The book is based on my lecture notes "Infinite dimensional Morse theory and its applications," 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as...
The book is based on my lecture notes "Infinite dimensional Morse theory and its applications," 1985, Montreal, and one semester of graduate lectures ...
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some...
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representatio...
This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor ical combinators (Hardin, Yokouchi),...
This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit ...
This edition has been updated to include advances in computational prime number theory and in factorization, as well as re-computed and enlarged tables, accompanied by new tables reflecting research by both the author and his co-workers, and by independent researchers.
This edition has been updated to include advances in computational prime number theory and in factorization, as well as re-computed and enlarged table...
Aimed at graduates and potential researchers, this is a comprehensive introduction to the mathematical aspects of spin glasses and neural networks. It should be useful to mathematicians in probability theory and theoretical physics, and to engineers working in theoretical computer science.
Aimed at graduates and potential researchers, this is a comprehensive introduction to the mathematical aspects of spin glasses and neural networks. It...
This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.
This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend conce...
Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.
Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance ...
What is high dimensional probability? Under this broad term one finds a collection of topics associated by the fact that plays a key role in each, whether the idea of high dimension is expressed in the problem or in the methods by which it is approached. For example, the study of probability in Banach spaces gave impetus to a number of methods whose importance has gone far beyond the original goal of extending limit laws to the vector valued case. Familiar applications are in the areas of empirical processes, the use of majorizing measures to study regularity of stochastic processes, and the...
What is high dimensional probability? Under this broad term one finds a collection of topics associated by the fact that plays a key role in each, whe...
The second conference on Fractal Geometry and Stochastics was held at Greifs- wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The...
The second conference on Fractal Geometry and Stochastics was held at Greifs- wald/Koserow, Germany from August 28 to September 2, 1998. Four years ha...
In this book a hierarchy of macroscopic models for semiconductor devices is presented. Three classes of models are studied in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each of the models is shown, including physical discussions. Furthermore, the corresponding mathematical problems are analyzed, using modern techniques for nonlinear partial differential equations. The equations are discretized employing mixed finite-element methods. Also, numerical simulations for modern semiconductor devices are performed,...
In this book a hierarchy of macroscopic models for semiconductor devices is presented. Three classes of models are studied in detail: isentropic dr...
