Expected publication date is December 20,
2002
Description
In this book, G.V. Badalyan addresses the
fundamental problems of
the theory of infinitely-differentiable functions
using the
theory of functions of quasianalytic classes.
A certain class of functions $C$ on an interval
is called
quasianalytic if any function in $C$ is uniquely
determined by
the values of its derivatives at any point.
The obvious question,
then, is how to reconstruct such a function
from the sequence of
values of its derivatives at a certain point.
In order to answer
that question, Badalyan combines a study
of expanding functions
in generalized factorial series with a study
of quasipower series.
The theory of quasipower series and its application
to the
reconstruction problem are explained in detail
in this research
monograph. Along the way other, related problems
are solved, such
as Borel's hypothesis that no quasianalytic
function can have all
positive derivatives at a point.
Originally published in Russian, this English
translation
contains additional materials that treat
the problems of
classification of infinitely-differentiable
functions, conditions
for absolute convergence of quasipower series
in terms of the
functions that generate them, and the possibility
of representing
analytic functions by quasipower series in
non-circular domains.
While the treatment is technical, the theory
is developed chapter
by chapter in detail, and the first chapter
is of an introductory
nature. The quasipower series technique explained
here provides
the means to extend the previously known
results and elucidates
their nature in the most relevant manner.
This method also allows
for thorough investigation of numerous problems
of the theory of
functions of quasianalytic classes by graduate
students and
research mathematicians.
Contents
Quasianalytic classes of functions
Generalizations of the Taylor formula. Quasipower
series
Functions of Carleman's classes: Expansion
in quasipower series
Criteria for the possibility of expanding
functions in quasipower
and factorial series
Generalized completely monotone functions
and the condition for
absolute convergence of a quasipower series
(in the basic
interval)
On the use of quasipower series for representation
of analytic
functions in non-circular domains
Some applications of quasipower series to
the theory of functions
of quasianalytic classes
Bibliography
Details:
Series: Translations of Mathematical Monographs,Volume:
216
Publication Year: 2002
ISBN: 0-8218-2943-2
Paging: 183 pp.
Binding: Hardcover
Description
A. N. Parshin is a world-renowned mathematician
who has made
significant contributions to number theory
through the use of
algebraic geometry. Articles in this volume
present new research
and the latest developments in algebraic
number theory and
algebraic geometry and are dedicated to Parshin's
sixtieth
birthday. Well-known mathematicians contributed
to this volume,
including, among others, F. Bogomolov, C.
Deninger, and G.
Faltings.
The book is intended for graduate students
and research
mathematicians interested in number theory,
algebra, and
algebraic geometry.
Contents
V. Abrashkin -- Ramification theory for higher
dimensional local
fields
F. Bogomolov and Y. Tschinkel -- Unramified
correspondences
M. V. Bondarko -- Local Leopoldt's problem
for ideals in totally
ramified $p$-extensions of complete discrete
valuation fields
A. Buium -- Quotients of algebraic varieties
by Zariski dense
equivalence relations
C. Deninger -- A note on arithmetic topology
and dynamical
systems
G. Faltings -- A relation between two moduli
spaces studied by V.
G. Drinfeld
G. van der Geer and T. Katsura -- An invariant
for varieties in
positive characteristic
F. Lorenz and S. Vostokov -- Honda groups
and explicit pairings
on the modules of Cartier curves
A. Merkurjev -- Algebraic oriented cohomology
theories
Y. G. Zarhin -- Hyperelliptic Jacobians without
complex
multiplication, doubly transitive permutation
groups and
projective representations
I. Zhukov -- Ramification of surfaces: Artin-Schreier
extensions
Details:
Series: Contemporary Mathematics, Volume:
300
Publication Year: 2002
ISBN: 0-8218-3267-0
Paging: 220 pp.
Binding: Softcover
Expected publication date is December 12,
2002
Description
This volume honors Herb Clemens and his contributions
to
algebraic geometry. The exceptional gathering
of mathematicians
at the symposium attest to his remarkable
career. Papers in the
book address topics in which Clemens has
been active: the
geometry of threefolds, enumerative geometry,
Hodge theory, and
higher-order methods for attacking deformation
problems.
The volume is suitable for graduate students
and research
mathematicians interested in algebraic geometry.
