Juhl, A., Universitet Uppsala, Sweden
Cohomological Theory of Dynamical Zeta Functions
2001. X, 710 pages. Hardcover
ISBN 3-7643-6405-X
English
Progress in Mathematics 194
The periodic orbits of the geodesic flow
of compact locally symmetric spaces of
negative curvature give rise to
meromorphic zeta functions (generalized
Selberg zeta functions, Ruelle zeta
functions).
The book treats various aspects of the idea
to understand the analytical properties of
these zeta functions on the basis of
appropriate analogs of the Lefschetz fixed
point formula in which the periodic orbits
of
the flow take the place of the fixed points.
According to geometric quantization the
Anosov foliations of the sphere bundle
provide a natural source for the definition
of
the cohomological data in the Lefschetz
formula. The Lefschetz formula method can
be considered as a link between the
automorphic approach (Selberg trace
formula) and Ruelle痴 approach (transfer
operators). It yields a uniform cohomological
characterization of the zeros and poles of
the
zeta functions and a new understanding of
the functional equations from an index
theoretical point of view. The divisors of
the
Selberg zeta functi lso admit
characterizations in terms of harmonic
currents on the sphere bundle which
represent the cohomology classes in the
Lefschetz formulas in the sense of a Hodge
theory. The concept of harmonic currents
to
be used for that purpose is introduced here
for the first time. Harmonic currents for
the
geodesic flow of a noncompact hyperbolic
space with a compact convex core
generalize the Patterson-Sullivan measure
on
the limit set and are responsible for the
zeros
and poles of the corresponding zeta function.
The book describes the present state of the
research in a new field on the cutting edge
of
global analysis, harmonic analysis and
dynamical systems. It should be appealing
not only to the specialists on zeta functions
which will find their object of favorite
interest
connected in new ways with index theory,
geometric quantization methods, foliation
theory and representation theory. There are
many unsolved problems and the book
hopefully promotes further progress along
the lines indicated here.
Limnios, N., Universite de Technologie de Compiegne, France,
Oprisan, G., Universitede Technologie de
Compiegne, France
Semi-Markov Processes and Reliability
Approx. 229 pages. Hardcover
ISBN 3-7643-4196-3
English
Due in January 2001
Statistics for Industry and Technology
The book is a valuable resource for
understanding the latest developments
in Semi-Markov Processes and
reliability.
Practitioners, researchers and professionals
in applied mathematics, control and
engineering who work in areas of reliability,
lifetime data analysis, statistics, probability,
and engineering will find this book an
up-to-date overview of the field.
The theory of stochastic processes, for
science and engineering, can be considered
as an extension of probability theory allowing
modeling of the evolution of systems over
time. The modern theory of Markov
processes has its origins in the studies
of
A.A. Markov (1856-1922) on sequences of
experiments "connected in a chain"
and in the
attempts to describe mathematically the
physical phenomenon Brownian motion. The
theory of stochastic processes entered in
a
period of intensive development when the
idea of Markov property was brought in.
This book is a modern overall view of
semi-Markov processes and its applications
in reliability. It is accessible to readers
with a
first course in Probability theory (including
the basic notions of Markov chain). The text
contains many examples which aid in the
understanding of the theoretical notions
and
shows how to apply them to concrete
physical situations including algorithmic
simulati ons. Many examples of the concrete
applications in reliability are given.
Contents
1. Introduction and Renewal Process
2. Markov Renewal Process
3. Semi-Markov Process
4. Countable State Space SMP
5. Reliability of Semi-Markov Systems
6. Examples of Reliability Evaluation
A. Measures and Probability
B. Laplace-Stieltjes Transform
C. Weak Convregence
Kinderlehrer, D., Carnegie Mellon University, USA, (Ed.)
Lewy Selecta, Volume 1+2
Approx. 500 pages. Hardcover
English
Contemporary Mathematicians
Volume 1
ISBN 3-7643-3523-8
Volume 2
ISBN 3-7643-3524-6
Due in February 2001
The work of Hans Lewy (1904-1988) has
touched nearly every significant area of
functional analysis.
Famous for his originality and ingenuity,
Lewy illustrated and revealed fundamental
principles in the theory of partial differential
equations, involving in particular, elliptic
equations and free boundary problems.
The papers presented in this two-volume set
represent a selection of his best work and
are augmented by commentary from his
students, colleagues, and family.
Contributors to the volume include: E. Heinz,
D. Kinderlehrer, P. Lax, J. Leray, H. Lewy,
R. MacCamy, L. Nirenberg, and F. Treves.
Kolmogorov, A. N. Moscow State University, Russia,
Yushkevich, A. P. Institute of History of
Science and Technology,
Moscow,
Russia, (Eds)
Mathematics of the 19th Century, vol. 1:2nd rev. edition
Mathematical Logic Algebra Number Theory
Probability Theory
322 pages. Hardcover
ISBN 3-7643-6441-6
322 pages. Paperback
ISBN 3-7643-6442-4
Due in February 2001
New Edition! New in Paperback!
