Radio channel assignment has attracted considerable interest
over many years, spanning disciplines that include radio
engineering, electrical engineering, physics, mathematics,
computer science and economics. Over the last few years, there
has been a rapid growth in the demand for wireless communications
services, which has in turn created a need for Governments and
industry to develop sound theory, methods, and computational
tools for the effective and efficient management of the spectrum.
This book contains a collection of contributions from those
working in the field, which explore the various aspects of
current research in channel radio assignment. The collection
includes several chapters concerned with developing a sound
theoretical framework for channel assignment; other chapters are
concerned with developing state-of-the-art computational
algorithms for solving channel assignment problems. Two chapters
discuss the regulatory aspects of spectrum management and its
history. Also included are the modelling and efficient solution
of network design problems, which are becoming increasingly
important in wireless networks. Finally a chapter bridging the
regulatory and mathematical issues describes the benefit of
economic modelling in radio spectrum management.
This book illustrates a range of mathematical and computational
tools, including graph colouring, graph labelling, linear and
nonlinear optimization, meta-heuristics, constraint satisfaction
and multidisciplinary optimization. It is aimed at practising
engineers, university academics with an interest in the area, and
Government agencies responsible for the management of the radio
spectrum. This title is the latest in the Oxford Lecture Series
in Mathematics and its Applications, which aims to publish short
books aimed at first-year graduates and academics in mathematics
and related subjects. The Series focuses on future directions of
research with emphasis on attractive genuine applications of the
subject, particularly topics in the natural sciences.
0-19-850314-8
September 2002
Oxford Lecture Series in Mathematics and Its Applications 23
Paper | January 2003 | ISBN: 0-691-11332-7
Cloth | January 2003 | ISBN: 0-691-11331-9
192 pp. | 6 x 9
This book applies model theoretic methods to the study of certain
finite permutation groups, the automorphism groups of structures
for a fixed finite language with a bounded number of orbits on 4-tuples.
Primitive permutation groups of this type have been classified by
Kantor, Liebeck, and Macpherson, using the classification of the
finite simple groups.
Building on this work, Gregory Cherlin and Ehud Hrushovski here
treat the general case by developing analogs of the model
theoretic methods of geometric stability theory. The work lies at
the juncture of permutation group theory, model theory, classical
geometries, and combinatorics.
The principal results are finite theorems, an associated analysis
of computational issues, and an "intrinsic"
characterization of the permutation groups (or finite structures)
under consideration. The main finiteness theorem shows that the
structures under consideration fall naturally into finitely many
families, with each family parametrized by finitely many
numerical invariants (dimensions of associated coordinating
geometries).
The authors provide a case study in the extension of methods of
stable model theory to a nonstable context, related to work on
Shelah's "simple theories." They also generalize
Lachlan's results on stable homogeneous structures for finite
relational languages, solving problems of effectivity left open
by that case. Their methods involve the analysis of groups
interpretable in these structures, an analog of Zilber's
envelopes, and the combinatorics of the underlying geometries.
Taking geometric stability theory into new territory, this book
is for mathematicians interested in model theory and group theory.
Gregory Cherlin is Professor of Mathematics at Rutgers University.
He is the author of Model Theoretic Algebra: Selected Topics.
Ehud Hrushovski is Professor of Mathematics at the Hebrew
University of Jerusalem.
Series: Annals of Mathematics Studies
Paper | January 2003 | ISBN: 0-691-09085-8
Cloth | January 2003 | ISBN: 0-691-09084-X
712 pp. | 6 x 9 | 70 line illus.
The development of physical theory is one of our greatest
intellectual achievements. Its products--the currently prevailing
theories of physics, astronomy, and cosmology--have proved
themselves to possess intrinsic beauty and to have enormous
explanatory and predictive power. This anthology of primary
readings chronicles the birth and maturation of five such
theories (the heliocentric theory, the electromagnetic field
theory, special and general relativity, quantum theory, and the
big bang theory) in the words of the scientists who brought them
to life. It is the first historical account that captures the
rich substance of these theories, each of which represents a
fascinating story of the interplay of evidence and insight--and
of dialogue among great minds.
Readers sit in with Copernicus, Kepler, and Galileo as they
overturn the geocentric universe; observe the genius of Faraday
and Maxwell as they "discover" the electromagnetic
field; look over Einstein's shoulder as he works out the details
of relativity; listen in as Einstein and Bohr argue for the soul
of quantum mechanics in the Completeness Debate; and watch as
Hubble and others reveal the history of the universe.
