Edited by: Jane Cronin, Rutgers University, New Brunswick, NJ,
and Robert E. O'Malley, Jr., University of Washington, Seattle,
WA
Description
To understand multiscale phenomena, it is essential to employ
asymptotic methods to construct approximate
solutions and to design effective computational algorithms.
This volume consists of articles based on the AMS Short Course in
Singular Perturbations held at the annual
Joint Mathematics Meetings in Baltimore (MD). Leading experts
discussed the following topics which they expand
upon in the book: boundary layer theory, matched expansions,
multiple scales, geometric theory, computational
techniques, and applications in physiology and dynamic
metastability. Readers will find that this text offers an
up-to-date survey of this important field with numerous
references to the current literature, both pure and applied.
Contents
R. E. O'Malley, Jr. -- Figuring out singular perturbations after
a first course in ODEs
M. H. Holmes -- The method of multiple scales
S. Adjerid, M. Aiffa, and J. E. Flaherty -- Computational methods
for singularly perturbed systems
T. J. Kaper -- An introduction to geometric methods and dynamical
systems theory for singular perturbation problems
J. Cronin -- Analysis of cellular oscillations
M. J. Ward -- Exponential asymptotics and
convection-diffusion-reaction models
Index
Details:
Series: Proceedings of Symposia in Applied Mathematics, Volume:
56
Publication Year: 1999
ISBN: 0-8218-0929-6
Paging: 186 pp.
Binding: Hardcover
Edited by: T. Y. Lam, University of California, Berkeley, CA,
and A. R. Magid, University of Oklahoma, Norman, OK
Description
This volume includes expositions of key developments over the
past four decades in commutative and
non-commutative algebra, algebraic $K$-theory, infinite group
theory, and applications of algebra to topology.
Many of the articles are based on lectures given at a conference
at Columbia University honoring the 65th birthday of
Hyman Bass. Important topics related to Bass's mathematical
interests are surveyed by leading experts in the field.
Of particular note is a professional autobiography of Professor
Bass, and an article by Deborah Ball on mathematical
education. The range of subjects covered in the book offers a
convenient single source for topics in the field.
Contents
J. Ewing -- On the occasion of the 65th birthday of Hyman Bass
H. Bass -- A professional autobiography
D. L. Ball -- Crossing boundaries: Probing the interplay of
mathematics and pedagogy in elementary teaching
E. Formanek -- Bass's work on the Jacobian conjecture
R. M. Guralnick and C. J. Pappacena -- Torsion in genus class
groups
C. Huneke -- Hyman Bass and ubiquity: Gorenstein rings
I. Kaplansky -- A salute to Euler and Dickson on the occasion of
Hy's 65th birthday
T. Y. Lam -- Bass's work in ring theory and projective modules
A. Lubotzky -- One for almost all: Generation of $SL(n,p)$ by
subsets of $SL(n, \Bbb{Z})$
A. R. Magid -- Deformations of representations
S. Mozes -- Trees, lattices and commensurators
M. P. Murthy -- A survey of obstruction theory for projective
modules of top rank
A. S. Rapinchuk -- The congruence subgroup problem
P. B. Shalen -- Three-manifold topology and the tree for PSL$_2$:
The Smith conjecture and beyond
C. A. Weibel -- The development of algebraic $K$-theory before
1980
Details:
Series: Contemporary Mathematics, Volume: 243
Publication Year: 1999
ISBN: 0-8218-1087-1
Paging: approximately 237 pp.
Binding: Softcover
Leovigildo Alonso and Ana Jerem?as, Universidade de Santiago
de Compostela, Spain,
and Joseph Lipman, Purdue University, West Lafayette, IN
Description
This volume contains three papers on the foundations of
Grothendieck duality on Noetherian formal schemes
and on not-necessarily-Noetherian ordinary schemes.
The first paper presents a self-contained treatment for formal
schemes which synthesizes several duality-related topics,
such as local duality, formal duality, residue theorems,
dualizing complexes, etc. Included is an exposition of properties
of
torsion sheaves and of limits of coherent sheaves. A second paper
extends Greenlees-May duality to complexes on formal
schemes. This theorem has important applications to Grothendieck
duality. The third paper outlines methods for eliminating
the Noetherian hypotheses. A basic role is played by Kiehl's
theorem affirming conservation of pseudo-coherence of
complexes under proper pseudo-coherent maps.
