Krylov, N.V., University of Illinois at Chicago,
IL, USA
R?ckner, M., University of Bielefeld, Germany
Zabczyk, J., Polkiej Akademii Nauk, Warsaw, Poland
Da Prato, G., Pisa, Italy
(Ed.)
Lectures given at the 2nd Session of the Centro Internazionale
Matematico Estivo
(C.I.M.E.)held in Cetaro, Italy, August 24 - September 1, 1998
1999. VIII, 239 pp.
3-540-66545-5
Kolmogorov equations are second order parabolic equations with a
finite or an infinite number of variables. They
are deeply connected with stochastic differential equations in
finite or infinite dimensional spaces. They arise in
many fields as Mathematical Physics, Chemistry and Mathematical
Finance. These equations can be studied both
by probabilistic and by analytic methods, using such tools as
Gaussian measures, Dirichlet Forms, and stochastic
calculus. The following courses have been delivered: N.V. Krylov
presented Kolmogorov equations coming from
finite-dimensional equations, giving existence, uniqueness and
regularity results. M. R?ckner has presented an
approach to Kolmogorov equations in infinite dimensions, based on
an LP-analysis of the corresponding diffusion
operators with respect to suitably chosen measures. J. Zabczyk
started from classical results of L. Gross, on the
heat equation in infinite dimension, and discussed some recent
results.
Keywords: Kolmogorov equations, Dirichlet forms,
Ornstein-Uhlenbeck process
Contents: N.V. Krylov: On Kolmogorov's equations for finite
dimensional diffusions: Solvability of Ito's
stochastic equations; Markov property of solution; Conditional
version of Kolmogorov's equation; Differentiability
of solutions of stochastic equations with respect to initial
data; Kolmogorov's equations in the whole space; Some
Integral approximations of differential operators; Kolmogorov's
equations in domains.- M. Roeckner: LP-analysis
of finite and infinite dimensional diffusion operators: Solution
of Kolmogorov equations via sectorial forms;
Symmetrizing measures; Non-sectorial cases: perturbations by
divergence free vector fields; Invariant measures:
regularity, existence and uniqueness; Corresponding diffusions
and relation to Martingale problems.- J. Zabczyk:
Parabolic equations on Hilbert spaces: Heat equation; Transition
semigroups; Heat equation with a first order
term; General parabolic equations; Regularity and Quiqueness;
Parabolic equations in open sets; Applications.
Series: Lecture Notes in Mathematics.VOL. 1715
Coates, J., University of Cambridge, UK
Greenberg, R., University of Washington, Seattle, WA, USA
Ribet, K.A., University of California, Berkeley, CA, USA
Rubin, K., Stanford University, Stanford, CA, USA
Viola, C., University of Pisa, Italy
(Ed.)
Lectures given at the 3rd Session of the Centro Internazionale
Matematico Estivo
(C.I.M.E.)held in Cetaro, Italy, July 12-19, 1997
1999. VIII, 260 pp.
3-540-66546-3
This volume contains the expanded versions of the lectures given
by the authors at the C.I.M.E. instructional
conference held in Cetraro, Italy, from July 12 to 19, 1997. The
papers collected here are broad surveys of the
current research in the arithmetic of elliptic curves, and also
contain several new results which cannot be found
elsewhere in the literature. Owing to clarity and elegance of
exposition, and to the background material explicitly
included in the text or quoted in the references, the volume is
well suited to research students as well as to
senior mathematicians.
Keywords: elliptic curves, modular curves, complex
multiplication, Iwasawa theory, Birch and Swinnerton-Dyer
conjecture
Contents: John Coates: Fragments of the GL2 Iwasawa Theory of
Elliptic Curves without Complex
Multiplication.- Ralph Greenberg: Iwasawa Theory for Elliptic
Curves.- Kenneth A. Ribet: Torsion Points on
Jo(N) and Galois Representations.- Karl Rubin: Elliptic Curves
with Complex Multiplication and the Conjecture of
Birch and Swinnerton-Dyer.
Series: Lecture Notes in Mathematics.VOL. 1716
Lawrence, D.B., Drake University, Des Moines, IA, USA
1999. XV, 393 pp. 45 figs.
0-387-98706-1
This is a book about the evaluation and choice of information
sources by individuals and the design and
management of information systems by organizations. The book
studies the determinants of the value and cost of
information, both to the individual and to the organization,
provides technqiues for the assessment of the value of
information and the comparison of informativeness among
alternative sources, and presents principles for the
optimal design and management of information systems. These
topics are unified by the thesis that both
information sources and information systems are valuable to the
extent they contribute to better decision making.
By providing students, researchers, and practitioners with a
coherent notation and framework throughout, the
book integrates the decision-theoretic approach to the evaluation
of information with knowledge from Information
Science and Management Information Systems on the design,
management, and cost of cooperative information
systems, thereby demonstrating the multidisciplinary
applicability of a unifying approach based on decision theory.
