Series: Studies in Advanced Mathematics Volume: 44
ISBN: 1-58488-483-5
Publication Date: 11/15/2004
Number of Pages: 472
Builds a smooth transition from lower division mathematics to
real analysis at the senior level
Builds on the basics of Fourier analysis to introduce
contemporary ideas on wavelets and signal processing applications
Presents the methods of power series and characteristics and the
Picard existence and uniqueness theorem as a treatment of
differential equations
Describes multivariable analysis, the rudiments of Lebesgue
integration theory to invite further study, and a brief treatment
of Stokes's theorem and its variants
Students preparing for courses in real analysis often encounter
either very exacting theoretical treatments or books without
enough rigor to stimulate an in-depth understanding of the
subject. Further complicating this, the field has not changed
much over the past 150 years, prompting few authors to address
the lackluster or overly complex dichotomy existing among the
available texts.
The enormously popular first edition of Real Analysis and
Foundations gave students the appropriate combination of
authority, rigor, and readability that made the topic accessible
while retaining the strict discourse necessary to advance their
understanding. The second edition maintains this feature while
further integrating new concepts built on Fourier analysis and
ideas about wavelets to indicate their application to the theory
of signal processing. The author also introduces relevance to the
material and surpasses a purely theoretical treatment by
emphasizing the applications of real analysis to concrete
engineering problems in higher dimensions.
Expanded and updated, this text continues to build upon the
foundations of real analysis to present novel applications to
ordinary and partial differential equations, elliptic boundary
value problems on the disc, and multivariable analysis. These
qualities, along with more figures, streamlined proofs, and
revamped exercises make this an even more lively and vital text
than the popular first edition.
ISBN: 0-8493-2313-4
Publication Date: 8/27/2004
Number of Pages: 392
Presents a comprehensive treatment of sensor placement including
many original solutions
Offers a chapter dedicated to engineering applications
Demonstrates the use of MATLAB and Maple to implement the
proposed algorithms
Contains 52 figures and 6 tables to illustrate the numerical
examples
For dynamic distributed systems modeled by partial differential
equations, existing methods of sensor location in parameter
estimation experiments are either limited to one-dimensional
spatial domains or require large investments in software systems.
With the expense of scanning and moving sensors, optimal
placement presents a critical problem.
Optimal Measurement Methods for Distributed Parameter System
Identification discusses the characteristic features of the
sensor placement problem, analyzes classical and recent
approaches, and proposes a wide range of original solutions,
culminating in the most comprehensive and timely treatment of the
issue available. By presenting a step-by-step guide to
theoretical aspects and to practical design methods, this book
provides a sound understanding of sensor location techniques.
Both researchers and practitioners will find the case studies,
the proposed algorithms, and the numerical examples to be
invaluable. This text also offers results that translate easily
to MATLAB and to Maple. Assuming only a basic familiarity with
partial differential equations, vector spaces, and probability
and statistics, and avoiding too many technicalities, this is a
superb resource for researchers and practitioners in the fields
of applied mathematics, electrical, civil, geotechnical,
mechanical, chemical, and environmental engineering.
Series: Discrete Mathematics and Applications Volume: 4
ISBN: 0-8493-3156-0
Publication Date: 12/15/2004
Number of Pages: 392
Demonstrates the rich periodic character of nonlinear difference
equations of order greater than one
Puts forth many thought-provoking questions, open problems, and
conjectures worthy of investigation
Presents significant progress in the development of the basic
theory of nonlinear difference equations of order greater than
one
Sharkovsky's Theorem, Li and Yorke's "period three implies
chaos" result, and the (3x+1) conjecture are beautiful and
deep results that demonstrate the rich periodic character of
first-order, nonlinear difference equations. To date, however, we
still know surprisingly little about higher-order nonlinear
difference equations.
During the last ten years, the authors of this book have been
fascinated with discovering periodicities in equations of higher
order which for certain values of their parameters have one of
the following characteristics:
1. Every solution of the equation is periodic with the same
period.
2. Every solution of the equation is eventually periodic with a
prescribed period.
3. Every solution of the equation converges to a periodic
solution with the same period.
This monograph presents their findings along with some thought-provoking
questions and many open problems and conjectures worthy of
investigation. The authors also propose investigation of the
global character of solutions of these equations for other values
of their parameters and working toward a more complete picture of
the global behavior of their solutions.
With the results and discussions it presents, Periodicities in
Nonlinear Difference Equations places a few more stones in the
foundation of the basic theory of nonlinear difference equations.
Researchers and graduate students working in difference equations
and discrete dynamical systems will find much to intrigue them
and inspire further work in this area.
Expected publication date is January 20, 2005
"There is a wealth of very pretty examples of Schrodinger
operators here which could be presented ... in an elementary
quantum mechanics course."