Contents
D. Allcock, J. A. Carlson, and D. Toledo
-- Orthogonal complex
hyperbolic arrangements
E. Arbarello -- Sketches of KdV
A. Beauville -- Vector bundles on the cubic
threefold
A. Bertram -- Using symmetry to count rational
curves
R. Friedman and J. W. Morgan -- Exceptional
groups and del Pezzo
surfaces
M. Green and P. Griffiths -- The regulator
map for a general
curve
S. Katz -- Versal deformations and superpotentials
for rational
curves in smooth threefolds
J. Kollar -- The Nash conjecture for nonprojective
threefolds
Y. Lee -- Bounds and $\mathbb{Q}$-Gorenstein
smoothings of
smoothable stable log surfaces
M. V. Nori -- The integral of powers of a
function
Z. Ran -- On semipositivity of sheaves of
differential operators
and the degree of a unipolar $\mathbb{Q}$-Fano
variety
Y. Ruan -- Stringy geometry and topology
of orbifolds
R. Smith and R. Varley -- The Prym Torelli
problem: An update and
a reformulation as a question in birational
geometry
C. Voisin -- On the punctual Hilbert scheme
of a symplectic
fourfold
Details:
Series: Contemporary Mathematics,Volume:
312
Publication Year: 2002
ISBN: 0-8218-2152-0
Paging: 291 pp.
Binding: Softcover
Description
A classic problem in mathematics is solving
systems of polynomial
equations in several unknowns. Today, polynomial
models are
ubiquitous and widely used across the sciences.
They arise in
robotics, coding theory, optimization, mathematical
biology,
computer vision, game theory, statistics,
and numerous other
areas.
This book furnishes a bridge across mathematical
disciplines and
exposes many facets of systems of polynomial
equations. It covers
a wide spectrum of mathematical techniques
and algorithms, both
symbolic and numerical.
The set of solutions to a system of polynomial
equations is an
algebraic variety--the basic object of algebraic
geometry. The
algorithmic study of algebraic varieties
is the central theme of
computational algebraic geometry. Exciting
recent developments in
computer software for geometric calculations
have revolutionized
the field. Formerly inaccessible problems
are now tractable,
providing fertile ground for experimentation
and conjecture.
The first half of the book gives a snapshot
of the state of the
art of the topic. Familiar themes are covered
in the first five
chapters, including polynomials in one variable,
Grobner bases of
zero-dimensional ideals, Newton polytopes
and Bernstein's
Theorem, multidimensional resultants, and
primary decomposition.
The second half of the book explores polynomial
equations from a
variety of novel and unexpected angles. It
introduces
interdisciplinary connections, discusses
highlights of current
research, and outlines possible future algorithms.
Topics include
computation of Nash equilibria in game theory,
semidefinite
programming and the real Nullstellensatz,
the algebraic geometry
of statistical models, the piecewise-linear
geometry of
valuations and amoebas, and the Ehrenpreis-Palamodov
theorem on
linear partial differential equations with
constant coefficients.
Throughout the text, there are many hands-on
examples and
exercises, including short but complete sessions
in MapleR,
MATLABR, Macaulay 2, Singular, PHCpack, CoCoA,
and SOSTools.
These examples will be particularly useful
for readers with no
background in algebraic geometry or commutative
algebra. Within
minutes, readers can learn how to type in
polynomial equations
and actually see some meaningful results
on their computer
screens.
Prerequisites include basic abstract and
computational algebra.
The book is designed as a text for a graduate
course in
computational algebra.
R Waterloo Maple, Inc., Ontario, Canada.
R MATLAB, The MathWorks, Inc., Natick, MA.
Singular is a free software distributed under
the GNU license.
cDepartment of Mathematics, and Centre for
Computer Algebra,
University of Kaiserslautern, Germany.
Macaulay 2, c Daniel R. Grayson and Michael
E. Stillman (1993-2001)
and is distributed under the GNU license.
PHCpack c1998, Katholieke Universiteit Leuven,
Department of
Computer Science, Heverlee, Belgium.
CoCoA, A. Capani, G. Niesi, L. Robbiano,
a system for doing
Computations in Commutative Algebra, available
via anonymous ftp
from: http://cocoa.dima.unige.it.