This is the second revised edition of the
first
volume of the outstanding collection of
historical studies of mathematics in the
nineteenth century compiled in three volumes
by A. N. Kolmogorov and A. P.
Yushkevich.
This second edition was carefully revised
by
Abe Shenitzer, York University, Ontario,
Canada.
The historical period covered in this book
extends from the early nineteenth century
up
to the end of the 1930s, as neither 1801
nor
1900 are, in themselves, turning points in
the
history of mathematics, although each date
is
notable fo a remarkable event: the first
for
the publication of Gauss・"Disquisitiones arithmeticae", the second for Hilbert's
"Mathematical Problems."
Beginning in the second quarter of the
nineteenth century mathematics underwent
a
revolution as crucial and profound in its
consequences for the general world outlook
as the mathematical revolution in the
beginning of the modern era. The main
changes included a new statement of the
problem of the existence of mathematical
objects, particulary in the calculus, and
soon
thereafter the formation of non-standard
structures in geometry, arithmetic and
algebra.
The primary objective of the work has been
to treat the evolution of mathematics in
the
nineteenth century as a whole; the discussion
is concentrated on the essential concepts,
methods, and algorithms.
Reiss, R.D., Thomas, M., both Universitat-Gesamthochschule Siegen, Germany
Statistical Analysis of Extreme Values with
Applications to
Insurance,
2nd, extended edition. Finance, Hydrology and Other Fields
Approx. 472. Softcover
ISBN 3-7643-6487-4
Due in February 2001
The statistical analysis of extreme data
is important for various disciplines,
including hydrology, insurance, finance,
engineering and environmental sciences.
This book provides a self-contained
introduction to the parametric modeling,
exploratory analysis and statistical inference
for extreme values.
Besides numerous data-based examples, the
book contains special chapters about flood
frequency analysis (coauthored by J.R.M.
Hosking), insurance (coauthored by M.
Radtke) and finance (coauthored by C.G. de
Vries and S. Caserta). In addition, five
longer case studies are included that replace
those presented in the first edition.
The assessment of the adequacy of the
parametric modeling and the statistical
inference is facilitated by the included
statistical software Academic Xtremes, an
interactive menu-driven system which runs
under Windows 95, 98, 2000, NT. The
applicability of the system is enhanced by
the
integrated programming language StatPascal.
It is the declared aim of the second extended
edition to enforce the characteristic of
the
book of providing a broad statistical
background. The new highlights, elaborated
on about 160 pages, include
* the statistical modeling of tails in
conjunction with the global modeling of
distributions with special emphasis laid
on
heavy-tailed distributions;
* the Bayesian methodology with
applications to regional flood frequency
analysis and credibility estimation in
reinsurance business;
* a thorough treatment of the phenomenon
of penultimate distributions;
* a section about conditional extremes;
* an extension of the chapter about
multivariate extreme value models, especially
for the Gumbel-McFadden model with an
application to the theory of economic choice
behavior;
* a chapter about the multivariate
peaks-over-threshold method;
* risk assessment of financial assets and
portfolios in the presence of fat and
heavy-tailed distributions by means of the
Value-at-Risk (VaR);
* sections about corrosion analysis and the
oldest-old problem.
Siegmund-Schultze, R., Agder University College, Kritiansand, Norway
Rockefeller and the Internationalization
of Mathematics
Between the Two World Wars
Approx. 350 pages, Hardcover
ISBN 3-7643-6468-8
Due in February 2001
Science Networks HistoricalStudies, Vol.
25
Philanthropies funded by the
Rockefeller family have been prominent
in the social history of the twentieth
century for their involvement in
medicine and applied science.
This book provides the first detailed study
of
their relatively brief but nonetheless influential
foray into the field of mathematics.
The careers of a generation of pathbreakers
in modern mathematics, such as S.Banach,
B.L.van der Waerden and Andr・Weil, were
decisively affected by their becoming fellows
of the Rockefeller-funded International
Education Board in the 1920s. To help
promote cooperation between physics and
mathematics Rockefeller funds supported the
erection of the new Mathematical Institute
in
Gtingen between 1926 and 1929, while
the rise of probability and mathematical
statistics owes much to the creation of the
Institut Henri Poincar・in Paris by American
philanthropy at about the same time.
This account draws upon the documented
evaluation processes behind these personal
and institutional involvements of
philanthropies. It not only sheds light on
important events in the history of
mathematics and physics of the 20th century
developments of mathematics in Europe and
the United States. Several of the documents
are given in their entirety as significant
witnesses to the gradual shift of the centre
of
world mathematics to the USA. This shift
was strengthened by the Nazi purge of
German and European mathematics after
1933 to which the Rockefeller Foundation
reacted with emergency programs that
subsequently contributed to the American
war effort.