The editors' approach highlights the moments of discovery that
rise from scientific creativity, and the presentation humanizes
the scientific process, revealing the extent to which great
scientists were the first to consider the philosophical
implications of their work. But, most significantly, the editors
offer this as their central thesis: although each was ushered in
by a revolution, and each contains counterintuitive elements that
delayed its acceptance, these five theories exhibit a continuous
rational development that has led them to a permanent place in
the worldview of science.
Accessible to the general reader yet sufficiently substantive
that working scientists will find value in it, The Tests of Time
offers an intimate look into how physical theory has been
developed, by the brilliant people who have developed it.
Lisa M. Dolling, Arthur F. Gianelli, and Glenn N. Statile teach
the history and philosophy of science on both the graduate and
undergraduate levels at St. John's University. Arthur Gianelli is
Chair of the Philosophy Department and the coeditor of The
Metaphysical Quest. Lisa Dolling has written and lectured on the
philosophy of Niels Bohr and directs the Science and Religion
project at St. John's. Glenn Statile has lectured and written on
topics in cosmology and the philosophy of science.
Endorsements:
"This excellent work collects a judiciously chosen group of
writings on what are universally regarded as five of the most
significant physical theories in the history of science. Each of
the selections serves to place the development and significance
of the physical theory in its historical setting as well as to
shed light on important philosophical issues it raises. This is
an extremely useful book that will be of benefit to anyone with
an interest in the history and philosophy of science. I for one
will certainly be using this volume as a source book for my
courses in the history and philosophy of the physical sciences."--Martin
Tamny, The City College and the Graduate Center, City University
of New York
"It is a pleasure to find an original addition to the small
list of worthwhile books on the history and philosophy of natural
science. The authors have done an excellent job assembling and
organizing a selection of texts that can be used equally well at
an elementary or more advanced level. No other anthology combines
breadth and accuracy so well."--Stephen Toulmin, University
of Southern California
Subject Areas:
Physics
History of Science and Medicine, Philosophy of Science
Astronomy and Cosmology
Cloth | August 2002 | ISBN: 0-691-05022-8
336 pp. | 6 x 9 | 12 halftones. 40 line illus.
This book brings together a number of lectures given between 1993
and 1999 as part of a special series hosted by the Federal
University of Pernambuco, in which internationally established
researchers came to Recife, Brazil, to lecture on classical or
celestial mechanics. Because of the high quality of the results
and the general interest in the lecturers' topics, the editors
have assembled nine of the lectures here in order to make them
available to mathematicians and students around the world. The
material presented includes a good balance of pure and applied
research and of complete and incomplete results. Bringing
together material that is otherwise quite scattered in the
literature and including some important new results, it will
serve graduate students and researchers interested in Hamiltonian
dynamics and celestial mechanics.
The contributors are Dieter Schmidt, Ernesto Perez-Chavela, Mark
Levi, Placido Taboas and Jack Hale, Jair Koiller et al.,
Hildeberto Cabral, Florin Diacu, and Alain Albouy. The topics
covered include central configurations and relative equilibria
for the N-body problem, singularities of the N-body problem, the
two-body problem, normal forms of Hamiltonian systems and
stability of equilibria, applications to celestial mechanics of
Poincare's compactification, the motion of the moon, geometrical
methods in mechanics, momentum maps and geometric phases,
holonomy for gyrostats, microswimming, and bifurcation from
families of periodic solutions.
Hildeberto Cabral is Professor of Mathematics at the Federal
University of Pernambuco in Recife, Brazil. He has published on
periodic solutions, stability, and other topics in Hamiltonian
systems and celestial mechanics. Florin Diacu is Professor of
Mathematics and Director of the Pacific Institute for the
Mathematical Sciences at the University of Victoria. He is the
author of Singularities of the N-Body Problem and An Introduction
to Differential Equations and coauthor of Celestial Encounters (Princeton).
Endorsements:
"This is an excellent text and reference. I know of no
comparable book. Its scope is wide, and the quality of the
authors is extremely high."--James Meiss, University of
Colorado, Boulder
"These lectures, in addition to containing some new
significant results, perform the service of collecting together
the material on diverse topics in celestial mechanics in an
accessible form."--Edward Belbruno, Princeton University
Paper | October 2002 | ISBN: 0-691-10298-8
Cloth | 1998 | ISBN: 0-691-05872-5
400 pp. | 7 x 10 | 121 figures
Ever since the Irish mathematician William Rowan Hamilton
introduced quaternions in the nineteenth century--a feat he
celebrated by carving the founding equations into a stone bridge--mathematicians
and engineers have been fascinated by these mathematical objects.
