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.
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.
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.
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
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
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
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