This volume consists of a collection of tutorial papers, by leading experts, on statistical and probabilistic aspects of chaos and networks, in particular neural networks. While written for the non-expert, they are intended to bring the reader up to the forefront of knowledge and research in the subject areas concerned. The papers, which contain extensive references to the literature, can separately or in various combinations serve a...

Let f be a periodic measurable function and x (nk) an increasing sequence of positive integers. The authors study conditions under which the series k=1 Ckf(nkx)_ converges in mean and for almost every x. There is a wide classical literature on this problem going back to the 30's, but the results for general f are much less complete than in the trigonometric case f(x) = sin x. As it turns out, the convergence properties of k=1 ckf(nkx...

A very valuable source for many techniques in the representation theory of general Lie groups. These techniques are beautiful combinations of methods in abstract harmonic analysis and others which are more specific to Lie theory and related to coadjoint orbits. I can recommend the book to everyone interested in general and abstract aspects of the representation theory of Lie groups.

After Karl Jöreskog's first presentation in 1970, Structural Equation Modelling or Sem has become a main statistical tool in many fields of science. It is the standard approach of factor analytic and causal modelling in such diverse fields as sociology, education, psychology, economics, management and medical sciences. In addition to an extension of its application area, Structural Equation Modelling also features a continual renewal...

This monograph, authored by a leading expert and main contributor in the field, is very painstakingly written ... The book offers an ideal road of entry into the subject, for everybody with an interest in local Galois module theory or in the theory of Hopf algebras. This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results...

Modern model theory began with Morley's categoricity theorem: A countable first-order theory that has a unique (up to isomorphism) model in one uncountable cardinal (i.e., is categorical in cardinality) if and only if the same holds in all uncountable cardinals. Over the last 35 years Shelah made great strides in extending this result to infinitary logic, where the basic tool of compactness fails. He invented the notion of an Abstrac...

The results of this book are given with complete proofs and also an emphasis on the intuitive understanding of the results. This extends the audience beyond mathematicians to include engineers, physicists and biologists with a good background in Analysis and PDEs. --Mathematical Reviews

The purpose of this book is to develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic...

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied in...

It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic char...