Expected publication date is July 31, 2005
Description
Lively discussions and stimulating research were part of a five-day
conference on Mathematical Methods in Nonlinear Wave Propagation
sponsored by the NSF and CBMS. This volume is a collection of
lectures and papers stemming from that event. Leading experts
present dynamical systems and chaos, scattering and spectral
theory, nonlinear wave equations, optimal control, optical
waveguide design, and numerical simulation.
The book is suitable for a diverse audience of mathematical
specialists interested in fiber optic communications and other
nonlinear phenomena. It is also suitable for engineers and other
scientists interested in the mathematics of nonlinear wave
propagation.
Contents
R. E. Mickens -- An introduction to wave equations
M. Klaus -- On the Zakharov-Shabat eigenvalue problem
T. Aktosun -- Solitons and inverse scattering transform
J. Yang -- A tail-matching method for the linear stability of
multi-vector-soliton bound states
R. H. Goodman, R. E. Slusher, M. I. Weinstein, and M. Klaus --
Trapping light with grating defects
B. N. Borah -- Thermo-elastic-plastic transition
A. B. Smirnova -- Regularized quasi-Newton method with continuous
inversion of $F'+\varepsilon I$ for monotone ill-posed operator
equations
W. Huang -- Transition layers for a singularly perturbed neutral
delay differential equation
C. Y. Loh -- Nonlinear aeroacoustics computations by the CE/SE
method
S. C. Chang, A. Himansu, C. Y. Loh, X. Y. Wang, and S. T. Yu --
Robust and simple non-reflecting boundary conditions for the
Euler equations-A new approach based on the space-time CE/SE
method
G. Tang, D. Clemence, C. Jackson, Q. Lin, and V. Burbach --
Physical and numerical modeling of seismic wave propagation
Details:
Series: Contemporary Mathematics,Volume 379
Publication Year: 2005
ISBN: 0-8218-3349-9
Paging: 213 pp.
Binding: Softcover
Expected publication date is August 19, 2005
Description
This graduate-level textbook introduces the classical theory of
complex tori and abelian varieties, while presenting in parallel
more modern aspects of complex algebraic and analytic geometry.
Beginning with complex elliptic curves, the book moves on to the
higher-dimensional case, giving characterizations from different
points of view of those complex tori which are abelian varieties,
i.e., those that can be holomorphically embedded in a projective
space. This allows, on the one hand, for illuminating the
computations of nineteenth-century mathematicians, and on the
other, familiarizing readers with more recent theories. Complex
tori are ideal in this respect: One can perform "hands-on"
computations without the theory being totally trivial.
Standard theorems about abelian varieties are proved, and moduli
spaces are discussed. Recent results on the geometry and topology
of some subvarieties of a complex torus are also included.
The book contains numerous examples and exercises. It is a very
good starting point for studying algebraic geometry, suitable for
graduate students and researchers interested in algebra and
algebraic geometry.
Contents
Preface to the English edition
Preface to the French edition
Lattices and complex tori
Elliptic curves
Differential forms and de Rham cohomology
Theta functions and divisors
Line bundles, sheaf cohomology, and first Chern class
Abelian varieties
Moduli spaces
Subvarieties of a complex torus
Bibliography
Index
Details:
Series: SMF/AMS Texts and Monographs, Volume: 11
Publication Year: 2005
ISBN: 0-8218-3165-8
Paging: 109 pp.
Binding: Softcover
Expected publication date is August 31, 2005
Description
Two conferences, Logic and Its Applications in Algebra and
Geometry and Combinatorial Set Theory, Excellent Classes, and
Schanuel Conjecture, were held at the University of Michigan (Ann
Arbor). These events brought together model theorists and set
theorists working in these areas. This volume is the result of
those meetings. It is suitable for graduate students and
researchers working in mathematical logic.