This work gives a detailed introduction to the subject of
Grothendieck Duality. The approach is unique in its presentation
of a complex series of special cases that build up to the main
results.
Contents
Duality and Flat Base Change on Formal Schemes
Duality and flat base change on formal schemes
Greenlees-May Duality on Formal Schemes
Greenlees-May duality on formal schemes
Non-Noetherian Grothendieck Duality
Non-noetherian Grothendieck duality
Index
Details:
Series: Contemporary Mathematics,Volume: 244
Publication Year: 2000
ISBN: 0-8218-1942-9
Paging: 126 pp.
Binding: Softcover
Edited by: Pierre Hansen, Ecole des Hautes Etudes
Commerciales, Montreal, PQ, Canada,
and Odile Marcotte, University du Quebec Montreal, PQ, Canada
Description
This volume presents the proceedings of the CRM workshop on graph
coloring and applications. The articles span a wide spectrum
of topics related to graph coloring, including: list-colorings,
total colorings, colorings and embeddings of graphs, chromatic
polynomials, characteristic polynomials, chromatic scheduling,
and graph coloring problems related to frequency assignment.
Outstanding researchers in combinatorial optimization and graph
theory contributed their work. A list of open problems is
included.
Contents
D. K. Arrowsmith and J. W. Essam -- Chromatic polynomials and mod
$\lambda$ flows on directed graphs and their applications
K. L. Collins and J. P. Hutchinson -- Four-coloring six-regular
graphs on the torus
M. Dror, G. Finke, S. Gravier, and W. Kubiak -- On the complexity
of a restricted list-coloring problem
G. M. Hamilton, A. J. W. Hilton, and H. R. F. Hind -- Totally
critical graphs and the conformability conjecture
F. Harary and M. Plantholt -- Graphs whose radio coloring number
equals the number of nodes
O. Marcotte and P. Hansen -- The height and length of colour
switching
H. Sachs -- Characteristic polynomials in the theory of polyhedra
T. R. Walsh -- The number of edge 3-colourings of the $n$-prism
T. R. Walsh -- The cost of radio-colouring paths and cycles
D. de Werra -- Restricted graph coloring: Some mathematical
programming models
Open problems
Details:
Series: CRM Proceedings & Lecture Notes, Volume: 23
Publication Year: 1999
ISBN: 0-8218-1955-0
Paging: 149 pp.
Binding: Softcover
Hiraku Nakajima, Kyoto University, Japan
Description
The Hilbert scheme $X^{[n]}$ of a surface $X$ describes
collections of $n$ (not necessarily distinct) points on $X$.
More precisely, it is the moduli space for $0$-dimensional
subschemes of $X$ of length $n$. Recently it was realized
that Hilbert schemes originally studied in algebraic geometry are
closely related to several branches of mathematics,
such as singularities, symplectic geometry, representation
theory-even theoretical physics. The discussion in the book
reflects this feature of Hilbert schemes.
For example, a construction of the representation of the infinite
dimensional Heisenberg algebra (i.e., Fock space) is presented.
This representation has been studied extensively in the
literature in connection with affine Lie algebras, conformal
field theory,
etc. However, the construction presented in this volume is
completely unique and provides the unexplored link between
geometry
and representation theory.
The book offers a nice survey of current developments in this
rapidly growing subject. It is suitable as a text
at the advanced graduate level.
Contents
Introduction
Hilbert scheme of points
Framed moduli space of torsion free sheaves on $\Bbb{P}^2$
Hyper-K?hler metric on $(\Bbb{C}^2)^{[n]}$
Resolution of simple singularities
Poincar? polynomials of the Hilbert schemes (1)
Poincar? polynomials of Hilbert schemes (2)
Hilbert scheme on the cotangent bundle of a Riemann surface
Homology group of the Hilbert schemes and the Heisenberg algebra
Symmetric products of an embedded curve, symmetric functions and
vertex operators
Bibliography
Index
Details:
Series: University Lecture Series, Volume: 18
Publication Year: 1999
ISBN: 0-8218-1956-9
Paging: 132 pp.
