Expected publication date is August 9, 2003
Description
Recurrence sequences are of great intrinsic
interest and have
been a central part of number theory for
many years. Moreover,
these sequences appear almost everywhere
in mathematics and
computer science. This book surveys the modern
theory of linear
recurrence sequences and their generalizations.
Particular
emphasis is placed on the dramatic impact
that sophisticated
methods from Diophantine analysis and transcendence
theory have
had on the subject. Related work on bilinear
recurrences and an
emerging connection between recurrences and
graph theory are
covered. Applications and links to other
areas of mathematics are
described, including combinatorics, dynamical
systems and
cryptography, and computer science. The book
is suitable for
researchers interested in number theory,
combinatorics, and graph
theory.
Contents
Definitions and techniques
Zeros, multiplicity and growth
Periodicity
Operations on power series and linear recurrence
sequences
Character sums and solutions of congruences
Arithmetic structure of recurrence sequences
Distribution in finite fields and residue
rings
Distribution modulo 1 and matrix exponential
functions
Applications to other sequences
Elliptic divisibility sequences
Sequences arising in graph theory and dynamics
Finite fields and algebraic number fields
Pseudo-random number generators
Computer science and coding theory
Appendix: Sequences from the on-line encyclopedia
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs,
Volume: 104
Publication Year: 2003
ISBN: 0-8218-3387-1
Paging: 318 pp.
Binding: Hardcover
Expected publication date is October 5, 2003
Description
This volume contains 36 research papers written
by prominent
researchers. The papers are based on a large
satellite conference
on scientific computing held at the International
Congress of
Mathematics (ICM) in Xi'an, China.
Topics covered include a variety of subjects
in modern scientific
computing and its applications, such as numerical
discretization
methods, linear solvers, parallel computing,
high performance
computing, and applications to solid and
fluid mechanics, energy,
environment, and semiconductors. The book
will serve as an
excellent reference work for graduate students
and researchers
working with scientific computing for problems
in science and
engineering.