Contents
J. T. Baldwin -- Ehrenfeucht-Mostowski models in abstract
elementary classes
A. Blass -- Unsplit families, dominating families, and
ultrafilters
A. Bovykin -- Several proofs of PA-unprovability
M. Di Nasso and M. Forti -- Ultrafilter semirings and nonstandard
submodels of the Stone-Cech compactification of the natural
numbers
S. Gao -- Unitary group actions and Hilbertian polish metric
spaces
R. Grossberg and O. Lessmann -- Abstract decomposition theorem
and applications
G. Hjorth -- A dichotomy theorem for being essentially countable
T. Huuskonen and Y. Zhang -- Mad families are small
T. Hyttinen -- Random logarithm and homogeneity
J. Iovino -- Definability, semidefinability, and asymptotic
structure in analysis
A. Kolesnikov -- Dependence relations in non-elementary classes
O. Lessmann -- An introduction to excellent classes
D. Mushtari -- Ultrafilters and nuclear spaces
J. Steprans -- Many quotient algebras of the integers modulo co-analytic
ideals
V. Tolstykh -- What does the automorphism group of a free abelian
group $A$ know about $A$?
B. Zilber -- A categoricity theorem for quasi-minimal excellent
classes
Details:
Series: Contemporary Mathematics,Volume 380
Publication Year: 2005
ISBN: 0-8218-3474-6
Paging: 306 pp.
Binding: Softcover
Expected publication date is September 21, 2005
Description
For over two centuries, the work of the St. Petersburg
mathematicians in number theory has constituted a glorious
contribution to mathematics. The Russian book, The St. Petersburg
School of Number Theory, is about the life and work of prominent
members of this school, such as Chebyshev, Korkin, Zolotarev,
Markov, Voronoi, and Vinogradov. These mathematicians are indeed
a very distinguished group, and their work in number theory is of
the highest quality and continues to have lasting significance.
This English translation acquaints the reader with the most
important works of these six eminent members of the St.
Petersburg school. A short biography is given for each of them,
followed by an exposition of some of his most significant
contributions. Each contribution features the author's original
terminology and notation and is followed by commentary. Certain
works receive relatively complete expositions, while others are
dealt with more briefly.
With a Foreword written for the English edition, this volume will
appeal to a broad mathematical audience, including mathematical
historians. It is particularly suitable for graduate students and
researchers interested in number theory.
Contents
Pafnutii L'vovich Chebyshev (1821-1894)
Pafnutii L'vovich Chebyshev
Chebyshev's articles on prime numbers
Aleksandr Nikolaevich Korkin (1837-1908)
Aleksandr Nikolaevich Korkin
The articles by Korkin and Zolotarev on the minima of positive
quadratic forms
Egor Ivanovich Zolotarev (1847-1878)
Egor Ivanovich Zolotarev
Zolotarev's memoirs on the theory of ideal numbers
Andrei Andreevich Markov (1856-1922)
Andrei Andreevich Markov
On binary quadratic forms of positive determinant
Georgii Fedoseevich Voronoii (1868-1908)
Georgii Fedoseevich Voronoi
Voronoi's dissertations on algebraic numbers of the third degree
Voronoi's memoir of 1903: "On a problem from the theory of
asymptotic functions"
Voronoi's memoirs on quadratic forms
Ivan Matveevich Vinogradov (1891-1983)
Ivan Matveevich Vinogradov
Works of Vinogradov from the first period of his mathematical
activity
Waring's problem
The Goldbach problem
Estimation of Weyl sums and the problem of the fractional parts
of a polynomial
Bibliography
Details:
Series: History of Mathematics, Volume: 26
Publication Year: 2005
ISBN: 0-8218-3457-6
Paging: approximately 296 pp.
Binding: Hardcover
Expected publication date is September 8, 2005
Description
In the Summer of 2001, the Mathematical Sciences Research
Institute (MSRI) hosted the Clay Mathematics Institute Summer
School on the Global Theory of Minimal Surfaces. During that
time, MSRI became the world center for the study of minimal
surfaces: 150 mathematicians--undergraduates, post-doctoral
students, young researchers, and world experts--participated in
the most extensive meeting ever held on the subject in its 250-year
history. The unusual nature of the meeting made it possible to
put together this collection of expository lectures and
specialized reports, giving a panoramic view of a vital subject
presented by leading researchers in the field.
