Radjavi, H., Dalhousie University, Halifax, NS,
Canada
Rosenthal, P., University of Toronto, ON, Canada
2000. Approx. 200 pp.
0-387-98466-6
A collection of matrices is said to be triangularizable if there
is an invertible matrix S such that S1 AS is upper
triangular for every A in the collection. This generalization of
commutativity is the subject of many classical
theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The
concept has been extended to collections of
bounded linear operators on Banach spaces: such a collection is
defined to be triangularizable if there is a maximal
chain of subspaces of the Banach space, each of which is
invariant under every member of the collection. Most of
the classical results have been generalized to compact operators,
and there are also recent theorems in the
finite-dimensional case. This book is the first comprehensive
treatment of triangularizability in both the finite and
infinite-dimensional cases. It contains numerous very recent
results and new proofs of many of the classical
theorems. It provides a thorough background for research in both
the linear-algebraic and operator-theoretic
aspects of triangularizability and related areas. More generally,
the book will be useful to anyone interested in
matrices or operators, as many of the results are linked to other
topics such as spectral mapping theorems,
properties of spectral radii and traces, and the structure of
semigroups and algebras of operators. It is essentially
self-contained modulo solid courses in linear algebra (for the
first half) and functional analysis (for the second
half), and is therefore suitable as a text or reference for a
graduate course. ^
Contents: 1: Algebras of Matrices. 2: Semigroups of Matrices. 3:
Semigroups over fields of Characteristic Zero.
4: Semigroups of Non-negative Matrices. 5: Compact Operators and
Invariant Subspaces. 6: Algebras of Compact
Operators. 7: Semigroups of Compact Operators. 8: Bounded
Operators.
Fields: Linear and Multilinear Algebras,Matrix Theory; Functional
Analysis,Operator Theory
Written for: Mathematicians, grad math students
Book category: Monograph
Publication language: English
Series: Universitext.
Bethuel, F., Universite Paris Sud, Orsay, France
Huisken, G., University of T?bingen, Germany
Mueller, S., Max-Planck Institute for Mathematics, Leipzig,
Germany
Steffen, K., University of D?sseldorf, Germany
Hildebrandt, S., University of Bonn, Germany
Struwe, M., ETH-Zentrum Z?rich, Switzerland
(Eds.)
Lectures given at the 2nd Session of the Centro Internazionale
Matematico Estivo
(C.I.M.E.)held in Cetaro, Italy, June 15-22, 1996
1999. VII, 294 pp.
3-540-65977-3
The international summer school on Calculus of Variations and
Geometric Evolution Problems was held at Cetraro,
Italy, 1996. The contributions to this volume reflect quite
closely the lectures given at Cetraro which have
provided an image of a fairly broad field in analysis where in
recent years we have seen many important
contributions. Among the topics treated in the courses were
variational methods for Ginzburg-Landau equations,
variational models for microstructure and phase transitions, a
variational treatment of the Plateau problem for
surfaces of prescribed mean curvature in Riemannian manifolds -
both from the classical point of view and in the
setting of geometric measure theory.
Contents: F. Bethuel: Variational methods for Ginzburg-Landau
equations.- G. Huisken and A. Polden:
Geometric equations for hypersurfaces.- S. M?ller: Variational
models for microstructure and phase transitions.-
K. Steffen: Parametric surfaces of prescribed mean curvature.
Fields: Calculus of Variations and Control Theory; Differential
Geometry, Hyperbolic
Geometry; Differential,Difference and Integral Equations
Written for: Graduate students and researchers in these fields
Book category: Monograph
Publication language: English
Series: Lecture Notes in Mathematics.VOL. 1713
Dineen, S., University College Dublin, Ireland
1999. XV, 543 pp.
1-85233-158-5
This book considers basic questions connected with, and arising
from, the locally convex space structures that
may be placed on the space of holomorphic functions over a
locally convex space. The first three chapters
introduce the basic properties of polynomials and holomorphic
functions over locally convex spaces. These are
followed by two chapters concentrating on relationships between
the compact open topology, the ported or
Nachbin topology and the topology generated by the countable open
covers. The concluding chapter examines
the interplay between the various concepts introduced earlier as
being intrinsic to infinite dimensional
holomorphy. The comprehensive notes, historical background,
exercises, appendix and bibliography make this
book an invaluable reference whilst the presentation and
synthesis of ideas from different areas will appeal to
mathematicians from many different backgrounds.
Contents: Polynomials.- Duality Theory for Polynomials.-
Holomorphic Mappings Between Locally Convex
Spaces.- Decompositions of Holomorphic Functions.- Riemann
Domains.- Holomorphic Extensions.
Fields: Complex Analysis; Functional Analysis,Operator Theory;
Topology
Written for: Research mathematicians, graduate students,
practitioners
Book category: Monograph
Publication language: English
Series: Springer Monographs in Mathematics.
Dyke, P.P.G., University of Plymouth, UK
2000. XII, 248 pp. 51 figs.
1-85233-015-5
This book is a self-contained introduction to Laplace Transforms
and Fourier Series; emphasising the applications
of Laplace transforms throughout, the book also provides coverage
of the underlying pure mathematical structures.
