuller spaces.

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics.

Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws.

The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach.

These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems.

The Paris-Princeton Lectures in Financial Mathematics, of which this is the first volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming!

The Paris-Princeton Lectures in Financial Mathematics, of which this is the second volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming!

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA.

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent.

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions.

In World Mathematical Year 2000 the traditional St.

The present book includes a set of selected papers from the fourth "e;International Conference on Informatics in Control Automation and Robotics"e; (ICINCO 2007), held at the University of Angers, France, from 9 to 12 May 2007.

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology.

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampere and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.

Antennas represent a critical technology in any of these wireless systems.

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere.

The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes.

This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory.

This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "e;multiscale"e; or "e;multilevel"e; paradigm.

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics.

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V.

In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.

Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science.

At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation.

This is yet another indispensable volume for all probabilists and collectors of the Saint-Flour series, and is also of great interest for mathematical physicists.

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.