Progress in Probability, vol.53.
2003. 216 pages. 15.5 x 23.5 cm. Hardcover
ISBN 3-7643-6998-1
English
Over the last years, stochastic analysis
has had an enormous
progress with the impetus originating from
different branches of
mathematics: PDE`s and the Malliavin calculus,
quantum physics,
path space analysis on curved manifolds via
probabilistic
methods, and more.
This volume contains selected contributions
which were presented
at the 8th Silivri Workshop on Stochastic
Analysis and Related
Topics, held in September 2000 in Gazimagusa,
North Cyprus.
The topics include stochastic control theory,
generalized
functions in a nonlinear setting, tangent
spaces of manifold-valued
paths with quasi-invariant measures, and
applications in game
theory, theoretical biology and theoretical
physics.
Contributors: A.E. Bashirov, A. Bensoussan
and J. Frehse, U.
Capar and H. Aktuglul, A.B. Cruzeiro and
Kai-Nan Xiang, E.
Hausenblas, Y. Ishikawa, N. Mahmudov, P.
Malliavin and U. Taneri,
N. Privault, A.S. Ustunel
Advanced Courses in Mathematics
2003. 235 pages. Softcover
ISBN 3-7643-2167-9
English
Among all the Hamiltonian systems, the alics
integrable ones -
those which have many conserved quantities
- have special
geometric properties; in particular, their
solutions are very
regular and quasi-periodic. The quasi-periodicity
of the
solutions of an integrable system is a result
of the fact that
the system is invariant under a (semi-global)
torus action. It is
thus natural to investigate the symplectic
manifolds that can be
endowed with a (global) torus action. This
leads to symplectic
toric manifolds (part B of this book), which
are examples of
extremely symmetric Hamiltonian systems.
Physics makes a
surprising come-back in part A: to describe
Mirror Symmetry, one
looks for a special kind of Lagrangian submanifolds
and
integrable systems, the special Lagrangians.
Furthermore,
integrable Hamiltonian systems on punctured
cotangent bundles are
a starting point for the study of contact
toric manifolds (part C
of this book). Along the way, tools from
many different areas of
mathematics are brought to bear on the questions
at hand, in
particular, actions of Lie groups in symplectic
and contact
manifolds, the Delzant theorem, Morse theory,
sheaves and
\v{C}ech cohomology, and aspects of Calabi-Yau
manifolds.
This book contains an expanded version of
the lectures delivered
by the authors at the CRM Barcelona in July
2001. It serves as an
introduction to symplectic and contact geometry
for graduate
students and will be useful to research mathematicians
interested
in integrable systems.
Table of contents
Lagrangian Submanifolds (M. Audin) (.-) Symplectic
Toric
Manifolds (A. Cannas da Silva) (.-) Geodesic
Flows and Contact
Toric Manifolds (E. Lerman)
Operator Theory,vol.142
2003. 404 pages. Hardcover
ISBN 3-7643-6947-7
English
This book contains the proceedings of the
International Workshop
on Operator Theory and Applications held
in Faro, Portugal,
September 12 to 15, 2000. It includes 20
selected articles
centered on the analysis of various classes
of singular
operators, the factorization of operator
and matrix functions,
algebraic methods in approximation theory,
and applications in
diffraction theory. Some papers are related
to topics from
fractional calculus, complex analysis, operator
algebras, and
partial differential equations.
Table of contents
Contributions by
J. Arazy and H. Upmeier; M.A. Bastos, A.
Bravo and Y. Karlovich;
A. Bottcher, S. Grudsky and I. Spitkovsky;
L.P. de Castro and F.-O.
Speck; A. Conceicao, V. Kravchenko and F.
Teixeira; K. Gurlebeck
and A. Hommel; V. Hardt, R. Mennicken and
A.K. Motovilov; A.N.
Karapetyants and E.R. de Arellano; A. Karlovich,
Y. Karlovich and
A. Lebre; A.K. Kilbas; V. Kravchenko, A.
Lebre and J. Rodriguez;
W.E. Longstaff; E. Luneburg and H.A. Serbest;
E. Meister; V.S.
Rabinovich and S. Roch; S. Roch; L. Rodman,
I.M. Spitkovsky and H.J.
Woerdeman; N. Samko; S. Samko; P.A. Santos
and B. Silbermann
July 2003 | Paperback (Hardback) | 60 exercises
| ISBN: 0-521-54218-9
The first edition of this book was the indispensable
reference
for researchers in the theory of pro-p groups.
In this second
edition the presentation has been improved
and important new
material has been added. The first part of
the book is group-theoretic.
It develops the theory of pro-p groups of
finite rank, starting
from first principles and using elementary
methods. Part II
introduces p-adic analytic groups: by taking
advantage of the
theory developed in Part I, it is possible
to define these, and
derive all the main results of p-adic Lie
theory, without having
to develop any sophisticated analytic machinery.
Part III,
consisting of new material, takes the theory
further. Among those
topics discussed are the theory of pro-p
groups of finite
coclass, the dimension subgroup series, and
its associated graded
Lie algebra. The final chapter sketches a
theory of analytic
groups over pro-p rings other than the p-adic
integers.
Contents
Prelude; Part I. Pro-p Groups: 1. Profinite
groups and pro-p
groups; 2. Powerful p-groups; 3. Pro-p groups
of finite rank; 4.
Uniformly powerful groups; 5. Automorphism
groups; Interlude A.