Contents
R. Abgrall, M. Papin, and L. Hallo -- A scheme
for compressible
two-phase flows and interface problems
S. Amini and A. T. J. Profit -- Multi-level
fast multipole
Galerkin method for the boundary integral
solution of the
exterior Helmholtz equation
T. Arbogast -- An overview of subgrid upscaling
for elliptic
problems in mixed form
D. N. Arnold and R. Winther -- Mixed finite
elements for
elasticity in the stress-displacement formulation
W. Auzinger, O. Koch, and E. Weinmuller --
New variants of defect
correction for boundary value problems in
ordinary differential
equations
Z. Chen, R. Glowinski, and J. He -- Scientific
computing in
energy and environment
S.-S. Chow and G. F. Carey -- Approximate
analysis of extended
Williamson fluids for Powell-Sabin-Heindl
elements
P. Cummings and X. Feng -- Frequency domain
method for the scalar
wave equation with second order absorbing
boundary condition
Z. Dostal and D. Horak -- Scalable FETI with
optimal dual penalty
for semicoercive variational inequalities
C. C. Douglas and G. Haase -- Algebraic multigrid
and Schur
complement strategies within a multilayer
spectral element ocean
model
J. Douglas, Jr., S. Kim, and H. Lim -- An
improved alternating-direction
method for a viscous wave equation
Q. Du -- Diverse vortex dynamics in superfluids
R. E. Ewing, J. Liu, and H. Wang -- Adaptive
wavelet methods for
advection-reaction equations
J. L. Guermond and P. D. Minev -- Approximation
of an MHD problem
using Lagrange finite elements
B. Guo -- Best approximation for the $p$-version
of the finite
element method in three dimensions in the
framework of the Jacobi-weighted
Besov spaces
B.-Y. Guo and L.-L. Wang -- Non-isotropic
Jacobi spectral method
N. Herrmann -- Improved method for solving
the heat equation with
BEM and collocation
M. Hokr, J. Maryska, and J. Sembera -- Modelling
of transport
with non-equilibrium effects in dual-porosity
media
Y. Hou and K. Li -- Error estimate for a
two-level scheme of
Newton type for the Navier-Stokes equations
Y. Kuznetsov, K. Lipnikov, S. Lyons, and
S. Maliassov --
Mathematical modeling and numerical algorithms
for poroelastic
problems
M.-C. Lai -- Fast Poisson solver in a three-dimensional
ellipsoid
B. Li, Z. Chen, and G. Huan -- Modeling horizontal
wells with the
CVFA method in black oil reservoir simulations
J. Li and Y. Chen -- Radial basis function
based meshless method
for groundwater modeling
D. Liang -- Upwinding finite covolume methods
for unsteady
convection-diffusion problems
J. Liu, Z. Chen, R. E. Ewing, G. Huan, B.
Li, and Z. Wang --
Parallel computing in the black oil model
J. Maryska, J. Novak, P. Ralek, and J. Sembera
-- Finite element
model of piezoelectric resonator
B. Riviere and M. F. Wheeler -- Discontinuous
finite element
methods for acoustic and elastic wave problems
L. Schaefer and P. Wang -- Heuristics for
developing variations
on future air traffic schedule characteristics
for air traffic
simulation
J. Sembera, J. Maryska, and J. Novak -- FEM/FVM
modelling of
processes in a combustion engine
J. Shi, D. L. S. McElwain, and E. Donskoi
-- A finite control
volume method for the reduction of an iron
ore-coal composite
pellet in an axisymmetric temperature field
J. Tausch -- The fast multipole method for
arbitrary Green's
functions
R. Wang and Z. Chen -- A mathematical model
for ESP simulation
M. Vohralik, J. Maryska, and O. Severyn --
Mixed-hybrid discrete
fracture network model
H. Xu, C. Zhang, and R. M. Barron -- A new
numerical algorithm
for treatment of convective terms and its
applications to PDEs
J. Xu, S. Dong, M. R. Maxey, and G. E. Karniadakis
-- Direct
numerical simulation of turbulent channel
flow with bubbles
X. Yu and Q. Dai -- RKDG finite element schemes
combined with a
gas-kinetic method for one-dimensional compressible
Euler
equations
Details:
Series: Contemporary Mathematics,Volume:
329
Publication Year: 2003
ISBN: 0-8218-3261-1
Paging: approximately 392 pp.
Binding: Softcover
Expected publication date is August 29, 2003
Description
This volume contains 21 articles based on
invited talks given at
two international conferences held in France
in 2001. Most of the
papers are devoted to various problems of
commutative algebra and
their relation to properties of algebraic
varieties.
The book is suitable for graduate students
and research
mathematicians interested in commutative
algebra and algebraic
geometry.
Contents
J. Montaner and S. Zarzuela -- Linearization
of local cohomology
modules
M. Brion -- Multiplicity-free subvarieties
of flag varieties
R.-O. Buchweitz -- Morita contexts, idempotents,
and Hochschild
cohomology--with applications to invariant
rings--
A. Campillo and S. Encinas -- Some applications
of two
dimensional complete ideals
S. D. Cutkosky -- Generically finite morphisms
and simultaneous
resolution of singularities
J. Elias -- Two results on the number of
generators
K. Eto -- When is a binomial ideal equation
equal to a lattice
ideal up to radical?