Binding: Softcover
Steve Batterson, Emory University, Atlanta, GA
Description
In 1957 Stephen Smale startled the mathematical world by showing
that it is possible to turn a sphere inside out without
cutting, tearing, or crimping. A few years later, from the
beaches of Rio, he introduced the horseshoe map, demonstrating
that simple functions could have chaotic dynamics. His next
stunning mathematical accomplishment was to solve the higher
-dimensional Poincar? conjecture, thus demonstrating that higher
dimensions are simpler than the more familiar three.
In 1966 in Moscow, he was awarded the Fields Medal, the most
prestigious prize in mathematics.
Smale's vision and influence extended beyond mathematics into two
vastly different realms. In 1965 in Berkeley, he initiated
a program with Jerry Rubin of civil disobedience directed at
ending the Vietnam war. And as a mineral collector, he
accumulated a museum-quality collection that ranks among the
finest in the world. Despite these diverse accomplishments,
Smale's name is
virtually unknown outside mathematics and mineralogy. One of the
objectives of this book is to bring his life and work to the
attention of a larger community.
There are few good biographies of mathematicians. This makes
sense when considering that to place their lives in perspective
requires some appreciation of their theorems. Biographical
writers are not usually trained in mathematics, and
mathematicians
do not usually write biographies. Though the author, Steve
Batterson, is primarily a mathematician, he has long been
intrigued
by the notion of working on a biography of Smale. In this book,
Batterson records and makes known the life and accomplishments
of this great mathematician and significant figure in
intellectual history.
"Transparent Peach Eversion" cover art used with
permission from the "Outside In" video project,
generated at the Geometry Center (University of MN); distributed
by A. K. Peters (Natick, MA).
Contents
One room schoolhouse
Marxism and mathematics at Ann Arbor
Early mathematical audacity
On the beaches of Rio
Berkeley to Columbia and back to Berkeley
The Lone Ranger of the antiwar movement
The summer of 1966
Smale versus the National Science Foundation
The aesthetic side: Minerals and photography
Adventure and physical risks
Other people
Smale the mathematician
Mathematical appendix A: Smale's thesis
Mathematical appendix B: Everting the sphere
Mathematical appendix C: Chaos and the horseshoe
Mathematical appendix D: The higher dimensional Poincar?
conjecture
Notes
Index
Details:
Publication Year: 2000
ISBN: 0-8218-2045-1
Paging: approximately 265 pp.
Binding: Hardcover
John Locker, Colorado State University, Fort Collins, CO
Description
This monograph develops the spectral theory of an $n$th order
non-self-adjoint two-point differential operator $L$
in the Hilbert space $L^2[0,1]$. The mathematical foundation is
laid in the first part, where the spectral theory is
developed for closed linear operators and Fredholm operators. An
important completeness theorem is established for
the Hilbert-Schmidt discrete operators. The operational calculus
plays a major role in this general theory.
In the second part, the spectral theory of the differential
operator $L$ is developed by expressing $L$ in the form $L
= T + S$, where $T$ is the principal part determined by the $n$th
order derivative and $S$ is the part determined by
the lower-order derivatives. The spectral theory of $T$ is
developed first using operator theory, and then the spectral
theory of $L$ is developed by treating $L$ as a perturbation of
$T$. Regular and irregular boundary values are allowed
for $T$, and regular boundary values are considered for $L$.
Special features of the spectral theory for $L$ and $T$
include the following: calculation of the eigenvalues, algebraic
multiplicities and ascents; calculation of the associated
family of projections which project onto the generalized
eigenspaces; completeness of the generalized eigenfunctions;
uniform bounds on the family of all finite sums of the associated
projections; and expansions of functions in series of
generalized eigenfunctions of $L$ and $T$.
Contents
Unbounded linear operators
Fredholm operators
Introduction to the spectral theory of differential operators
Principal part of a differential operator
Projections and generalized eigenfunction expansions
Spectral theory for general differential operators
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 73
Publication Year: 2000
ISBN: 0-8218-2049-4
Paging: 252 pp.
Binding: Hardcover