Researchers and graduate students in economics, operations
research, management information systems, and
information science will find this book useful.
Contents: Preface.- Introduction and overview.- The Value of the
Informed Decision.- Measures of the Value of
Information.- The Assessment of Statistical Information.- Models
with Convenient Assessment and Interpretation.-
Statistical Determinants of Information Value.- Stochastic
Preference and Information Value.- Information Demand
and Procurement.- Economics of Valuable Information Systems.-
References.- Acknowledgements.- Symbol
Glossary.
Schneider, P., Max-Planck-Institut f?r
Astrophysik, Garching, Germany
Ehlers, J., Max-Planck-Institut f?r Gravitationsphysik, Potsdam,
Germany
Falco, E.E., Harvard-Smithsonian Center for Astrophysics,
Cambridge, MA, USA
1st ed. 1992. 2nd printing 1999. XIV, 560 pp., 112 figs.
3-540-66506-4
Light observed from distant objects is found to be deflected by
the gravitational field of massive objects near the
line of sight - an effect predicted by Einstein in his first
paper setting forth the general theory of relativity, and
confirmed by Eddington soon afterwards. If the source of the
light is sufficiently distant and bright, and if the
intervening object is massive enough and near enough to the line
of sight, the gravitational field acts like a lens,
focusing the light and producing one or more bright images of the
source. This book, by renowned researchers in
the field, begins by discussing the basic physics behind
gravitational lenses: the optics of curved space-time. It
then derives the appropriate equations for predicting the
properties of these lenses. In addition, it presents
up-to-date observational evidence for gravitational lenses and
describes the particular properties of the observed
cases. The authors also discuss applications of the results to
problems in cosmology.
Keywords: Gravitational Lensing, Geometrical Optics, Redshift,
Gravitation, Extragalactic Cosmology, Quasars
.
Contents: Introduction.- Basic Facts and the Observational
Situation.- Optics in Curved Spacetime.- Derivation
of the Lens equation.- Properties of the Lens Mapping.- Lensing
Near Critical Points.- Wave Optics in
Gravitational Lensing.- Simple Lens Models.- Multiple Light
Deflection.- Numerical Methods.- Statistical
Gravitational Lensing: General Considerations.- Statistical
Gravitational Lensing: Applications.- Gravitational
Lenses as Astrophysical Tools.- References.- Index.
Series: Astronomy and Astrophysics Library.
Diekmann, O., University of Utrecht, The
Netherlands
Durrett, R., University of Cornell, WI, USA
Hadeler, K.-P., University of T?bingen, Germany
Maini, P., Oxford University, UK
Smith, H., Arizona State University, Tempe, AZ, USA
Capasso, V., University of Milan, Milano, Italy
Diekmann, O., University of Utrecht, The Netherlands
(Eds.)
1999. VII, 268 pp.
3-540-66522-6
The summer school on Mathematics inspired by Biology was held at
Martina Franca, Apulia, Italy in 1997. This
volume presents five series of six lectures each. The common
theme is the role of structure in shaping transient
and ultimate dynamics. But the type of structure ranges from
spatial (hadeler and maini in the deterministic
setting, Durrett in the stochastic setting) to physiological
(Diekmann) and order (Smith). Each contribution
sketches the present state of affairs while, by including some
wishful thinking, pointing at open problems that
deserve attention.
Contents: O. Diekmann: Modeling and analysing physiologically
structured populations.- R. Durett: Stochastic
Spatial Models.- K.P. Hadeler: Reaction Transport Systems in
Biological Modeling.- P. Maini: Mathematical
Models in Morphogenesis.- H. Smith: Dynamics of Competition.
Series: Lecture Notes in Mathematics.VOL. 1714
Cohn, P.M., University College London, UK
2000. X, 230 pp. 12 figs.
1-85233-206-9
Most parts of algebra have undergone great changes this century,
perhaps none more so than ring theory. In this
volume, Paul Cohn provides a clear and structured introduction to
the subject.
After a chapter on the definition of rings and modules there are
brief accounts of Artinian rings, commutative
Noetherian rings and ring constructions, such as the direct
product. Tensor product and rings of fractions,
followed by a description of free rings. The reader is assumed to
have a basic understanding of set theory, group
theory and vector spaces. Over two hundred carefully selected
exercises are included, most with outline
solutions.
Contents: Basics.- Linear Algebras and Artinian Rings.-
Noetherian Rings.- Ring Constructions.- General
Rings.- Outline Solutions.- List of Notations.- Bibliography.-
Index.
Series: Springer Undergraduate Mathematics Series.
