Edited by: Alexandre V. Borovik, University of Manchester Institute of Science and Technology, United Kingdom, and Alexei G. Myasnikov, City University of New York, New York

Computational and Experimental Group Theory

Expected publication date is June 25, 2004

Description

Since its origin in the early 20th century, combinatorial group theory has been primarily concerned with algorithms for solving particular problems on groups given by generators and relations: word problems, conjugacy problems, isomorphism problems, etc. Recent years have seen the focus of algorithmic group theory shift from the decidability/undecidability type of result to the complexity of algorithms. Papers in this volume reflect that paradigm shift.

Articles are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science.

The volume is suitable for graduate students and research mathematicians interested in computational problems of group theory.

Contents

M. Batty, S. L. Braunstein, A. J. Duncan, and S. Rees -- Quantum algorithms in group theory
R. F. Booth, D. Y. Bormotov, and A. V. Borovik -- Genetic algorithms and equations in free groups and semigroups
R. H. Gilman and A. G. Myasnikov -- One variable equations in free groups via context free languages
A. D. Miasnikov and A. G. Myasnikov -- Whitehead method and genetic algorithms
B. Khan -- The structure of automorphic conjugacy in the free group of rank two
R. M. Haralick, A. D. Miasnikov, and A. G. Myasnikov -- Pattern recognition approaches to solving combinatorial problems in free groups
D. Y. Bormotov -- Experimenting with primitive elements in $F_2$

Details:

Series: Contemporary Mathematics, Volume: 349
Publication Year: 2004
ISBN: 0-8218-3483-5
Paging: 224 pp.
Binding: Softcover

S. V. Duzhin, Steklov Institute of Mathematics, St. Petersburg, Russia, and B. D. Chebotarevsky, Minsk, Belarus

Transformation Groups for Beginners

Expected publication date is September 11, 2004

Description

The notion of symmetry is important in many disciplines, including physics, art, and music. The modern mathematical way of treating symmetry is through transformation groups. This book offers an easy introduction to these ideas for the relative novice, such as undergraduates in mathematics or even advanced undergraduates in physics and chemistry.

The first two chapters provide a warm-up to the material with, for example, a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. The notions of a transformation group and of an abstract group are then introduced. Group actions, orbits, and invariants are covered in the next chapter. The final chapter gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.

Throughout the text, examples are drawn from many different areas of mathematics. Plenty of figures are included, and many exercises with hints and solutions will help readers master the material.

Contents

Algebra of points
Plane movements
Transformation groups
Arbitrary groups
Orbits and ornaments
Other types of transformations
Symmetries of differential equations
Answers, hints and solutions to exercises
Index

Details:

Series: Student Mathematical Library, Volume: 25
Publication Year: 2004
ISBN: 0-8218-3643-9
Paging: approximately 256 pp.
Binding: Softcover

Edited by: Hershy Kisilevsky, Concordia University, Montreal, Quebec, Canada, and Eyal Z. Goren, McGill University, Montreal, Quebec, Canada

Number Theory

Expected publication date is July 8, 2004

Description

This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered include algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation. The volume contains both research and expository papers suitable for graduate students and researchers interested in number theory.

Contents

M. J. Bertin -- Mesure de Mahler et regulateur elliptique: Preuve de deux relations exotiques
A. Besser -- The $p$-adic height pairings of Coleman-Gross and of Nekovar
J. M. Borwein and K.-K. S. Choi -- Dirichlet series for squares of sums of squares: A summary
D. Burns -- Equivariant Whitehead torsion and refined Euler characteristics
A. C. Cojocaru -- Questions about the reductions modulo primes of an elliptic curve
C. Consani and M. Marcolli -- New perspectives in Arakelov geometry
H. Darmon -- A fourteenth lecture on Fermat's last theorem
S. J. Gurak -- Period polynomials for $\mathbb{F}_q$ of fixed small degree
J. Hanke -- Some recent results about (ternary) quadratic forms
L. Jones -- An extension of a theorem of D. H. Lehmer
S.-i. Katayama, C. Levesque, and T. Nakahara -- On a family of real bicyclic biquadratic fields
C. Khare -- Belyi parametrisations of elliptic curves and congruence defects
H. H. Kim -- An application of exterior square functoriality of $GL_4$; Asai lift
M. Laurent -- Totally real integral points on a plane algebraic curve
L. Murata and C. Pomerance -- On the largest prime factor of a Mersenne number
M. R. Murty and S. Sumner -- On the $p$-adic series $\sum_{n=1}^{\infty} n^k\cdot n!$
K. Ono -- Hecke operators and the $q$-expansion of modular forms
D. P. Roberts -- An ABC construction of number fields
D. Roy -- Diophantine approximation in small degree
L. Smithline -- Compact operators with rational generation
V. Talamanca -- The canonical height of a finite etale $K$-algebra

Details:

Series: CRM Proceedings & Lecture Notes, Volume: 36
Publication Year: 2004
ISBN: 0-8218-3331-6
Paging: approximately 320 pp.
Binding: Softcover

Edited by: Saber Elaydi, Trinity University, San Antonio, TX, Gerry Ladas, University of Rhode Island, Kingston, RI, Jianhong Wu, York University, North York, ON, Canada, and Zingfu Zou, Memorial University of Newfoundland, St. John's, NL, Canada

Difference and Differential Equations

Expected publication date is July 25, 2004

Description
This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures.

Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems.

The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.