SOSTools is a MATLABR toolbox and freely
available under the GNU
license at http://www.cds.caltech.edu/sostools
or http://www.aut.ee.ethz.ch/~parrilo/sostools.
Contents
Polynomials in one variable
Grobner bases of zero-dimensional ideals
Bernstein's theorem and fewnomials
Resultants
Primary decomposition
Polynomial systems in economics
Sums of squares
Polynomial systems in statistics
Tropical algebraic geometry
Linear partial differential equations with
constant coefficients
Bibliography
Index
Details:
Series: CBMS Regional Conference Series in
Mathematics,Number: 97
Publication Year: 2002
ISBN: 0-8218-3251-4
Paging: 152 pp.
Binding: Softcover
Expected publication date is November 22,
2002
Description
Swift progress and new applications characterize
the area of
solitons and the inverse scattering transform.
There are rapid
developments in current nonlinear optical
technology: Larger
intensities are more available; pulse widths
are smaller;
relaxation times and damping rates are less
significant. In
keeping with these advancements, exactly
integrable soliton
equations, such as $3$-wave resonant interactions
and second
harmonic generation, are becoming more and
more relevant in
experimental applications. Techniques are
now being developed for
using these interactions to frequency convert
high intensity
sources into frequency regimes where there
are no lasers. Other
experiments involve using these interactions
to develop intense
variable frequency sources, opening up even
more possibilities.
This volume contains new developments and
state-of-the-art
research arising from the conference on the
"Legacy of the
Inverse Scattering Transform" held at
Mount Holyoke College
(South Hadley, MA). Unique to this volume
is the opening section,
"Reviews". This part of the book
provides reviews of
major research results in the inverse scattering
transform (IST),
on the application of IST to classical problems
in differential
geometry, on algebraic and analytic aspects
of soliton-type
equations, on a new method for studying boundary
value problems
for integrable partial differential equations
(PDEs) in two
dimensions, on chaos in PDEs, on advances
in multi-soliton
complexes, and on a unified approach to integrable
systems via
Painleve analysis.
This conference provided a forum for general
exposition and
discussion of recent developments in nonlinear
waves and related
areas with potential applications to other
fields. The book will
be of interest to graduate students and researchers
interested in
mathematics, physics, and engineering.
Contents
D. J. Kaup -- The legacy of the IST
V. Zakharov -- Application of inverse scattering
method to
problems of differential geometry
V. S. Gerdjikov -- Algebraic and analytic
aspects of soliton type
equations
A. S. Fokas -- Differential forms, spectral
theory, and boundary
value problems
Y. C. Li -- Chaos in partial differential
equations
N. N. Akhmediev, A. A. Sukhorukov, and A.
Ankiewicz -- Multi-soliton
complexes
S. R. Choudhury -- A unified approach to
integrable systems via
Painleve analysis
V. S. Buslaev and C. Sulem -- Asymptotic
stability of solitary
waves for nonlinear Schrodinger equations
A. de Bouard and A. Debussche -- Finite-time
blow-up in the
additive supercritical stochastic nonlinear
Schrodinger equations:
The real noise case
O. I. Bogoyavlenskij -- Method of symmetry
transforms for ideal
magnetohydrodynamics equilibrium equations
R. Young -- The $p$-system I: The Riemann
problem
G. J. Morrow and S. Chakravarty -- Statistical
analysis of
collision-induced timing shifts in a wavelength-division-multiplexed
optical soliton-transmission system
R. Grimshaw, G. A. Green, and B. A. Malomed
-- Cuspons and
peakons vis-a-vis regular solitons and collapse
in a three-wave
system
S. Chakravarty and R. G. Halburd -- First
integrals and gradient
flow for a generalized Darboux-Halphen system
L. Casian and Y. Kodama -- Blow-ups of the
Toda lattices and
their intersections with the Bruhat cells
M. Kovalyov -- Superposition principle for
oscillatory solutions
of integrable systems
H. Steudel -- Scattering at truncated solitons
and inverse
scattering on the semiline
Details:
Series: Contemporary Mathematics,Volume:
301
Publication Year: 2002
ISBN: 0-8218-3161-5
Paging: 338 pp.
Binding: Softcover