H.-B. Foxby and S. Iyengar -- Depth and amplitude
for unbounded
complexes
A. Guerrieri and I. Swanson -- On the ideal
of minors of matrices
of linear forms
M. Hashimoto -- Surjectivity of multiplication
and $F$-regularity
of multigraded rings
J. Herzog, D. Popescu, and M. Vladoiu --
On the Ext-modules of
ideals of Borel type
M. R. Johnson -- Sums of linked tepli ideals
B. Malgrange -- Cartan involutiveness = Mumford
regularity
C. Miller -- The Frobenius endomorphism and
homological
dimensions
U. Nagel -- Characterization of some projective
subschemes by
locally free resolutions
O. Piltant -- On unique factorization in
semigroups of complete
ideals
J.-E. Roos -- Modules with strange homological
properties and
Chebychev polynomials
M. E. Rossi and I. Swanson -- Notes on the
behavior of the
Ratliff-Rush filtration
S. Sather-Wagstaff -- On symbolic powers
of prime ideals
W. V. Vasconcelos -- Multiplicities and the
number of generators
of Cohen-Macaulay ideals
K.-i. Watanabe -- Chains of integrally closed
ideals
Details:
Series: Contemporary Mathematics, Volume:
331
Publication Year: 2003
ISBN: 0-8218-3233-6
Paging: 376 pp.
Binding: Softcover
Expected publication date is September 14,
2003
From reviews for Volumes I and II:
"A valuable resource."
-- American Mathematical Monthly
"Would be an ideal choice for tutorial
or problem-solving
seminars. The volume is also suitable for
self-study ...
presentation of material is designed to help
student
comprehension and to encourage them to ask
their own questions
and to start research ... a really useful
book for practice in
mathematical analysis."
-- Zentralblatt MATH
"Belongs to the great tradition of Eastern
European problem
books ... if you love mathematics and are
serious about
understanding analysis, this book is a must."
-- MAA Online
"A very stimulating problem book ...
The style ... is proven
to be a motivating approach in constructing
and conveying
mathematical knowledge ... leads the readers
to find new
solutions and hence boosts their ability
to carry out further
research ... thorough coverage of some topics
that are covered
very briefly in other compatible books ...
of interest to anyone
who wishes to pursue research in mathematical
analysis and its
applications ... also excellent for students
who want to enhance
their skills in real analysis ... a useful
supplement to any
graduate textbook in mathematical analysis
... some problems are
also suitable for undergraduate students."
-- MAA Online
Description
The best way to penetrate the subtleties
of the theory of
integration is by solving problems. This
book, like its two
predecessors, is a wonderful source of interesting
and
challenging problems. As a resource, it is
unequaled. It offers a
much richer selection than is found in any
current textbook.
Moreover, the book includes a complete set
of solutions.
This is the third volume of Problems in Mathematical
Analysis.
The topic here is integration for real functions
of one real
variable. The first chapter is devoted to
the Riemann and the
Riemann-Stieltjes integrals. Chapter 2 deals
with Lebesgue
measure and integration.
The authors include some famous, and some
not so famous,
inequalities related to Riemann integration.
Many of the problems
for Lebesgue integration concern convergence
theorems and the
interchange of limits and integrals. The
book closes with a
section on Fourier series, with a concentration
on Fourier
coefficients of functions from particular
classes and on basic
theorems for convergence of Fourier series.
The book is mainly geared toward students
studying the basic
principles of analysis. However, given its
selection of problems,
organization, and level, it would be an ideal
choice for tutorial
or problem-solving seminars, particularly
those geared toward the
Putnam exam. It is also suitable for self-study.
The presentation
of the material is designed to help student
comprehension, to
encourage them to ask their own questions,
and to start research.
The collection of problems will also help
teachers who wish to
incorporate problems into their lectures.
The problems are
grouped into sections according to the methods
of solution.
Solutions for the problems are provided.
Problems in Mathematical Analysis I and II
are available as
Volumes 4 and 12 in the AMS series, Student
Mathematical Library.
Contents
Problems
The Riemann-Stieltjes integral
The Lebesgue integral
Solutions
The Riemann-Stieltjes integral
The Lebesgue integral
Bibliography
Index
Details:
Series: Student Mathematical Library,Volume:
21
Publication Year: 2003
ISBN: 0-8218-3298-0
Paging: approximately 368 pp.
Binding: Softcover