Fascicule de resultats: pro-p groups of finite
rank; Part II.
Analytic Groups: 6. Normed algebras; 7. The
group algebra;
Interlude B. Linearity criteria; 8. p-adic
analytic groups;
Interlude C. Finitely generated groups, p-adic
analytic groups
and Poincare series; 9. Lie theory; Part
III. Further Topics: 10.
Pro-p groups of finite co-class; 11. Dimension
subgroup methods;
12. Some graded algebras; Interlude D. The
Golod Shafarevic
inequality; Interlude E. Groups of sub-exponential
growth; 13.
Analytic groups over pro-p rings.
Publication is planned for August 2003 |
Paperback | 390 pages
50 line diagrams | ISBN: 0-521-54013-5
The subject of Kleinian groups and hyperbolic
3-manifolds is
currently undergoing explosively fast development,
with many old
problems and conjectures close to resolution.
This volume,
proceedings of the Warwick workshop in September
2001, contains
expositions of many of these breakthroughs
including Minsky's
lectures on the first half of the proof of
the Ending Lamination
Conjecture, the Bers Density Conjecture by
Brock and Bromberg,
the Tameness Conjecture by Kleineidam and
Souto, the state of the
art in cone manifolds by Hodgson and Kerckhoff,
and the counter
example to Thurston’s K=2 conjecture by
Epstein, Marden and
Markovic. It also contains Jorgensen's famous
paper ‘On pairs
of once punctured tori’ in print for the
first time. The
excellent collection of papers here will
appeal to graduate
students, who will find much here to inspire
them, and
established researchers who will find this
valuable as a snapshot
of current research.
Contents
Part I. Hyperbolic 3-Manifolds: 1. Combinatorial
and geometrical
aspects of hyperbolic 3-manifolds Y. Minsky;
2. Harmonic
deformations of hyperbolic 3-manifolds C.
D. Hodgson and S. P.
Kerchoff; 3. Cone-manifolds and the density
conjecture J. F.
Brock and K. W. Bromberg; 4. Les geodesiques
fermes d’une
variete hyperbolique en tant que noeuds J.-P.
Otal; 5. Ending
laminations in the Masur domain G. Kleineidam
and J. Souto; 6.
Quasi-arcs in the limit set of a singly degenerate
group with
bounded geometry H. Miyachi; 7. On hyperbolic
and spherical
volumes for knot and link cone-manifolds
A. D. Mednykh; 8.
Remarks on the curve complex: classification
of surface
homeomorphisms W. J. Harvey; Part II. Once-punctured
tori: 9. On
pairs of once-punctured tori T. Jorgensen;
10. Comparing two
convex hull constructions for cusped hyperbolic
manifolds H.
Akiyoshi and M. Sakuma; 11. Jorgensen’s
picture of punctured
torus groups and its refinement H. Akiyoshi,
M. Sakuma, M. Wada
and Y. Yamashita; 12. Tetrahedral decompositions
of punctured
torus bundles J. R. Parker; 13. On the boundary
of the Earle
slice for punctured torus groups Y. Komori;
Part III. Related
Topics: 14. Variations on a theme of Horowitz
J. W. Anderson; 15.
Complex angle scattering D. B. A. Epstein,
A. Marden and V.
Markovic; 16. Schwarz’s lemma and the Kobayashi
and
Caratheodory pseudometrics on complex Banach
manifolds C. J.
Earle, L. A. Harris, J. H. Hubbard and S.
Mitra.
Publication is planned for August 2003 |
Hardback | 584 pages
| ISBN: 0-521-83344-2
Now available in a fully revised and updated
new edition, this
well established textbook provides a straightforward
introduction
to the theory of probability. The presentation
is entertaining
without any sacrifice of rigour; important
notions are covered
with the clarity that the subject demands.
Topics covered include
conditional probability, independence, discrete
and continuous
random variables, basic combinatorics, generating
functions and
limit theorems, and an introduction to Markov
chains. The text is
accessible to undergraduate students and
provides numerous worked
examples and exercises to help build the
important skills
necessary for problem solving.
Reviews
‘… this book is a superb resource of theory
and application,
which should be on every lecturer’s shelves,
and those of many
students. You may never need to buy another
book on probability.’
Keith Hirst, The Mathematical Gazette
‘Excellent! A vast number of well-chosen
worked examples and
exercises guide the reader through the basic
theory of
probability at the elementary level … an
excellent text which I
am sure will give a lot of pleasure to students
and teachers
alike.’ International Statistics Institute
‘… would make a fine addition to an undergraduate
library. A
student with a solid background in calculus,
linear algebra, and
set theory will find many useful tools of
elementary probability
here.’ Phil Gilbert, The Mathematics Teacher
‘Stirzaker does an excellent job of developing
problem-solving
skills in an introductory probability text.
Numerous examples and
practice exercises are provided that only
serve to enhance a
student’s problem solving abilities … Highly
recommended.’
D. J. Gougeon, Choice
‘The book would make an excellent text for
the properly
prepared class, a solid instructor’s reference
for both
probability applications and problems, as
well as a fine work for
purposes of self-study.’ J. Philip Smith,
School Science and
Mathematics
Contents
1. Probability; 2. Conditional probability
and independence; 3.
Counting; 4. Random variables: distribution
and expectation; 5.
Random vectors: independence and dependence;
6. Generating
functions and their applications; 7. Continuous
random variables;
8. Jointly continuous random variables; 9.
Markov chains;
Appendix.