Today, they are used in applications as various as describing the
geometry of spacetime, guiding the Space Shuttle, and developing
computer applications in virtual reality. In this book, J. B.
Kuipers introduces quaternions for scientists and engineers who
have not encountered them before and shows how they can be used
in a variety of practical situations.
The book is primarily an exposition of the quaternion, a 4-tuple,
and its primary application in a rotation operator. But Kuipers
also presents the more conventional and familiar 3 x 3 (9-element)
matrix rotation operator. These parallel presentations allow the
reader to judge which approaches are preferable for specific
applications. The volume is divided into three main parts. The
opening chapters present introductory material and establish the
book's terminology and notation. The next part presents the
mathematical properties of quaternions, including quaternion
algebra and geometry. It includes more advanced special topics in
spherical trigonometry, along with an introduction to quaternion
calculus and perturbation theory, required in many situations
involving dynamics and kinematics. In the final section, Kuipers
discusses state-of-the-art applications. He presents a six degree-of-freedom
electromagnetic position and orientation transducer and concludes
by discussing the computer graphics necessary for the development
of applications in virtual reality.
J. B. Kuipers is Professor Emeritus of Mathematics at Calvin
College. In addition to publishing papers and research notes on
quaternions, he spent seventeen years in the aerospace industry
where his work included developing applications of quaternion
theory for aerospace systems. He also developed a six-dimensional
graphics system and, as a consequence, is regarded by some as the
founder of virtual reality.
Reviews:
"This book will appeal to anyone with an interest in three-dimensional
geometry. It is a competent and comprehensive survey. . . . This
book is unique in that it is probably the only modern book to
treat quaternions seriously. . . . A valuable asset."--Aeronautical
Journal
"The text is written in a clear and readable style well
suited for students wishing to master fundamental quaternion
concepts."--Mark C. Allman, Senior Engineer, The Boeing
Company
Cloth | November 2002 | ISBN: 0-691-08973-6
480 pp. | 6 x 9 | 148 line illus. 41 tables.
In recent years, interest-rate modeling has developed rapidly in
terms of both practice and theory. The academic and
practitioners' communities, however, have not always communicated
as productively as would have been desirable. As a result, their
research programs have often developed with little constructive
interference. In this book, Riccardo Rebonato draws on his
academic and professional experience, straddling both sides of
the divide to bring together and build on what theory and trading
have to offer.
Rebonato begins by presenting the conceptual foundations for the
application of the LIBOR market model to the pricing of interest-rate
derivatives. Next he treats in great detail the calibration of
this model to market prices, asking how possible and advisable it
is to enforce a simultaneous fitting to several market
observables. He does so with an eye not only to mathematical
feasibility but also to financial justification, while devoting
special scrutiny to the implications of market incompleteness.
Much of the book concerns an original extension of the LIBOR
market model, devised to account for implied volatility smiles.
This is done by introducing a stochastic-volatility, displaced-diffusion
version of the model. The emphasis again is on the financial
justification and on the computational feasibility of the
proposed solution to the smile problem. This book is must reading
for quantitative researchers in financial houses, sophisticated
practitioners in the derivatives area, and students of finance.
Riccardo Rebonato is Head of Group Market Risk and Head of the
Quantitative Research Centre (QUARC) for the Royal Bank of
Scotland Group. He is also a Visiting Lecturer at Oxford
University's Mathematical Institute, where he teaches for the MSC/Diploma
in Mathematical Finance. His books include Interest-Rate Option
Models and Volatility and Correlation in Option Pricing.
Endorsements:
"This book is a significant contribution to the field. It
offers plenty of empirical work and case studies illustrating the
application of the models each step of the way. Unlike other
treatments, it emphasizes the market rationale for modeling
choices, and is not driven by purely mathematical considerations.
Reference is continually made to market features, the behaviour
of instruments, and empirical features, with all of this backed
up by the author's considerable experience."--Nick Webber,
University of Warwick
"There are many books that get bogged down in mathematical
technicalities before they get to the point and are therefore of
little use to practitioners. Rebonato takes the opposite approach:
he gets to the point. People working in the mathematical finance
industry will love this book."--Jeff Dewynne, Oxford
University