Contents

Survey articles
H. Brunner -- The discretization of Volterra functional integral equations with proportional delays
J. M. Cushing -- The LPA model
X. Z. Qian and Z. C. Wang -- A survey on oscillation of linear delay difference equations
Y. Yi -- On almost automorphic oscillations
Research articles
R. M. Abu-Saris and K. I. Al-Dosary -- Complex exponential Vandermonde determinant with application to discrete boundary value problem
Y. Cao -- A convergence theorem related to iterative mean clustering
A. Chen and L. Huang -- Global attractivity in a model of bobwhite quail with delay
S. S. Cheng, C.-W. Chen, and T. Y. Wu -- Linear time discrete periodic diffusion networks
B. Dai, X. Qian, and L. Huang -- Convergence of solutions for a discrete-time system
T. Furumochi, S. Murakami, and Y. Nagabuchi -- Stabilities in Volterra difference equations on a Banach space
S. Guo and L. Huang -- Periodic oscillation for a class of delay difference systems
Z. Guo and J. Yu -- Applications of critical point theory to difference equations
D. Levi -- Lie symmetries for lattice equations
X. Li and Z. Wang -- Global attractivity for a logistic equation with piecewise constant arguments
X. Lin -- Bounded oscillation for a class of second order neutral delay difference equations
K. Liu and H. Zhang -- Asymptotic behavior in nonlinear discrete-time neural networks with delayed feedback
Y. Liu, L. Huang, and Z. Yuan -- Asymptotic behavior and periodicity of solutions for a difference equation with piecewise constant nonlinearity
Y. Liu, Z. Zhou, and W. Ge -- Positive solutions of a non-autonomous delay model of single population
H. Matsunaga -- Stability regions for a class of delay difference systems
M. Migda -- Oscillation and nonoscillation results for higher-order nonlinear difference equations
C. Potzsche -- Stability of center fiber bundles for nonautonomous difference equations
R. J. Sacker and H. F. von Bremen -- Bifurcation of maps and cycling in genetic systems
E. Schmeidel -- Nonoscillation and oscillation theorems for a fourth order nonlinear difference equation
H. Sedaghat -- On the equation $x_{n+1}=cx_{n}+f(x_{n}-x_{n-1})$
C. Tian, J. Zhang, and Z. Ji -- Stability criteria for a kind of delay functional equation
L. Wang and X. Zou -- Exponential stability of delay difference equations with applications to neural networks
X. Wang and L. Liao -- Asymptotic behavior of solutions of linear difference-differential equations with oscillating coefficients
W. Wendi -- Analysis of a discrete predator-prey model
H.-W. Wu and Y.-T. Xu -- Oscillation for nonautonomous neutral difference equations with variable coefficients
Z. Yinggao -- Oscillation of higher-order nonlinear delay difference equations
Z. Yuan, L. Huang, and Z. Zhou -- Coexistence of multiple attractive periodic solutions in a discrete-time neural network
R. Y. Zhang, Z. C. Wang, and J. S. Yu -- Necessary and sufficient conditions for the existence of positive solutions of nonlinear difference equations
Z. Zhou and Q. Zhang -- Periodic solutions of a class of difference systems
H. Zhu and L. Huang -- Dynamic analysis of a discrete-time network of two neurons with delayed feedback
Open problems and conjectures
S. Elaydi -- Open problems and conjectures
H. Brunner -- Discretization of Volterra integral equations with weakly singular kernels
S. Elaydi -- Nonautonomous difference equations: Open problems and conjectures
E. A. Grove and G. Ladas -- On period-two solutions of $x_{n+1} =\frac{\alpha + \beta x_{n}+\gamma x_{n-1}}{A + Bx_{n}+ C x_{n-1}}$
R. J. Sacker and H. F. von Bremen -- Open problems on cycling in genetic systems
J. Wu -- On periodic solutions of systems of two difference equations

Details:

Series: Fields Institute Communications, Volume: 42
Publication Year: 2004
ISBN: 0-8218-3354-5
Paging: approximately 448 pp.
Binding: Hardcover

Edited by: Abbas Bahri, Rutgers University, New Brunswick, NJ, Sergiu Klainerman, Princeton University, NJ, and Michael Vogelius, Rutgers University, New Brunswick, NJ

Noncompact Problems at the Intersection of Geometry, Analysis, and Topology

Expected publication date is July 1, 2004

Description

This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry.

Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian.

The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Contents

M. O. Ahmedou -- Conformal deformations of Riemannian metrics via "critical point theory at infinity": The conformally flat case with umbilic boundary
H. Bahouri and J.-Y. Chemin -- Cubic quasilinear wave equation and bilinear estimates
F. Bethuel and G. Orlandi -- Ginzburg-Landau functionals, phase transitions and vorticity
S.-Y. A. Chang, J. Qing, and P. Yang -- On the topology of conformally compact Einstein 4-manifolds
F. R. Cohen -- On loop spaces of configuration spaces, and related spaces
L. A. Caffarelli, D. Jerison, and C. E. Kenig -- Global energy minimizers for free boundary problems and full regularity in three dimensions
M. Dafermos -- Stability and instability of the Reissner-Nordstrom Cauchy horizon and the problem of uniqueness in general relativity
E. Hebey -- Nonlinear elliptic equations of critical Sobolev growth from a dynamical viewpoint
F. Helein -- Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory
F. H. Lin -- Revisit the topology of Sobolev maps
Y. Martel and F. Merle -- Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations
R. Mazzeo -- Recent advances in the global theory of constant mean curvature surfaces
P. Mironescu -- On some properties of $S^1$-valued fractional Sobolev spaces
P. H. Rabinowitz -- Homoclinics for a semilinear elliptic PDE
S. Serfaty and E. Sandier -- Vortices for Ginzburg-Landau equations: With magnetic field versus without
G. Tian -- Some regularity problems of stationary harmonic maps

Details:

Series: Contemporary Mathematics, Volume: 350
Publication Year: 2004
ISBN: 0-8218-3635-8
Paging: 252 pp.
Binding: Softcover