The subjects covered include minimal and constant-mean-curvature
submanifolds, geometric measure theory and the double-bubble
conjecture, Lagrangian geometry, numerical simulation of
geometric phenomena, applications of mean curvature to general
relativity and Riemannian geometry, the isoperimetric problem,
the geometry of fully nonlinear elliptic equations and
applications to the topology of three-dimensional manifolds. The
wide variety of topics covered make this volume suitable for
graduate students and researchers interested in differential
geometry.
Titles in this series are published by the AMS for the Clay
Mathematics Institute (Cambridge, MA).
Contents
F. Morgan and M. Ritore -- Geometric measure theory and the proof
of the double bubble conjecture
M. Weber -- Classical minimal surfaces in Euclidean space by
examples: Geometric and computational aspects of the Weierstrass
representation
K. Polthier -- Computational aspects of discrete minimal surfaces
R. Schoen -- Mean curvature in Riemannian geometry and general
relativity
H. Karcher -- Introduction to conjugate Plateau constructions
J. Perez and F. J. Lopez -- Parabolicity and minimal surfaces
A. Ros -- The isoperimetric problem
M. Wolf -- Flat structures, Teichmuller theory and handle
addition for minimal surfaces
M. Weber, D. Hoffman, and M. Wolf -- The genus-one helicoid as a
limit of screw-motion invariant helicoids with handles
D. Hoffman -- Computing minimal surfaces
J. Spruck -- Geometric aspects of the theory of fully nonlinear
elliptic equations
H. Karcher -- Hyperbolic surfaces of constant mean curvature one
with compact fundamental domains
J. Choe -- Isoperimetric inequalities of minimal submanifolds
F. Martin -- Complete nonorientable minimal surfaces in
$\mathbb{R}^3$
F. J. Lopez -- Some Picard-type results for properly immersed
minimal surfaces in $\mathbb{R}^3$
M. Ritore -- Optimal isoperimetric inequalities for three-dimensional
Cartan-Hadamard manifolds
T. H. Colding and W. P. Minicozzi II -- Embedded minimal disks
M. Traizet -- Construction of minimal surfaces by gluing
Weierstrass representations
W. H. Meeks III -- Global problems in classical minimal surface
theory
W. H. Meeks III and H. Rosenberg -- Minimal surfaces of finite
topology
N. Kapouleas -- Constructions of minimal surfaces by gluing
minimal immersions
R. Mazzeo, F. Pacard, and D. Pollack -- The conformal theory of
Alexandrov embedded constant mean curvature surfaces in
$\mathbb{R}^3$
W. Rossman, M. Umehara, and K. Yamada -- Constructing mean
curvature 1 surfaces in $H^3$ with irregular ends
R. Kusner -- Conformal structures and necksizes of embedded
constant mean curvature surfaces
J. Perez, W. H. Meeks III, and A. Ros -- Uniqueness of the
Riemann minimal surfaces
Y. Fang -- The mathematical protein folding problem
K. Tenenblat -- Minimal and CMC surfaces obtained by Ribaucour
transformations
R. Sa Earp and E. Toubiana -- Meromorphic data for surfaces of
mean curvature one in hyperbolic space, II
R. Schoen -- Special Lagrangian submanifolds
D. Joyce -- Lectures on special Lagrangian geometry
J. Wolfson -- Variational problems in Lagrangian geometry:
$\mathbb{Z}_2$-currents
J. Hass -- Minimal surfaces and the topology of three-manifolds
J. H. Rubinstein -- Minimal surfaces in geometric 3-manifolds
K. Grose-Brauckmann -- Cousins of constant mean curvature
surfaces
P. Topping -- An approach to the Willmore conjecture
C. Mese -- Minimal surfaces and harmonic maps into singular
geometry
J. H. Rubinstein -- Shortest networks in 2 and 3 dimensions
List of participants
Details:
Series: Clay Mathematics Proceedings, Volume: 2
Publication Year: 2005
ISBN: 0-8218-3587-4
Paging: approximately 816 pp.
Binding: Softcover