Bøger i Lecture Notes in Mathematics serien

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration).

Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. This text illustrates developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) is included.

This volume contains three state-of-the-art texts on: large deviations and iterating random walks; Dawson-Watanabe superprocesses and measure-valued diffusions; and semiparametric statistics.

This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori.

The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes.

This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis.

This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications.

In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry.

The book gathers the lectures given at the C.I.M.E. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.

From the contents: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- L¿ processes.- Occupation times of a linear Brownian motion.- Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- .....

This book on Banach space theory focuses on what have been called three-space problems. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods.

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena.

Zeta functions have been a powerful tool in mathematics over the last two centuries. The book examines many important examples of zeta functions, providing an important database of explicit examples and methods for calculation.

Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic.

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence.

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type.

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory.

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it.

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This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. A fairly complete description of available results in dimension 1 is given.

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 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. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt.

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory.

The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(*): R ? R , usually described by a set of equality and - n n m equality constraints: F = {x ? R : h(x)=0,h(*): R ? 0, n p g(*): R ?