-- MathSciNet
Description
This monograph presents a detailed study of a class of solvable
models in quantum mechanics that describe the motion of a
particle in a potential having support at the positions of a
discrete (finite or infinite) set of point sources. Both
situations-where the strengths of the sources and their locations
are precisely known and where these are only known with a given
probability distribution-are covered.
The authors present a systematic mathematical approach to these
models and illustrate its connections with previous heuristic
derivations and computations. Results obtained by different
methods in disparate contexts are thus unified and a systematic
control over approximations to the models, in which the point
interactions are replaced by more regular ones, is provided.
The first edition of this book generated considerable interest
for those learning advanced mathematical topics in quantum
mechanics, especially those connected to the Schrodinger
equations. This second edition includes a new appendix by Pavel
Exner, who has prepared a summary of the progress made in the
field since 1988. His summary, centering around two-body point
interaction problems, is followed by a bibliography focusing on
essential developments made since 1988.
The material is suitable for graduate students and researchers
interested in quantum mechanics and Schrodinger operators.
Contents
Introduction
The one-center point interaction
The one-center point interaction in three dimensions
Coulomb plus one-center point interaction in three dimensions
The one-center delta-interaction in one dimension
The one-center delta'-interaction in one dimension
The one-center point interaction in two dimensions
Point interactions with a finite number of centers
Finitely many point interactions in three dimensions
Finitely many delta-interactions in one dimension
Finitely many delta'-interactions in one dimension
Finitely many point interactions in two dimensions
Point interactions with infinitely many centers
Infinitely many point interactions in three dimensions
Infinitely many delta-interactions in one dimension
Infinitely many delta'-interactions in one dimension
Infinitely many point interactions in two dimensions
Random Hamiltonians with point interactions
Appendices
Self-adjoint extensions of symmetric operators
Spectral properties of Hamiltonians defined as quadratic forms
Schrodinger operators with interactions concentrated around
infinitely many centers
Boundary conditions for Schrodinger operators on (0,infty)
Time-dependent scattering theory for point interactions
Dirichlet forms for point interactions
Point interactions and scales of Hilbert spaces
Nonstandard analysis and point interactions
Elements of probability theory
Relativistic point interactions in one dimension
References
Author Index
Subject Index
Seize ans apres
Bibliography
Errata and addenda
Details:
Series: AMS Chelsea Publishing
Publication Year: 2005
ISBN: 0-8218-3624-2
Paging: 488 pp.
Binding: Hardcover
Expected publication date is February 13, 2005
Description
This classic book is intended to be the first introduction to
probability and statistics written with an emphasis on the
analytic approach to the problems discussed. Topics include the
axiomatic setup of probability theory, polynomial distribution,
finite Markov chains, distribution functions and convolution, the
laws of large numbers (weak and strong), characteristic
functions, the central limit theorem, infinitely divisible
distributions, and Markov processes.
Written in a clear and concise style, this book by Gnedenko can
serve as a textbook for undergraduate and graduate courses in
probability.
Contents
The concept of probability
Sequences of independent trials
Markov chains
Random variables and distribution functions
Numerical characteristics of random variables
The law of large numbers
Characteristic functions
The classical limit theorem
The theory of infinitely divisible distribution laws
The theory of stochastic processes
Elements of queueing theory
Elements of statistics
Tables
Bibliography
Index
Answers to the exercises
Details:
Series: AMS Chelsea Publishing
Publication Year: 1962
ISBN: 0-8218-3746-X
Paging: 529 pp.
Binding: Hardcover
Expected publication date is January 20, 2005
Description
The main theme of this book is the "path integral technique"
and its applications to constructive methods of quantum physics.
The central topic is probabilistic foundations of the Feynman-Kac
formula. Starting with main examples of Gaussian processes (the
Brownian motion, the oscillatory process, and the Brownian bridge),
the author presents four different proofs of the Feynman-Kac
formula. Also included is a simple exposition of stochastic Ito
calculus and its applications, in particular to the Hamiltonian
of a particle in a magnetic field (the Feynman-Kac-Ito formula).
Among other topics discussed are the probabilistic approach to
the bound of the number of ground states of correlation
inequalities (the Birman-Schwinger principle, Lieb's formula, etc.),
the calculation of asymptotics for functional integrals of
Laplace type (the theory of Donsker-Varadhan) and applications,
scattering theory, the theory of crushed ice, and the Wiener
sausage.
Written with great care and containing many highly illuminating
examples, this classic book is highly recommended to anyone
interested in applications of functional integration to quantum
physics. It can also serve as a textbook for a course in
functional integration.
Contents
Introduction
The basic processes
Bound state problems
Inequalities
Magnetic fields and stochastic integrals
Asymptotics
Other topics
References
Index
Bibliographic supplement
Bibliography
Details:
Series: AMS Chelsea Publishing
Publication Year: 2005
ISBN: 0-8218-3582-3
Paging: 306 pp.
Binding: Hardcover