Edited by:
Teresa Faria, Universidade de Lisboa, Portugal,
and Pedro Freitas, Instituto Superior Ternico, Lisboa, Portugal

Topics in Functional Differential and Difference Equations

Expected publication date is March 15, 2001
Description

This volume contains papers written by participants at the Conference on Functional Differential and Difference Equations held at the Instituto Superior Tιcnico in Lisbon, Portugal. The conference brought together mathematicians working in a wide range of topics, including qualitative properties of solutions, bifurcation and stability theory, oscillatory behavior, control theory and feedback systems, biological models, state-dependent delay equations, Lyapunov methods, etc. Articles are written by leading experts in the field. A comprehensive overview is given of these active areas of current research. The book will be of interest to both theoretical
and applied mathematical scientists.

Contents

S. Amraoui and S. Lalaoui Rhali -- Monotonicity for some reaction-diffusion systems with delay and Dirichlet boundary conditions
O. V. Anashkin -- Lyapunov's direct method and parametric resonance in linear systems with delay
O. Arino, E. Sαnchez, and A. Fathallah -- State-dependent delay differential equations in population dynamics: Modeling and analysis
M. Bachar and P. Magal -- Existence of periodic solution for a class of delay differential equations with impulses
A. Bαtkai and S. Piazzera -- Damped wave equations with delay
H. Bouzahir and K. Ezzinbi -- Global attractor for a class of partial functional differential equations with infinite delay
R. Ceppitelli and L. Faina -- Differential equations with hereditary structure induced by a Volterra type property
G. Derfel and F. Vogl -- Asymptotic analysis of binomial recurrences
L. Fichmann and W. M. Oliva -- Collision of global orbits in $C^\infty$ retarded functional differential equations
L. Fichmann and W. M. Oliva -- One-to-oneness and hyperbolicity
W. E. Fitzgibbon, M. Langlais, and J. J. Morgan -- Modeling the spread of feline leukemia virus in heterogeneous habitats
F. Giannakopoulos, C. Hauptmann, and A. Zapp -- Bursting activity in a model of a neuron with recurrent synaptic feedback
E. A. Grove, C. Kent, G. Ladas, and M. A. Radin -- On $x_{n+1}=\mbox{max}\left\{\frac{1}{x_{n}},\frac{A_{n}}{x_{n-1}}\right\}$ with a period 3
parameter
I. Gyφri and F. Hartung -- Stability in delay perturbed differential and difference equations
J. K. Hale -- Some problems in FDE
U. an der Heiden -- Non-linear feedback systems with memory: From 0-th to higher order, discrete and continuous
L. Huang and J. Wu -- Dynamics of inhibitory artificial neural networks with threshold nonlinearity
W. Huang -- Dimension of space of solutions for a linear nonautonomous infinite delay differential equation
T. Krisztin -- Unstable sets of periodic orbits and the global attractor for delayed feedback
E. Litsyn, Y. V. Nepomnyashchikh, and A. Ponosov -- Uniform exponential stability of controlled quasilinear systems and functional differential equations
S.-i. Nakagiri -- Finite pole assignment of retarded dynamical systems in Hilbert spaces
S. M. Verduyn Lunel -- Inverse problems for nonself-adjoint evolutionary systems
H.-O. Walther -- Contracting return maps for some delay differential equations
M. Weedermann -- Normal forms for neutral functional differential equations
G. J. Wirsching -- A functional differential equation and $3n+1$ dynamics

Details:

Series: Fields Institute Communications, Volume: 29
Publication Year: 2001
ISBN: 0-8218-2701-4
Paging: 378 pp.
Binding: Hardcover

Edited by: Mikhail Lyubich, John W. Milnor,
and Yair N. Minsky, SUNY at Stony Brook, NY

Laminations and Foliations in Geometry, Topology, and Dynamics

Expected publication date is March 1, 2001

Description

This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event.

Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.

Contents

F. Bonahon -- Geodesic laminations on surfaces
C. Camacho -- Dicritical singularities of holomorphic vector fields
J. E. Fornζss and N. Sibony -- Dynamics of $\mathbb{P}^2$ (Examples)
D. Gabai -- 3 lectures on foliations and laminations on 3-manifolds
J. Kiwi -- Rational laminations of complex polynomials
J. Seade and A. Verjovsky -- Actions of discrete groups on complex projective spaces
S. Zakeri -- Dynamics of singular holomorphic foliations on the complex projective plane

Details:

Series: Contemporary Mathematics,Volume: 269
Publication Year: 2001
ISBN: 0-8218-1985-2
Paging: approximately 232 pp.
Binding: Softcover

Kenji Ueno, Kyoto University, Japan

Algebraic Geometry 2: Sheaves and Cohomology

Expected publication date is May 9, 2002

Description

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes (see Volume 185 in the same series, Translations of Mathematical Monographs). In the present book, Ueno turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local
holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves. The primary tool in understanding sheaves is cohomology. For example, in studying ampleness, it is frequently useful to translate a property of sheaves into a statement about its cohomology.

The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as ...

coherent and quasicoherent sheaves.
proper and projective morphisms.
direct and inverse images.
Cech cohomology.

For the mathematician unfamiliar with the language of schemes and sheaves, algebraic geometry can seem distant. However, Ueno makes the topic seem natural through his concise style and his insightful explanations. He explains why things are done this way and supplements his explanations with illuminating examples. As a result, he is able to make algebraic geometry very accessible to a wide audience of non-specialists.

The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry.

Contents

Coherent sheaves
Proper and projective morphisms
Cohomology of coherent sheaves
Solutions to problems
Solutions to exercises
Index

Details:

Series: Translations of Mathematical Monographs, Volume: 197
Subseries: Iwanami Series in Modern Mathematics
Publication Year: 2001
ISBN: 0-8218-1357-9
Paging: approximately 200 pp.
Binding: Softcover

Author: Cupillari

The Nuts and Bolts of Proofs, 2nd Ed.

ISBN: 0121994511
Cover: Paperback
Published: February 2001

SECOND EDITION

Antonella Cupillari Pennsylvania State Erie, Behrend College, Erie, Pennsylvania

This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of
definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers is provided, enabling students to practice on their
own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments.