Description
This volume contains six detailed papers
written by participants
of the special session on value distribution
theory and complex
dynamics held in Hong Kong at the First Joint
International
Meeting of the AMS and the Hong Kong Mathematical
Society in
December 2000. It demonstrates the strong
interconnections
between the two fields and introduces recent
progress of leading
researchers from Asia.
In the book, W. Bergweiler discusses proper
analytic maps with
one critical point and generalizes a previous
result concerning
Leau domains. W. Cherry and J. Wang discuss
non-Archimedean
analogs of Picard's theorems. P.-C. Hu and
C.-C. Yang give a
survey of results in non-Archimedean value
distribution theory
related to unique range sets, the $abc$-conjecture,
and
Shiffman's conjecture. L. Keen and J. Kotus
explore the dynamics
of the family of $f_\lambda(z)=\lambda\tan(z)$
and show that it
has much in common with the dynamics of the
familiar quadratic
family $f_c(z)=z^2+c$. R. Oudkerk discusses
the interesting
phenomenon known as parabolic implosion and,
in particular, shows
the persistence of Fatou coordinates under
perturbation. Finally,
M. Taniguchi discusses deformation spaces
of entire functions and
their combinatorial structure of singularities
of the functions.
The book is intended for graduate students
and research
mathematicians interested in complex dynamics,
function theory,
and non-Archimedean function theory.
Contents
W. Bergweiler -- On proper analytic maps
with one critical point
W. Cherry and J. T.-Y. Wang -- Non-Archimedean
analytic maps to
algebraic curves
P.-C. Hu and C.-C. Yang -- Some progress
in non-Archimedean
analysis
L. Keen and J. Kotus -- On period doubling
phenomena and
Sharkovskii type ordering for the family
$\lambda\tan(z)$
R. Oudkerk -- The parabolic implosion: Lavaurs
maps and strong
convergence for rational maps
M. Taniguchi -- Synthetic deformation space
of an entire function
Details:
Series: Contemporary Mathematics, Volume:
303
Publication Year: 2002
ISBN: 0-8218-2980-7
Paging: 136 pp.
Binding: Softcover
Description
Mark Vishik's Partial Differential Equations
seminar held at
Moscow State University was one of the world's
leading seminars
in PDEs for over 40 years. This book celebrates
Vishik's
eightieth birthday. It comprises new results
and survey papers
written by many renowned specialists who
actively participated
over the years in Vishik's seminars.
Contributions include original developments
and methods in PDEs
and related fields, such as mathematical
physics, tomography, and
symplectic geometry. Papers discuss linear
and nonlinear
equations, particularly linear elliptic problems
in angles and
general unbounded domains, linear elliptic
problems with a
parameter for mixed order systems, infinite-dimensional
Schrodinger equations, Navier-Stokes equations,
and nonlinear
Maxwell equations. The book ends on a historical
note with a
paper about Vishik's seminar as a whole and
a list of selected
talks given from 1964 through 1989.
The book is suitable for graduate students
and researchers in
pure and applied mathematics and mathematical
physics.
Contents
A. Babin and A. Figotin -- Multilinear spectral
decomposition for
nonlinear Maxwell equations
R. Denk and L. Volevich -- Elliptic boundary
value problems with
large parameter for mixed order systems
A. Dynin -- Feynman integral for functional
Schrodinger equations
B. Fedosov -- On normal Darboux coordinates
A. Fursikov -- Real process corresponding
to the 3D Navier-Stokes
system, and its feedback stabilization from
the boundary
A. Komech, A. Merzon, and P. Zhevandrov --
A method of complex
characteristics for elliptic problems in
angles, and its
applications
S. B. Kuksin -- On exponential convergence
to a stationary
measure for nonlinear PDEs, perturbed by
random kick-forces, and
the turbulence-limit
V. P. Palamodov -- Impedance tomography,
inverse scattering, and
phase space analysis
A. Volpert and V. Volpert -- Normal solvability
and properness of
elliptic problems
M. S. Agranovich -- Mark Vishik's seminar
at Moscow state
university
M. Shubin -- List of selected talks at M.
I. Vishik's seminar in
Moscow
Details:
Series: American Mathematical Society Translations--Series
2,
Volume: 206
Publication Year: 2002
ISBN: 0-8218-3303-0
Paging: 278 pp.
Binding: Hardcover
Expected publication date is November 20,
2002
Description
The properties of knotted and linked configurations
in space have
long been of interest to physicists and mathematicians.
More
recently and more widely, they have become
important to
biologists, chemists, computer scientists,
and engineers. The
depth and breadth of their applications are
widely appreciated.
Nevertheless, fundamental and challenging
questions remain to be
answered.
Based on a Special Session at the AMS Sectional
Meeting in Las
Vegas (NV) in April 2001, this volume discusses
critical
questions and introduces new ideas that will
stimulate multi-disciplinary
applications.
Some of the papers are primarily theoretical;
others are
experimental. Some are purely mathematical;
others deal with
applications of mathematics to theoretical
computer science,
engineering, physics, biology, or chemistry.
