This book is ideally suited for a two-term
undergraduate
algebra course culminating in a discussion
on Galois theory. It
provides an introduction to group theory
and ring theory en route.
In addition, there is a chapter on groups
・including
applications to error-correcting codes and
to solving Rubik's
cube. The concise style of the book will
facilitate student吠nstructor
discussion, as will the selection of exercises
with various
levels of difficulty. For the second edition,
two chapters on
modules over principal ideal domains and
Dedekind domains have
been added, which are suitable for an advanced
undergraduate
reading course or a first-year graduate course.
Contents:
Group Theory
Ring Theory
Galois Theory
Rings and Modules
Dedekind Domains
Readership: Upper level undergraduates and
graduate students in
mathematics.
220pp (approx.) Pub. date: Scheduled Fall
2003
ISBN 981-238-576-2
ISBN 981-238-600-9(pbk)
Contents:
On Gaussian and Poisson White Noises (N Asai)
Renormalization, Orthogonalization, and Generating
Functions (I
Kubo et al.)
Insider Trading in Continuous Time (E Barucci
et al.)
Existence, Uniqueness, Consistency and Dependency
on Diffusion
Coefficients of Generalized Solutions of
Nonlinear Diffusion
Equations in Colombeau's Algebra (H Deguchi)
On Mathematical Treatment of Quantum Communication
Gate on Fock
Space (W Freudenberg et al.)
A Frontier of White Noise Analysis (T Hida)
An Interacting Fock Space with Periodic Jacobi
Parameter Obtained
from Regular Graphs in Large Scale Limit
(A Hora & N Obata)
Error Exponents of Codings for Stationary
Gaussian Channels (S
Ihara)
White Noise Analysis on Classical Wiener
Space Revisited (Y-J Lee
& H-H Shih)
Fractional Brownian Motions and the Levy
Laplacian (K Nishi et al.)
Recognition and Teleportation (M Ohya)
Jump Finding of a Stable Process (Si Si et
al.)
On Entropy Production of a One-Dimensional
Lattice Conductor (S
Tasaki)
Quantum Information and Spacetime Structure
(I V Volovich)
Readership: Researchers in probability &
statistics,
mathematical physics, functional analysis
and mathematical
biology.
250pp (approx.) Pub. date: Scheduled Winter
2003
ISBN 981-238-585-1
This is a book for those who want to understand
the main ideas
in the theory of optimal problems. It provides
a good
introduction to classical topics (under the
heading of "the
calculus of variations") and more modern
topics (under the
heading of "optimal control").
It employs the language
and terminology of functional analysis to
discuss and justify the
setup of problems that are of great importance
in applications.
The book is concise and self-contained, and
should be suitable
for readers with a standard undergraduate
background in
engineering mathematics.
Contents:
Basic Calculus of Variations
Elements of Optimal Control Theory
Functional Analysis
Some Applications in Mechanics
Readership: Graduate students, academics
and practitioners in
engineering, applied physics and applied
mathematics.
400pp (approx.) Pub. date: Scheduled Winter
2003
ISBN 981-238-581-9
September 2003 | Hardback | 188 pages 5 half-tones
40 figures
1 colour figure | ISBN: 0-521-82657-8
September 2003 | Paperback | 188 pages 5
half-tones 40 figures 1
colour figure | ISBN: 0-521-53394-5
Many phenomena in nature, engineering or
society when seen at an
intermediate distance, in space or time,
exhibit the remarkable
property of self-similarity: they reproduce
themselves as scales
change, subject to so-called scaling laws.
Itｿs crucial to know
the details of these laws, so that mathematical
models can be
properly formulated and analysed, and the
phenomena in question
can be more deeply understood. The author
describes and teaches
the art of discovering scaling laws, starting
from dimensional
analysis and physical similarity, which are
here given a modern
treatment. He demonstrates the concepts of
intermediate
asymptotics and the renormalisation group
as natural attributes
of self-similarity and shows how and when
these notions and tools
can be used to tackle the task at hand, and
when they cannot.
Based on courses taught to undergraduate
and graduate students,
the book can also be used for self-study
by biologists, chemists,
astronomers, engineers and geoscientists.
Contents
Foreword; Introduction; 1. Dimensional analysis
and physical
similarity; 2. Self-similarity and intermediate
asymptotics; 3.
Scaling laws and self-similar solutions which
cannot be obtained
by dimensional analysis; 4. Complete and
incomplete similarity; 5.
Scaling and transformation groups and the
renormalisation group;
6. Self-similar solutions and traveling waves;
7. Scaling laws
and fractals; 8. Scaling laws for turbulent
wall-bounded shear
flows at very large Reynolds numbers; References;
Index.
September 2003 | Hardback | 408 pages 16
line diagrams | ISBN:
0-521-82721-3
Variational methods are very powerful techniques
in nonlinear
analysis and are extensively used. They are
extensively used in
many disciplines of pure and applied mathematics
(including
ordinary and partial differential equations,
mathematical
physics, gauge theory, geometrical analysis).
This book presents
min-max methods through a comprehensive study
of the different
faces of the celebrated Mountain Pass Theorem
(MPT) of Ambrosetti
and Rabinowitz. The reader is gently led
from the most accessible
results to the forefront of the theory, and
at each step in this
walk between the hills, the author presents
the extensions and
variants of the MPT in a complete and unified
way. Coverage
includes standard topics: the classical and
dual MPT; second-order
information from PS sequences; symmetry and
topological index
theory; perturbations from symmetry; convexity
and more. But it
also covers other topics covered nowhere
else in book form: the
non-smooth MPT; the geometrically constrained
MPT; numerical
approaches to the MPT; and even more exotic
variants. Each
chapter has a section with supplementary
comments and
bibliographical notes, and there is a rich
bibliography and a
detailed index to aid the reader. The book
is suitable for
researchers and graduate students. Nevertheless,
the style and
the choice of the material make it accessible
to all newcomers to
the field.
Contents
1. Retrospective; Part I. First Steps Toward
the Mountains: 2.
Palais-Smale condition. Definitions and examples;
3. Variational
principle; 4. Deformation lemma; Part II.
Reaching the Mountain
Pass Through Easy Climbs: 5. The finite dimensional
MPT; 6. The
topological MPT; 7. The classical MPT; 8.
The multidimensional
MPT; Part III. A Deeper Insight in Mountain
Topology: 9. The
limiting case in the MPT; 10. Palais-Smale
condition versus
asymptotic behavior; 11. Symmetry and the
MPT; 12. The structure
of the critical set in the MPT; 13. Weighted
Palais-Smale
conditions; Part IV. The Landscape Becoming
Less Smooth: 14. The
semismooth MPT; 15. The nonsmooth MPT; 16.
The metric MPT; Part V.
Speculating about the Mountain Pass Geometry:
17. The MPT on
convex domains; 18. A MPT in order intervals;
19. The linking
principle; 20. The intrinsic MPT; 21. Geometrically
contrained
MPT; Part VI. Technical Climbs: 22. Numerical
MPT
implementations; 23. Perturbation from symmetry
and the MPT; 24.
Applying the MPT in bifurcation problems;
25. More climbs; A.
Background material.