Zuo, K., University of Kaiserslautern, Germany
1999. Approx. 150 pp.
3-540-66312-6
Using harmonic maps, non-linear PDE and techniques from algebraic
geometry this book enables the reader to
study the relation between fundamental groups and algebraic
geometry invariants of algebraic varieties. The reader
should have a basic knowledge of algebraic geometry and
non-linear analysis. This book can form the basis for
graduate level seminars in the area of topology of algebraic
varieties. It also contains present new techniques for
researchers working in this area.
Keywords: fundamental group algebraic variety harmonic map vector
bundle
Contents: Introduction.- Preliminaries.- Review of Algebraic
groups over arbitrary fields.- Representations of
phi1 and the Moduli space.- p-adic norm on a vector space and
Bruhat-Tits buildings.- Harmonic metric on flat
vector bundle.- Pluriharmonic map of finite energy.-
Pluriharmonic maps of possibly infinite energy but with
controlled growth at infinity.- Non-abelian Hodge theory,
factorization theorems for non rigid or p-adic unbound
representations.- Higgs bundles for archimedean representations
and equivariant holomorphic 1-forms for p-adic
representations.- Albanese maps and a Lefschetz type theorem for
holomorphic 1-forms.- Factorizations for
nonrigid representations into almost simple complex algebraic
groups.- Factorization for p-adic unbounded
representations into almost simple p-adic algebraic groups.-
Simpson's construction of families on non rigid
representations.- Shavarevich maps for representations of phi1,
Kodaira dimension and Chern-hyperbolicity of
Shavarevich varieties...
Series: Lecture Notes in Mathematics.VOL. 1708
Schwartz, N., University of Passau,
Germany
Madden, J.J., Louisiana State University, Baton Rouge, LA, USA
1999. XII, 279 pp.
3-540-66460-2
The book lays algebraic foundations for real geometry through a
systematic investigation of partially ordered rings
of semi-algebraic functions. Real spectra serve as primary
geometric objects, the maps between them are
determined by rings of functions associated with the spectra. The
many different possible choices for these rings
of functions are studied via reflections of partially ordered
rings. Readers should feel comfortable using basic
algebraic and categorical concepts. As motivational background
some familiarity with real geometry will be helpful.
The book aims at researchers and graduate students with an
interest in real algebra and geometry, ordered
algebraic structures, topology and rings of continuous functions.
Keywords: semi - algebraic functions partially ordered ring
formally real field real spectrum reflective
subcategory
Contents: Preface.- List of contents.- Introduction.- Preordered
and partially ordered rings.- Reflective
subcategories.- Totally ordered and real closed fields.- Real
spectra of preordered rings: Epimorphisms of
reduced porings.- Functions and representable porings.-
Semi-algebraic functions.- Comparing reflectors.-
Constructing reflectors.- H-closed epireflectors.-
Quotient-closed reflectors.- The real closure reflector.-
Arities of reflectors and approximations by H-closed reflectors.-
Epimorphic extensions of reduced porings.-
Essential monoreflectors.- Reflections of totally ordered
fields.- von Neumann regular f-rings.- Totally ordered
domains.- Reduced f-rings.- Rings of continuous piecewise
polynomial functions.- Rings of continuous piecewise
rational functions.- Discontinuous semi-algebraic functions.- The
lattice of H-closed monoreflectors.-
Bibliography.- List of categories.- Index.
Series: Lecture Notes in Mathematics.VOL. 1712
Ricker, W., University of New South Wales, Sydney, NSW, Australia
1999. XVII, 159 pp. 7 figs.
3-540-66461-0
This book presents a systematic investigation of the theory of
those commutative, unital subalgebras (of bounded
linear operators acting in a Banach space) which are closed for
some given topology and are generated by a
uniformly bounded Boolean algebra of projections. One of the main
aims is to employ the methods of vector
measures and integration as a unifying theme throughout. This
yields proofs of several classical results which are
quite different to the classical ones. This book is directed to
both those wishing to learn this topic for the first
time and to current experts in the field.
