Khoshnevisan, D., University of Utah, Salt Lake City, UT, USA

Multiparameter Processes
An Introduction to Random Fields

2002. Approx. 590 pp. 8 figs. Hardcover
0-387-95459-7

Multiparameter processes extend the existing one-parameter theory of random processes in an elegant way, and have found connections to diverse disciplines such as probability theory, real and functional analysis, group theory, analytic number theory, and group renormalization in mathematical physics, to name a few.

This book lays the foundation of aspects of the rapidly-developing subject of random fields, and is designed for a second graduate course in probability and beyond. Its intended audience is pure, as well as applied, mathematicians.

Davar Khoshnevisan is Professor of Mathematics at the University of Utah. His research involves random fields, probabilistic potential theory, and stochastic analysis.

Keywords: Random Fields, Probability, Stochastics, Multi-parameter processes

Contents: Discrete-Parameter Random Fields: Discrete Parameter. Martingales. Two Applications in Analysis. Random Walks. Multiparameter Walks. Gaussian Random Walks. Limit Theorems.- Continuous-Parameter Random Fields: Continuous Parameter Martingales. Constructing Markov Processes. Generation of Markov Processes. Probabilistic Potential Theory. Multiparameter Markov Processes. Brownian Sheet and Potential Theory.- Appendices: Kolmogorov's Consistency Theorem. Laplace Transforms. Hausdorff Dimensions and Measures. Energy and Capacity.

Series: Springer Monographs in Mathematics.

Koch, H., Humboldt-Universitat zu Berlin, Germany

Galois Theory of p-Extensions

2002. XIV, 191 pp. Hardcover
3-540-43629-4

First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal p-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers.The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included.

Keywords: pro-p groups, class field towers, cohomology of groups

Series: Springer Monographs in Mathematics.

Paun, G., Romanian Academy, Bucuresti, Romania

Membrane Computing : An Introduction

2002. XI, 429 pp. 37 figs., 5 tabs. Hardcover
3-540-43601-4

Like quantum computing or DNA computing, membrane computing is an unconventional model of computation associated with a new computing paradigm. The field of membrane computing was initiated in 1998 by the author of this book; it is a branch of natural computing inspired by the structure and functioning of the living cell and devises distributed parallel computing models in the form of membrane systems, also called P systems.
This book is the first monograph surveying the new field in a systematic and coherent way. It presents the central notions and results: the main classes of P systems, the main results about their computational power and efficiency, a complete bibliography, and a series of open problems and research topics. Thus, the book is indispensible reading for anybody interested in molecular computing.

Keywords: Natural computing, Turing computability, Computational complexity, Biology ofthe cell, New Computing Paradigms, Biocomputing, Biologically motivated computing, Membrane computing, P systems, DNA computing

Contents: Preface.- 1. Introduction: Membrane Computing, What It Is and What It Is Not.- 2. Prerequisites.- 3. Membrane Systems with Symbol-Objects.- 4. Trading Evolution for Communication.- 5. Structuring Objects.- 6. Networks of Membranes.- 7. Trading Space for Time.- 8. Further Technical Results.- 9. (Attempts to Get) Back to Reality.- Open Problems.- Universality Results. Bibliography.- Index.

Series: Natural Computing Series.

Serre, J.-P., College de France, Paris, France

Oeuvres - Collected Papers, Volume 1: 1949 - 1959 (Paperback ed.)

1er ed. 1986. 2ieme tirage corigee 2002. Env. 600 pp. Broche
3-540-43562-X

Set price available.

From the reviews of vols I-III:"These volumes collect almost all of the research and expository papers of J-P. Serre published in mathematical journals through 1984, as well as some of his seminar reports, and a few items not previously published. Thirty-six pages of endnotes have been added (by Serre). Of the seventeen papers omitted, six are included in the Collected Papers of A. Borel and one in the Selected Papers of S.S. Chern. (...) Throughout his writings, Serre has liberally sprinkled open questions and conjectures. Most endnotes list subsequent progress made on these questions or improvements to the main results of the papers. Some make additional comments, and a few are corrections. These endnotes alone justify the publication of the collected works. Serre is one of the masters of mathematical exposition. In many cases the first account of a topic given in one of his papers remains the best." James Milne, University of Michigan, in Math Reviews

Keywords: Collected works, J-P . Serre, homotopy, loop spaces, duality, coherent sheaves, cohomology MSC ( 2000 ): 01A75, 01A65, 14, 18, 20, 32, 55

Serre, J.-P., College de France, Paris, France.