Alongside the Laplace transform, the notion of Fourier series is
developed from first principles. Exercises are
provided to consolidate understanding of the concepts and
techniques, and only a knowledge of elementary
calculus and trigonometry is assumed. For second and third year
students looking for a rigorous and practical
introduction to the subject, this book will be an invaluable
source.
Contents: The Laplace Transform.- Further Properties.-
Convolution and the Solutions.- Fourier Series.-
Partial Differential Equations.- Fourier Transforms.- Complex
Variables and Laplace Transforms.- Appendices: A:
Answers to Exercises.- B: Table of Laplace Transforms.- C: Linear
Spaces.
Fields: Analysis; Fourier Analysis/Abstract Harmonic Analysis
Written for: Undergraduate students
Book category: Undergraduate Textbook
Publication language: English
Series: Springer Undergraduate Mathematics Series.
Geometry of solutions to nonlinear problems
1999. VIII, 302 pp. 56 figs.
3-540-52118-6
Based on a lecture course at the Ecole Polytechnique (Paris),
this text gives a rigorous introduction to many of
the key ideas in nonlinear analysis, dynamical systems and
bifurcation theory including catastrophe theory.
Wherever appropriate it emphasizes a geometrical or
coordinate-free approach which allows a clear focus on the
essential mathematical structures. Taking a unified view, it
brings out features common to different branches of
the subject while giving ample references for more advanced or
technical developments.
Keywords: Dynamical Systems Singularities Bifurcations
Catastrophes Nonlinear
Publication date: December 1999
Fields: Differential Geometry, Hyperbolic Geometry; Global
Analysis and Analysis of Manifolds;
Differential,Difference and Integral Equations
Written for: Graduate students, undergraduate students
Book category: Graduate Textbook
Publication language: English
Series: Universitext.
Bapat, R.B., Indian Statistical Institute, New Delhi, India
2nd ed. 2000. Approx. 180 pp.
0-387-98871-8
The main purpose of Linear Algebra and Linear Models is to
provide a rigorous introduction to the basic
aspects of the theory of linear estimation and hypothesis
testing. The necessary prerequisites in matrices,
multivariate normal distribution and distributions of quadratic
forms are developed along the way. The book is
aimed at advanced undergraduate and first-year graduate masters
students taking courses in linear algebra, linear
models, multivariate analysis, and design of experiments. It
should also be of use to research mathematicians and
statisticians as a source of standard results and problems.
Keywords: Linear Algebra Linear Models Multevariate Analysis
Design of Experiments
Contents: Vector Spaces and Matrices.- Linear Estimation.- Tests
of Linear Hypotheses.- Singular Values and
Their Applications.- Block Designs and Optimality.- Rank
Additivity.
Fields: Linear and Multilinear Algebras,Matrix Theory;
Statistics, general
Written for: Undergraduate and graduate mathematics &
statistic students, mathematicians, statisticians
Book category: Undergraduate Textbook
Publication language: English
Series: Universitext.
Corke, P.I., CSIRO, Kenmore, QLD, Australia
Trevelyan, J., The University of Western Australia, Nedlands, WA,
Australia
(Eds.)
2000. XIX, 528 pp. 358 figs.
1-85233-210-7
This book presents the proceedings of the 6th International
Symposium on Experimental Robotics held in Sydney
in March 1999. The editors and contributors represent the leading
robotics research efforts from around the
world. Micro-machines, interplanetary exploration, minimally
invasive surgery and emerging humanoid robots are
among the most obvious attainments of leading robotics research
teams reported in this volume. Less obvious but
equally significant are the fundamental advances in robot
map-building and methods of communication between
humans and machines that are demonstrated through experimental
results. This collection of papers will provide
the reader with a concise report on the current achievements and
future trends in robotics research across the
world.
Contents: Index of Authors.- Keynotes.- Manipulation.- Vision.-
Control.- Applications.- Locomotion.-
Localization and Map Building.- Planning and Navigation.-
Programming and Learning.- Haptics.- Friction and
Flexibility.- Humanoid and Human Interaction.
Series: Lecture Notes in Control and Information Sciences.VOL.
250
Nagaosa, N., The University of Tokyo, Japan
1999. VIII, 170 pp. 18 figs.
3-540-65981-1
In this book the author extends the concepts previously
introduced in his "Quantum Field Theory in Condensed
Matter Physics" to situations in which the strong electronic
correlations are crucial for the understanding of the
observed phenomena. Starting from a model field theory to
illustrate the basic ideas, more complex systems are
analysed in turn. A special chapter is devoted to the description
of antiferromagnets, doped Mott insulators and
quantum Hall liquids from the point of view of gauge theory. This
advanced text is written for graduate students
and researchers working in related areas of physics.
Fields: Atoms, Molecules and Cluster; Condensed Matter and
Properties of Materials;
Quantum Physics
Written for: Graduate students, researchers
Book category: Monograph
Publication language: English
Series: Texts and Monographs in Physics.