Keywords: spectral measures operator algebras projections
Contents: Preface.- Introduction.- Vector measures and Banach
spaces.- Abstract Boolean algebras and Stone
spaces.- Boolean algebras of projections and uniformly closed
operator algebras.- Ranges of spectral measures and
Boolean algebras of projections.- Integral representation of the
strongly closed algebra generated by a Boolean
algebra of projections.- Bade functionals: an application to
scalar-type spectral operators.- The reflexivity
theorem and bicommutant algebras.- Bibliography.- Appendix.- List
of symbols.- Subject index.
Series: Lecture Notes in Mathematics.VOL. 1711
Benisty, H., Ecole Polytechnique,
Palaiseau, France
Gerard, J.-M., CNET, Bagneux, France
Houdre, R., Institut de micro et opto-electronique, Lausanne,
Switzerland
Rarity, J., Malvern, UK
Weisbuch, C., Ecole Polytechnique, Palaiseau, France
(Eds.)
Fundamentals and Applications
1999. X, 496 pp. 223 figs.
3-540-66435-1
This set of lecture notes provides a detailed and up-to-date
description of a field undergoing explosive growth,
that of confined photon systems in the shape of microcavities or
photonic crystals. Bringing together world leaders
in the field, it provides all the basic tools needed to master a
subject which will have both major impact in
fundamental studies and widescale applications. Confined photon
systems enable the study of low-dimensional
photonic systems, modified light-matter interaction, e.g. between
excitons and photons in all-solid-state
semiconductor microcavities, and of many phenomena of quantum
optics, including single photon generation,
squeezed light, quantum state entanglement, non-local quantum
measurements, and, potentially, quantum
computation. They are also on the verge of yielding new, high
performance optical devices for large-scale
industries such as telecommunications and display technology.
Keywords: Low - dimensional photonic systems, quantum optics,
optical devices, semiconductor microcavities
Contents: Basics of Quantum Optics and Cavity Quantum
Electrodynamics.- Basics of Dipole Emission from a
Planar Cavity.- Microscopic Theory of the Optical Semiconductor
Response Nearthe Fundamental Absorption
Edge.- An Introduction to Photonic Crystals.- Linear Optical
Properties of Semiconductor Microcavities with
Embedded Quantum Wells.- Spontaneous Emission Control and
Microcavity Light Emitters.- Cavity QED -
Where's the Q?- Quantum Optics in Semiconductors.- Semiconductor
Microcavities, Quantum Boxes, and the
Purcell Effect.- Single Photon Sources and Applications.-
Photonic Crystals for Nonlinear Optical Frequency
Conversion.- Physics of Light Extraction Efficiency in Planar
Microcavity Light-Emitting Diodes.- Measuring the
Optical Properties of Two-Dimensional Photonic Crystals in the
Near-Infrared.- Limitations to Optical
Communications.- Thoughts on Quantum Computing.
Series: Lecture Notes in Physics.531
Kriele, M., Technical University of Berlin, Germany
Foundations of General Relativity and
Differential Geometry
1999. XV, 432 pp.
3-540-66377-0
This textbook is for mathematicians and mathematical physicists
and is mainly concerned with the physical
justification of both the mathematical framework and the
foundations of the theory of general relativity. Previous
knowledge of the relevant physics is not assumed. This book is
also suitable as an introduction to
pseudo-Riemannian geometry with emphasis on geometrical concepts.
A significant part of the text is devoted to
the discussion of causality and singularity theorems. The
insights obtained are applied to black hole astrophysics,
thereby making the connection to current active research in
mathematical physics and cosmology.
Keywords: relativity, cosmology, gravitaion, causality,
singularity, differential geometry, spacetime
Contents: Local Theory of Space and Time.- Analysis on
Manifolds.- Space and Time from a Global Point of
View.- Pseudo Riemannian Manifolds.- General Relativity.-
Robertson-Walker Cosmology.- Spherical Symmetry.-
Causality.- Singularity Theorems.
System requirements: none
Series: Lecture Notes in Physics.Monograph Series 59
Varga, R.S., Kent State University, Kent, OH, USA
2nd, rev. and exp. ed.
