Graham Everest, University of East Anglia, Norwich, England, Alf van der Poorten and Igor Shparlinski, Macquarie University, Sydney, NSW, Australia, and Thomas Ward, University of East Anglia, Norwich, England

Recurrence Sequences

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

Edited by: Zhangxin Chen, Southern Methodist University, Dallas, TX, Roland Glowinski, University of Houston, TX, and Kaitai Li, Xi'an Jiaotong University, PRC

Current Trends in Scientific Computing

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

Edited by: Luchezar L. Avramov, University of Nebraska, Lincoln, NE, Marc Chardin, Universite de Paris VI, France, Marcel Morales, University of Grenoble I, St. Martin d'Heres, France, and Claudia Polini, University of Notre Dame, IN

Commutative Algebra: Interactions with Algebraic Geometry

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

W. J. Kaczor and M. T. Nowak, Marie Curie-Sklodowska University, Lublin, Poland

Problems in Mathematical Analysis III: Integration

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