Connections are made
between classical knot theory and the physical
world of
macromolecules, such as DNA, geometric linkages,
rope, and even
cooked spaghetti.
This book introduces the world of physical
knot theory in all its
manifestations and points the way for new
research. It is
suitable for a diverse audience of mathematicians,
computer
scientists, engineers, biologists, chemists,
and physicists.
Contents
J. Simon -- Physical knots
R. Randell -- The space of piecewise-linear
knots
J. A. Calvo -- Characterizing polygons in
R3
E. J. Rawdon and R. G. Scharein -- Upper
bounds for equilateral
stick numbers
K. C. Millett -- An investigation of equilateral
knot spaces and
ideal physical knot configurations
T. Deguchi and M. K. Shimamura -- Topological
effects on the
average size of random knots
A. Dobay, P.-E. Sottas, J. Dubochet, and
A. Stasiak -- Bringing
an order into random knots
E. J. J. van Rensburg -- The probability
of knotting in lattice
polygons
E. J. J. van Rensburg -- Knotting in adsorbing
lattice polygons
P. Pieranski and S. Przybyl -- In search
of the ideal trefoil
knot
Y. Diao and C. Ernst -- The crossing numbers
of thick knots and
links
R. Kusner -- On thickness and packing density
for knots and links
J. M. Sullivan -- Approximating ropelength
by energy functions
R. Langevin and J. O'Hara -- Conformal geometric
viewpoints for
knots and links I
O. Gonzalez, J. H. Maddocks, and J. Smutny
-- Curves, circles,
and spheres
G. Dietler, P. Pieranski, S. Kasas, and A.
Stasiak -- The rupture
of knotted strings under tension
L. H. Kauffman and S. Lambropoulou -- Classifying
and applying
rational knots and rational tangles
D. Roseman -- Untangling some spheres in
R4 by energy minimizing
flow
M. Soss and G. T. Toussaint -- Convexifying
polygons in 3D: A
survey
R. Connelly, E. D. Demaine, and G. Rote --
Infinitesimally locked
self-touching linkages with applications
to locked trees
L. H. Kauffman -- Biologic
Details:
Series: Contemporary Mathematics,Volume:
304
Publication Year: 2002
ISBN: 0-8218-3200-X
Paging: 342 pp.
Binding: Softcover
Description
This book is derived from lectures presented
at the 2001 John H.
Barrett Memorial Lectures at the University
of Tennessee,
Knoxville. The topic was computational mathematics,
focusing on
parallel numerical algorithms for partial
differential equations,
their implementation and applications in
fluid mechanics and
material science. Compiled here are articles
from six of nine
speakers. Each of them is a leading researcher
in the field of
computational mathematics and its applications.
A vast area that has been coming into its
own over the past 15
years, computational mathematics has experienced
major
developments in both algorithmic advances
and applications to
other fields. These developments have had
profound implications
in mathematics, science, engineering and
industry. With the aid
of powerful high performance computers, numerical
simulation of
physical phenomena is the only feasible method
for analyzing many
types of important phenomena, joining experimentation
and
theoretical analysis as the third method
of scientific
investigation.
The three aspects: applications, theory,
and computer
implementation comprise a comprehensive overview
of the topic.
Leading lecturers were Mary Wheeler on applications,
Jinchao Xu
on theory, and David Keyes on computer implementation.
Following the tradition of the Barrett Lectures,
these in-depth
articles and expository discussions make
this book a useful
reference for graduate students as well as
the many groups of
researchers working in advanced computations,
including
engineering and computer scientists.
Contents
J. Xu and A. Zhou -- Some multiscale methods
for partial
differential equations
D. E. Keyes -- Terascale implicit methods
for partial
differential equations
M. Peszynska, E. W. Jenkins, and M. F. Wheeler
-- Boundary
conditions for fully implicit two-phase flow
models
G. B. McFadden -- Phase-field models of solidification
Q. Nie, S. Tanveer, T. F. Dupont, and X.
Li -- Singularity
formation in free-surface Stokes flows
C. C. Douglas and D. T. Thorne -- A note
on cache memory methods
for multigrid in three dimensions
Details:
Series: Contemporary Mathematics, Volume:
306
Publication Year: 2002
ISBN: 0-8218-2970-X
Paging: 177 pp.
Binding: Softcover
Expected publication date is September 25,
2002
Contents
Introduction
The universal pseudo-quotient for a family
of subvarieties
Normal bundles of quadrics in $X$
Morphisms from quadrics to Grassmannians
Pointwise uniform vector bundles on non-singular
quadrics
Theory of extensions of families over Hilbert
schemes
Existence of algebraic quotient--proof of
Theorem 0.3
Appendix. Deformations of vector bundles
on infinitesimally rigid
projective varieties with null global $i$-forms
References
Details:
Series: Memoirs of the American Mathematical
Society, Volume: 763
Publication Year: 2002
ISBN: 0-8218-3225-5
Paging: 116 pp.
Binding: Softcover