Oeuvres - Collected Papers, Volume 2: 1960 - 1971 (Paperback ed.)

1er ed. 1986. 2ieme tirage corigee 2002. Env. 740 p. Broche
3-540-43563-8

Set price available.

From the reviews of vols I-III:"These volumes collect almost all of the research and expository papers of J-P. Serre published in mathematical journals through 1984, as well as some of his seminar reports, and a few items not previously published. Thirty-six pages of endnotes have been added (by Serre). Of the seventeen papers omitted, six are included in the Collected Papers of A. Borel and one in the Selected Papers of S.S. Chern. (...) Throughout his writings, Serre has liberally sprinkled open questions and conjectures. Most endnotes list subsequent progress made on these questions or improvements to the main results of the papers. Some make additional comments, and a few are corrections. These endnotes alone justify the publication of the collected works. Serre is one of the masters of mathematical exposition. In many cases the first account of a topic given in one of his papers remains the best." James Milne, University of Michigan, in Math Reviews

Keywords: Collected works, J-P . Serre, p-adic, cohomology, Galois groups, congruencesubgroups MSC ( 2000 ): 01A75, 01A65, 11, 14, 18, 20

Serre, J.-P., College de France, Paris, France

Oeuvres - Collected Papers, Volume 3: 1972 - 1984 (Paperback ed.)

1er ed. 1986. 2ieme tirage corigee 2002. Env. 730 p. Broche
3-540-43564-6

Set price available.

From the reviews of vols I-III:"These volumes collect almost all of the research and expository papers of J-P. Serre published in mathematical journals through 1984, as well as some of his seminar reports, and a few items not previously published. Thirty-six pages of endnotes have been added (by Serre). Of the seventeen papers omitted, six are included in the Collected Papers of A. Borel and one in the Selected Papers of S.S. Chern. (...) Throughout his writings, Serre has liberally sprinkled open questions and conjectures. Most endnotes list subsequent progress made on these questions or improvements to the main results of the papers. Some make additional comments, and a few are corrections. These endnotes alone justify the publication of the collected works. Serre is one of the masters of mathematical exposition. In many cases the first account of a topic given in one of his papers remains the best." James Milne, University of Michigan, in Math Reviews

Keywords: Collected works, J-P . Serre, p-adic, modular forms, Chebotarev, Galois representations . MSC ( 2000 ): 01A75, 01A65, 11, 14, 18, 20

Serre, J.-P., College de France, Paris, France

Oeuvres - Collected Papers, Volume 4: 1985 - 1998 (Paperback ed.)

1er ed. 2000. 2ieme tirage corigee 2002. VIII, 660 p. Broche
3-540-43565-4

Set price available.

The impact and influence of J-P. Serre's work has been notable ever since his doctoral thesis on homotopy groups: early international recognition of this was manifested in the award of the Fields Medal in 1954. The abundance of deep results and insight contained in his research and survey papers ranging through topology, several complex variables, and algebraic geometry to number theory, group theory, commutative algebra and modular forms, will continue to provide inspiring reading for mathematicians working in these areas, in their research and their teaching. Characteristic of Serre's publications are the many open questions he formulated pointing to further directions of of research. In this new edition of volume IV, two recently published articles have been added, one on the life and works of Andre Weil, the other one on Finite Subgroups of Lie Groups.

Keywords: Collected works, J-P . Serre, abelian varieties, Galois representations, modular conjectures, semisimplicity MSC ( 2000 ): 01A75, 01A65, 11, 14, 18, 20

Contents: Preface.- Papers published between 1985 and 1998.- Notes.-Modifications volumes I-III.- Errata volumes I-III.- Acknowledgements