Expected publication date is February 26,
2004
Description
This volume gathers the articles based on
a series of lectures
from a workshop held at the Institute of
Applied Mathematics of
the National University of Mexico. The aim
of the book is to
present to a non-specialized audience the
basic tools needed to
understand and appreciate new trends of research
on Schrodinger
operator theory.
Topics discussed include various aspects
of the spectral theory
of differential operators, the theory of
self-adjoint operators,
finite rank perturbations, spectral properties
of random
Schrodinger operators, and scattering theory
for Schrodinger
operators.
The material is suitable for graduate students
and research
mathematicians interested in differential
operators, in
particular, spectral theory of Schrodinger
operators.
Contents
A. M. Hinz -- Topics from spectral theory
of differential
operators
J. Brasche -- Spectral theory for self-adjoint
extensions
I. Veselic -- Integrated density of states
and Wegner estimates
for random Schrodinger operators
P. Kurasov -- Singular and supersingular
perturbations: Hilbert
space methods
F. Bentosela -- Scattering and spectral properties
of two surface
models
Details:
Series: Contemporary Mathematics,Volume:
340
Publication Year: 2004
ISBN: 0-8218-3297-2
Paging: 249 pp.
Binding: Softcover
Expected publication date is March 21, 2004
Description
Viewed locally, a closed one-form on a manifold
is a smooth
function up to an additive constant. The
global structure of a
closed one-form is mainly determined by its
de Rham cohomology
class. In this book, Michael Farber studies
fascinating
geometrical, topological, and dynamical properties
of closed one-forms.
In particular, he reveals the relations between
their global and
local features.
In 1981, S. P. Novikov initiated a generalization
of Morse theory
in which, instead of critical points of smooth
functions, one
deals with closed one-forms and their zeros.
The first two
chapters of the book, written in textbook
style, give a detailed
exposition of Novikov theory, which now plays
a fundamental role
in geometry and topology.
In the following chapters the author describes
the universal
chain complex that lives over a localization
(in the sense of P.
M. Cohn) of the group ring and relates the
topology of the
underlying manifold with information about
zeros of closed one-forms.
Using this complex, many different variations
and generalizations
of the Novikov inequalities are obtained,
including Bott-type
inequalities for closed one-forms, equivariant
inequalities, and
inequalities involving von Neumann Betti
numbers. Another
significant result in the book is a solution
of the problem about
exactness of the Novikov inequalities for
manifolds with the
infinite cyclic fundamental group.
One of the chapters deals with the problem
raised by E. Calabi
about intrinsically harmonic closed one-forms
and their Morse
numbers. Presented are the solution of this
problem and a
detailed study of topological properties
of singular foliations
of closed one-forms.
The last chapter suggests a completely new
Lusternik-Schnirelman-type
theory for dynamical systems. Closed 1-forms
appear in dynamics
through the concept of a Lyapunov 1-form
of a flow. As is shown
in the book, homotopy theory may be used
to predict the existence
of homoclinic orbits and homoclinic cycles
in dynamical systems
("focusing effect").
The book is suitable for graduate students
and researchers
interested in geometry and topology.
Contents
The Novikov numbers
The Novikov inequalities
The universal complex
Construction of the universal complex
Bott-type inequalities
Inequalities with von Neumann Betti numbers
Equivariant theory
Exactness of the Novikov inequalities
Morse theory of harmonic forms
Lusternik-Schnirelman theory, closed 1-forms,
and dynamics
Manifolds with corners
Morse-Bott function on manifolds with corners
Morse-Bott inequalities
Relative Morse theory
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs,
Volume: 108
Publication Year: 2004
ISBN: 0-8218-3531-9
Paging: approximately 256 pp.
Binding: Hardcover
Description
This new edition has been significantly revised
and updated to
reflect advances in the field since the publication
of the first
edition, such as the systematic experimental
testing of Preisach
models of hysteresis. The author has, however,
retained the two
most salient features of the original, the
emphasis on the
universal nature of mathematical models of
hysteresis and their
applicability to the description of hysteresis
phenomena in
various areas of science, technology and
economics and its
accessibility to a broad audience of researchers,
engineers, and
students.
Contents
The classical Preisach model of hysteresis,
Generalized scalar
Preisach models of hysteresis, Vector Preisach
models of
hysteresis, Stochastic aspects of hysteresis,
Superconducting
hysteresis, Eddy current hysteresis. Core
losses.