Saito, M., Hokkaido University, Sapporo, Japan
Sturmfels, B., University of California, Berkeley, CA, USA
Takayama, N., University of Kobe, Japan
2000. VIII, 254 pp. 14 figs.
3-540-66065-8
In recent years, new algorithms for dealing with rings of
differential operators have been discovered and
implemented. A main tool is the theory of Gr?bner bases, which is
reexamined here from the point of
view of geometric deformations. Perturbation techniques have a
long tradition in analysis; Gr?bner
deformations of left ideals in the Weyl algebra are the algebraic
analogue to classical perturbation
techniques. The algorithmic methods introduced here are
particularly useful for studying the systems of
multidimensional hypergeometric PDEs introduced by Gelfand,
Kapranov and Zelevinsky. The Gr?bner
deformation of these GKZ hypergeometric systems reduces problems
concerning hypergeometric
functions to questions about commutative monomial ideals, and
leads to an unexpected interplay
between analysis and combinatorics. This book contains a number
of original research results on
holonomic systems and hypergeometric functions, and raises many
open problems for future research in
this area.
Keywords: hypergeometric functions, Gr?bner bases, holonomic
systems, Weyl algebra, combinatorial
commutative algebra
Contents: Chapter 1. Basic Notions.- Chapter 2. Gr?bner
Deformations of Regular Holonomic
Systems.- Chapter 3. Hypergeometric Series.- Chapter 4. Rank
versus volume.- Chapter 5. Integration
of D-modules
Series: Algorithms and Computation in Mathematics.VOL. 6
Murota, K., Kyoto University, Kyoto, Japan
1999. XII, 483 pp., 64 figs.
3-540-66024-0
A matroid is an abstract mathematical structure that captures
combinatorial properties of matrices. This book offers
a unique introduction to matroid theory, emphasizing motivations
from matrix theory and applications to systems
analysis.
This book serves also as a comprehensive presentation of the
theory and application of mixed matrices, developed
primarily by the present author in the last decade. A mixed
matrix is a convenient mathematical tool for systems
analysis, compatible with the physical observation that
"fixed constants" and "system parameters" are
to be
distinguished in the description of engineering systems.
This book will be extremely useful to graduate students and
researchers in engineering, mathematics and
computer science.
Keywords: matroid theory, matrix theory, systems analysis,
discrete mathematics, algorithm
Series: Algorithms and Combinatorics.VOL. 20
Struwe, M., ETH Zurich, Switzerland
Applications to Nonlinear Partial Differential Equations and
Hamiltonian Systems
3rd ed. 2000. XVIII, 274 pp. 16 figs.
3-540-66479-3
Hilbert's talk at the second International Congress of 1900 in
Paris marked the beginning of a new era in the
calculus of variations. A development began which, within a few
decades, brought tremendous success,
highlighted by the 1929 theorem of Ljusternik and Schnirelman on
the existence of three distinct prime closed
geodesics on any compact surface of genus zero, and the 1930/31
solution of Plateau's problem by Douglas and
Rad?. The book gives a concise introduction to variational
methods and presents an overview of areas of current
research in the field. The third edition gives a survey on new
developments in the field. References have been
updated and a small number of mistakes have been rectified.
Keywords: Calculus of Variations, Partial Differential Equations,
Hamiltonian Systems, Mathematical Physics .
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys in
Mathematics.VOL. 34
Baden, S.B., University of California, San Diego,
La Jolla, CA, USA
Chrisochoides, N.P., University of Notre Dame, IN, USA
Gannon, D.B., Indiana University, Bloomington, IN, USA
Norman, M.L., University of Illinois at Urbana-Champaign, Urbana,
IL, USA
(Eds.)
1999. Approx. 185 pp. 66 figs.
0-387-98921-8
The papers presented here describe research to improve the
general understanding of the application of SAMR to
practical problems, to identify issues critical to efficient and
effective implementation on high performance
computers and to stimulate the development of a community code
repository for software including benchmarks to
assist in the evaluation of software and compiler technologies.
The ten chapters have been divided into two parts
reflecting two major issues in the topic: programming complexity
of SAMR algorithms and the applicability and
numerical challenges of SAMR methods.
Contents: Foreword.- Preface.- Part I: Programming Complexity of
SAMR Algorithms. Systems engineering for
high-performance computing software: The HDDA/DAGH infrastructure
for implementation of parallel structured
adaptive mesh. HAMR: The hierarchical adaptive mesh refinement
system. AMR++: A design for parallel
object-oriented adaptive mesh refinement. RSL: A parallel runtime
system library for regional atmospheric models
with nesting. Software abstractions and computational issues in
parallel structured adaptive mesh methods for
electronic structure calculations. Structured adaptive mesh
refinement using high performance fortran.- Part II:
Applicability and Numerical Challenges of SAMR Methods. The
dynamics of localized coherent structures and the
role of adaptive software in multiscale modeling. Progress,
results, and experiences in developing an adaptive
solver for steady state turbulent reacting flows in industrial
boilers and furnaces. Making arbitrarily small black
holes: Experiences with AMR in numerical relativity. A hybrid AMR
application for cosmology and astrophysics.-
List of Participants
Series: The IMA Volumes in Mathematics and its Applications.VOL.
117