Series: Undergraduate Texts in Mathematics
2005, XXII, 546 p. 119 illus., Hardcover
ISBN: 0-387-23059-9
About this textbook
This book integrates both classical and modern treatments of
difference equations. It contains the most updated and
comprehensive material, yet the presentation is simple enough for
the book to be used by advanced undergraduate and beginning
graduate students. This third edition includes more proofs, more
graphs, and more applications. The author has also updated the
contents by adding a new chapter on Higher Order Scalar
Difference Equations, and also recent results on local and global
stability of one-dimensional maps, a new section on the various
notions of asymptoticity of solutions, a detailed proof of Levin-May
Theorem, and the latest results on the LPA flour-beetle model.
Table of contents
* Preface * List of Symbols * Dynamics of First-Order Difference
Equations * Linear Difference Equations of Higher Order * Systems
of Linear Difference Equations * Stability Theory * Higher Order
Scalar Difference Equations * The Z-Transform Method and Volterra
Difference Equations * Oscillation Theory * Asymptotic Behavior
of Difference Equations * Applications to Continued Fractions and
Orthogonal Polynomials * Control Theory * Answers and Hints to
Selected Problems * Appendix A: Stability of Nonhyperbolic Fixed
Points of Maps on the Real Line * Vandermonde Matrix * Stability
of Nondifferentiable Maps * Stable Manifold and Hartman-Grobman-Cushing
Theorems * Levin-May Theorem * Classical Orthogonal Polynomials *
Identities and Formulas * References * Index
Series: Springer Texts in Statistics
2005, XII, 786 p. 20 illus., Hardcover
ISBN: 0-387-98864-5
About this textbook
This classic textbook, now available from Springer, summarizes
developments in the field of hypotheses testing. Optimality
considerations continue to provide the organizing principle.
However, they are now tempered by a much stronger emphasis on the
robustness properties of the resulting procedures. This book is
an essential reference for any graduate student in statistics.
Table of contents
The General Decision Problem.- The Probability Background.-
Uniformly Most Powerful Tests.- Unbiasedness: Theory and First
Applications.- Unbiasedness: Applications to Normal Distributions.-
Invariance.- Linear Hypotheses.- The Minimax Principle.- Multiple
Testing and Simultaneous Inference.- Conditional Inference.-
Basic Large Sample Theory.- Quadratic Mean Differentiable
Families.- Large Sample Optimality.- Testing Goodness of Fit.-
General Large Sample Methods.
Series: Springer Series in Computational Mathematics, Vol. 37
2005, XIII, 256 p., Hardcover
ISBN: 3-540-25268-1
About this book
Stochastic numerical methods play an important role in large
scale computations in the applied sciences. The first goal of
this book is to give a mathematical description of classical
direct simulation Monte Carlo (DSMC) procedures for rarefied
gases, using the theory of Markov processes as a unifying
framework. The second goal is a systematic treatment of an
extension of DSMC, called stochastic weighted particle method.
This method includes several new features, which are introduced
for the purpose of variance reduction (rare event simulation).
Rigorous convergence results as well as detailed numerical
studies are presented.
Written for:
Graduate students and researchers
Keywords:
Boltzmann equation
Monte Carlo methods
interacting particle systems
rarified gas dynamics
stochastic numerics
Series: International Series of Numerical Mathematics, Vol.
151
2005, XV, 281 p., Hardcover
ISBN: 3-7643-7124-2
About this book
This volume contains contributions from international experts in
the fields of constructive approximation. This area has reached
out to encompass the computational and approximation-theoretical
aspects of various interesting fields in applied mathematics such
as (multivariate) approximation methods, quasi-interpolation,and
approximation by (orthogonal) polynomials, as well as the modern
mathematical developments in neuro fuzzy approximation, RBF-networks,
industrial and engineering applications.
Table of contents
Preface.- Articles by: Adell, Lekuona, Altomare, Rasa, Braess, de
Bruin, Mache, Catinas, Davydov, Sestini, Morandi, Igel, Wiegand,
Friedrichs, Meyer, Mazure, Mhaskar, Michels, Obermaier, Szwarc,
Platte, Kuzmin, Fredebeul, Turek, Rasa, Sablonniere, Szabados,
Toussaint, Weishui, Della Vecchia, Mastroianni and Vertesi
2005, XII, 294 p. 60 illus., Hardcover
ISBN: 3-540-23889-1
About this book
The most important question addressed in this book is "what
is the nature (the ontological status) of spacetime?" or,
equivalently, "what is the dimensionality of the world at
the macroscopic level?" The answer to this question is
developed via a thorough analysis of relativistic effects and
explicitly asking whether the objects involved in those effects
are three-dimensional or four-dimensional. This analysis clearly
shows that if the world and the physical objects were three-dimensional,
none of the kinematic relativistic effects and the experimental
evidence supporting them would be possible. The implications of
this result for physics, philosophy, and our entire world view
are discussed.
Table of contents
Introduction.- On the Impossibility of Detecting Uniform Motion.-
Exploring the Internal Logic of Galileo's Principle of Relativity.-
Relativity in Euclidean Space and in Spacetime.- Relativity and
the Dimensionality of the World: Spacetime Is Real.- Quantum
Mechanics and the Nature of Spacetime.- The Nature of Spacetime
and the Validity of Scientific Theories.- Propagation of Light in
Non-inertial Reference Frames.- Calculating the Electric Field of
a Charge in a Non-inertial Reference Frame.- Inertia as a
Manifestation of the Reality of Spacetime.- Appendices.-
References.- Index.
Series: Systems & Control: Foundations & Applications
2005, XIV, 234 p., Hardcover
ISBN: 3-7643-2198-9
About this book
This volume is dedicated to the fundamentals of convex functional
analysis. It presents those aspects of functional analysis that
are extensively used in various applications to mechanics and
control theory. The purpose of the text is essentially two-fold.
On the one hand, a bare minimum of the theory required to
understand the principles of functional, convex and set-valued
analysis is presented. Numerous examples and diagrams provide as
intuitive an explanation of the principles as possible. On the
other hand, the volume is largely self-contained. Those with a
background in graduate mathematics will find a concise summary of
all main definitions and theorems.
Table of contents
Summary
The tradition of a publication based on the Gathering for Gardner
continues with this new carefully selected and edited collection
in which Martin Gardner and friends inspire and entertain.
The contributors to this volume?virtually a list of Whofs Who
in the World of Puzzles?trace their inspiration to Martin Gardnerfs
puzzle column in Scientific American and to his contributions to
the world of recreational mathematics.
Tribute to a Mathemagician contains an author index for the two
previous books in the collection of books based on the Gatherings
for Gardner.
Sample puzzles and games include:
Tripos
Black Jack
Chinese ceramic puzzle vessels
Paper folding
Mongolian interlocking puzzles
Rolling block puzzles
Sliding puzzles
Cryptic crosswords
The Panex puzzle
Polyonimo puzzles
and more
Details
ISBN: 1-56881-204-3
Year: 2004
Format: Hardcover
Pages: 350