1999. VI, 358 pp.
3-540-66321-5
This book is a revised version of the first edition, originally
published by Prentice Hall in 1962 and regarded as a
classic in its field. In some places, newer research results,
e.g. results on weak regular splittings, have been
incorported in the revision, and in other places, new material
has been added in the chapters, as well as at the
end of chapters, in the form of additional up-to-date references
and some recent theorems to give the reader
some newer directions to pursue. The material in the new chapters
is basically self-contained and more exercises
have been provided for the readers. While the original version
was more linear algebra oriented, the revision
attempts to emphasize tools from other areas, such as
approximation theory and conformal mapping theory, to
access newer results of interest. The book should be of great
interest to researchers and graduate students in the
field of numerical analysis.
Keywords: Gerschgorin circles, Perron - Frobenius theory,
iterative methods, semi - iterative methods
Series: Springer Series in Computational Mathematics.VOL. 27
Haken, H., University of Stuttgart, Germany
A Macroscopic Approach to Complex Systems
2nd ed. 1999. XII, 210 pp. 62 figs.
3-540-66286-3
This book presents the concepts needed to deal with
self-organizing complex systems from a unifying point of
view that uses macroscopic data. The various meanings of the
concept "information" are discussed and a general
formulation of the maximum information (entropy) principle is
used. With the aid of results from synergetics,
adequate objective constraints for a large class of
self-organizing systems are formulated and examples are given
from physics, biology, and computer science (pattern recognition
by parallel computers). The extensions
contained in the second edition show how, based on possibly
scarce and noisy data, unbiased guesses about
processes of complex systems can be made and the underlying
deterministic and random forces determined. This
procedure allows probabilistic predictions of processes, with
applications to numerous fields ranging from
technology through biology and medicine to economy. The
relationship to chaos theory is also addressed.
Keywords: Complex Systems, Synergetics, Self - Organization,
Information Theory, Chaos .
Contents: The Challenge of Complex Systems.- From the Microscopic
to the Macroscopic World ... .- ... and
Back Again: The Maximum Information Principle (MIP).- An Example
from Physics: Thermodynamics.- Application
of the Maximum Information Principle to Self-Organizing Systems.-
The Maximum Information Principle for
Nonequilibrium Phase Transitions: Determination of Order
Parameters, Enslaved Modes, and Emerging Patterns.-
Information, Information Gain, and Efficiency of Self-Organizing
Systems Close to Their Instability Points.- Direct
Determination of Lagrange Multipliers.- Unbiased Modeling of
Stochastic Processes: How to Guess Path
Integrals, Fokker-Planck Equations and Langevin to Equations.-
Application to Some Physical Systems.-
Transitions Between Behavioral Patterns in Biology. An Example:
Hand Movements.- Pattern Recognition.-
Quantum Systems.- Concluding Remarks and Outlook.- References.-
Subject Index.
Series: Springer Series in Synergetics.VOL. 40
Moreau, J., Lausanne, Suisse
Doudin, P.-A., Universite de Geneve, Suisse
Cazes, P., Universite de Paris IX, Paris, France
(Eds.)
Approches nouvelles pour l'analyse statistique
des donnees
1999. XVI, 266 p. 53 figs., 58 tabs.
3-540-66346-0
Cet ouvrage presente differents points de vue sur une meme
methode, l'analyse des correspondances. Il montre
comment cette methode s'est developpee pour traiter des donnees
de plus en plus variees et complexes et
comment elle s'est enrichie au contact d'autres courants de
pensee. De plus, cet ouvrage presente un panorama
des applications possibles. Cet ouvrage qui rassemble des
contributions de differents auteurs presente un expose
a la fois progressif sur le plan didactique et suffisamment vaste
pour rassembler en un seul volume des
developpements theoriques recents illustres par de multiples
applications en sciences humaines. Le caractere tres
general de la methode et la variete des types de donnees
consideres permettent ?l 'tudiant comme au
chercheur d'integrer cet outil statistique son domaine d'intrt.
Keywords: Analyse des correspondances, graphes, questionnaire,
modele, traitement des donnees
Contents: I: Fondements de la methode et applications
significatives.- II: Analyse des correspondances de
donnees structurees.- III: Methodes connexes.
Series: Mathematiques & Applications.VOL. 32