ISBN: 0-12-480873-5 Book/Hardback
Measurements: 152 X 229 mm
Pages: 300
Publication Date: 1 October 2003
Reviews
Stephen McDowall of Western Washington University
says:
" The topics covered are extensive.
The order and
organization are good, especially in terms
of
increasing sophistication of the mathematics
involved and in the
complexity of the Mathematica
programming necessary"
March 2003
Mark Lusk of The Colorado School of Mines
says:
" I am considering the adoption of this
book for my graduate
class in Simulation and Modeling. I
make very heavy use of Mathematica and have
a weekly computer lab.
I am tempted to make this
the sole, required text for that course"
March 2003
Description
The Third Edition of the Differential Equations
with Mathematica
integrates new applications from a variety
of fields,especially
biology, physics, and engineering. The new
handbook is also
completely compatible with Mathematica version
5.0 and is a
perfect introduction for Mathematica beginners.
The book/CD-ROM
package contains built-in commands that lets
the user solve
problems directly using graphical solutions.
Contents
Ch. 1 Introduction to Differential
Equations: Definitions and Concepts. Solutions
of Differential
Equations. Initial and Boundary Value Problems.
Direction
Fields.;
Ch. 2 First-Order Ordinary Differential Equations:
Theory of
First-Order Equations. A Brief
Discussion. Separation of Variables. Homogeneous
Equations. Exact
Equations. Linear
Equations. Numerical Approximations of Solutions
to First-Order
Equations; Ch. 3 Applications
of First-Order Ordinary Differential Equations:
Orthogonal
Trajectories. Population Growth
and Decay. Newton's Law of Cooling. Free-Falling
Bodies.; Ch. 4
Higher-Order Differential
Equations: Preliminary Definitions and Notation.
Solving
Homogeneus Equations with Constant
Coefficients. Introduction to Solving Nonhomogeneus
Equations
with Constant Coefficients.
Nonhomogeneous Equations with Constant Coefficients.
The Method
of Undetermined
Coefficients. Nonhomogeneus Equations with
Constant Coefficients.
Variation of Parameters;
Ch. 5 Applications of Higher-Order Differential
Equations: Simple
Harmonic Motion.
Damped Motion. Forced Motion. Other Applications.
The Pendulum
Problem; Ch. 6 Ordinary
Differential Equations with Nonconstant Coefficients:
Cauchy-Euler
Equations. Power
Series Review. Power Series Solutions About
Ordinary Points.
Series Solutions about Regular
Singular Points. Some Special Functions;
Ch. 7 Laplace Transform
Methods: The Laplace
Transform. The Inverse Laplace Transform.
Solving Initial-Value
Problems with the Laplace
Transform. Laplace Transforms of Step and
Periodic Functions. The
Convolution Theorem.
Applications of Laplace Transforms.; Ch.
8 Systems of Ordinary
Differential Equations:
Review of Matrix Algebra and Calculus. Systems
of Equations:
Preliminary Definitions and
Theory. Homogeneous Linear Systems with Constant
Coefficients.
Nonhomeogeneous
First-Order Systems: Undetermined Coefficients,
Variation of
Parameters and the Matrix
Exponential. The Laplace Transform Methods
Numerical Methods,
Nonlinear Systems,
Linearization, and Classificaction of Equilibrium
Points.; Ch. 9
Applications of Systems of
Ordinary Differential Equations Mechanical
and Electrical
Problems with First-Order Linear
Systems. Diffusion and Population Problems
with First-Order
Linear Systems. Applications
using Laplace Transforms. Applications that
Lead to Nonlinear
Systems Biological Systems; Ch.
10 Eigenvalue Problems and Fourier Series:
Boundary Value
Problems, Sturm-Liouville
Problems, Fourier Sine Series and Cosine
Series. Fourier Series.
Generalized Fourier Series;
Ch. 11 Partial Differential Equations: Introduction
to Partial
Differential Equations and
Separation of Variables. The One-Dimensional
Heat Equation. The
One-Dimensional Wave
Equation. Problems in Two Dimensions: Laplace's
Equation. Two-Dimensional
Problems in a
Circular Region. Appendix: Getting Started.
ISBN: 0-12-041562-3 Book/Paperback
Measurements: 191 X 235 mm
Pages: 750
Publication Date: 22 February 2004