2003 Approx. 295 p. Hardcover
0-387-00308-8
The conjoining of nonlinear dynamics and
biology has brought
about significant advances in both areas,
with nonlinear dynamics
providing a tool for understanding biological
phenomena and
biology stimulating developments in the theory
of dynamical
systems. This research monograph provides
an introduction to the
theory of nonautonomous semiflows with applications
to population
dynamics. It develops dynamical system approaches
to various
evolutionary equations such as difference,
ordinary, functional,
and partial differential equations, and pays
more attention to
periodic and almost periodic phenomena. The
presentation includes
persistence theory, monotone dynamics, periodic
and almost
periodic semiflows, traveling waves, and
global analysis of
typical models in population biology. Research
mathematicians
working with nonlinear dynamics, particularly
those interested in
applications to biology, will find this book
useful. It may also
be used as a textbook or as supplementary
reading for a graduate
special topics course on the theory and applications
of dynamical
systems.
Dr. Xiao-Qiang Zhao is a professor in applied
mathematics at
Memorial University of Newfoundland, Canada.
His main research
interests involve applied dynamical systems,
nonlinear
differential equations, and mathematical
biology. He is the
author of more than 40 papers and his research
has played an
important role in the development of the
theory of periodic and
almost periodic semiflows and their applications.
Contents: * Introduction * Discrete Dynamical
Systems * Monotone
Dynamics * Nonautonomous Semiflows * A Discrete-time
Chemostat
Model * N-species Competition in a Periodic
Chemostat * Almost
Periodic Competitive Systems * Competitor-Competitor-Mutualist
Systems * A Periodically Pulsed Bioreactor
Model * A Nonlocal and
Delayed Predator-Prey Model * Traveling Waves
in Bistable
Nonlinearities * Bibliography * Index
Series: CMS Books in Mathematics.
2003 Approx. 440 p. 67 illus. Hardcover
0-387-95449-X
This book covers numerical methods for partial
differential
equations: discretization methods such as
finite difference,
finite volume and finite element methods;
solution methods for
linear and nonlinear systems of equations
and grid generation.
The book takes account of both the theory
and implementation,
providing simultaneously both a rigorous
and an inductive
presentation of the technical details. It
contains modern topics
such as adaptive methods, multilevel methods
and methods for
convection-dominated problems. Detailed illustrations
and
extensive exercises are included.
It will provide mathematics students with
an introduction to the
theory and methods, guiding them in their
selection of methods
and helping them to understand and pursue
finite element
programming. For engineering and physics
students it will provide
a general framework for formulation and analysis
of methods
providing a broader perspective to specific
applications.
Contents: For Example: Modelling Processes
in Porous Media with
Differential Equations * For the Beginning:
The Finite Difference
Method for the Poisson Equation * The Finite
Element Method for
the Poisson Equation * The Finite Element
Method for Linear
Elliptic Boundary Value Problems of Second
Order * Grid
Generation and A Posteriori Error Estimation
* Iterative Methods
for Systems of Linear Equations * The Finite
Volume Method *
Discretization Methods for Parabolic Initial
Boundary Value
Problems * Iterative Methods for Nonlinear
Equations *
Discretization Methods for Convection Dominated
Problems *
Appendices
Series: Texts in Applied Mathematics. Vol..
44
1st ed. 2003 XIX, 398 p. Hardcover
3-540-00657-5
Queues and stochastic networks are analyzed
in this book with
purely probabilistic methods. The purpose
of these lectures is to
show that general results from Markov processes,
martingales or
ergodic theory can be used directly to study
the corresponding
stochastic processes. Recent developments
have shown that,
instead of having ad-hoc methods, a better
understanding of
fundamental results on stochastic processes
is crucial to study
the complex behavior of stochastic networks.
In this book, various aspects of these stochastic
models are
investigated in depth in an elementary way:
Existence of
equilibrium, characterization of stationary
regimes, transient
behaviors (rare events, hitting times) and
critical regimes, etc.
A simple presentation of stationary point
processes and Palm
measures is given. Scaling methods and functional
limit theorems
are a major theme of this book. In particular,
a complete chapter
is devoted to fluid limits of Markov processes.
Series: Applications of Mathematics. Vol..
52
2003 Approx. 600 p. 7 illus. Hardcover
0-387-95382-5
This graduate textbook covers topics in statistical
theory
essential for graduate students preparing
to undertake a Ph.D. in
statistics. The first chapter provides a
brief overview of
concepts and results in measure-theoretic
probability theory. The
second chapter introduces some fundamental
concepts in
statistical decision theory and inference.
Chapters 3-7 contain
detailed studies on some important topics:
unbiased estimation,
parametric estimation, nonparametric estimation,
hypothesis
testing, and confidence sets. A large number
of exercises in each
chapter provide not only practice problems
for students, but also
many additional results. In addition to the
classical results
that are typically covered in a textbook
of a similar level, this
book introduces some topics in modern statistical
theory that
have been developed in recent years, such
as Markov chain Monte
Carlo, quasi-likelihoods, empirical likelihoods,
statistical
functionals, generalized estimation equations,
the jackknife, and
the bootstrap.
Contents: Probability Theory * Fundamentals
of Statistics *
Unbiased Estimation * Estimation in Parametric
Models *
Estimation in Nonparametric Models * Hypothesis
Tests *
Confidence Sets
Series: Springer Texts in Statistics.
*****************************************************************************************************
2003 Approx. 335 p. Hardcover
3-540-00845-4
Most probability problems involve random
variables indexed by
space and/or time. These problems almost
always have a version in
which space and/or time are taken to be discrete.
This volume
deals with areas in which the discrete version
is more natural
than the continuous one, perhaps even the
only one than can be
formulated without complicated constructions
and machinery.
The 5 papers of this volume discuss problems
in which there has
been significant progress in the last few
years; they are
motivated by, or have been developed in parallel
with,
statistical physics. They include questions
about asymptotic
shape for stochastic growth models and for
random clusters;
existence, location and properties of phase
transitions; speed of
convergence to equilibrium in Markov chains,
and in particular
for Markov chains based on models with a
phase transition; cut-off
phenomena for random walks.
The articles can be read independently of
each other. Their
unifying theme is that of models built on
discrete spaces or
graphs. Such models are often easy to formulate.
Correspondingly,
the book requires comparatively little previous
knowledge of the
machinery of probability.
Contents:
D. Aldous, J.M. Steele: The Objective Method:
Probabilistic
Combinatorial Optimization and Local Weak
Convergence.- G.
Grimmett: The Random-Cluster Model.- C.G.
Howard: Models of First-Passage
Percolation.- F. Martinelli: Relaxation Times
of Markov Chains in
Statistical Mechanics and Combinatorial Structures.-
L. Saloff-Coste:
Random Walks on Finite Groups.- Index.
Series: Encyclopaedia of Mathematical Sciences.
Vol.. 110