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
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
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
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
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