Paper | May 2003 |ISBN: 0-691-11482-X
Cloth | May 2003 |ISBN: 0-691-11483-8
304 pp. | 6 x 9 | 50 line illus.
This book represents the first asymptotic analysis, via
completely integrable techniques, of the initial value problem
for the focusing nonlinear Schrodinger equation in the
semiclassical asymptotic regime. This problem is a key model in
nonlinear optical physics and has increasingly important
applications in the telecommunications industry. The authors
exploit complete integrability to establish pointwise asymptotics
for this problem's solution in the semiclassical regime and
explicit integration for the underlying nonlinear, elliptic,
partial differential equations suspected of governing the
semiclassical behavior. In doing so they also aim to explain the
observed gradient catastrophe for the underlying nonlinear
elliptic partial differential equations, and to set forth a
detailed, pointwise asymptotic description of the violent
oscillations that emerge following the gradient catastrophe.
To achieve this, the authors have extended the reach of two
powerful analytical techniques that have arisen through the
asymptotic analysis of integrable systems: the Lax-Levermore-Venakides
variational approach to singular limits in integrable systems,
and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase
method for the analysis of Riemann-Hilbert problems. In
particular, they introduce a systematic procedure for handling
certain Riemann-Hilbert problems with poles accumulating on
curves in the plane. This book, which includes an appendix on the
use of the Fredholm theory for Riemann-Hilbert problems in the
Holder class, is intended for researchers and graduate students
of applied mathematics and analysis, especially those with an
interest in integrable systems, nonlinear waves, or complex
analysis.
Spyridon Kamvissis is a researcher at the Max Planck Institute of
Mathematics in Bonn, Germany, and a Professor of Mathematics at
the National Technical University in Athens, Greece. Kenneth D. T-R
McLaughlin is Associate Professor of Mathematics at the
University of North Carolina, Chapel Hill. Peter D. Miller is
Assistant Professor of Mathematics at the University of Michigan,
Ann Arbor.
Series: Annals of Mathematics Studies
Cloth | May 2003 | ISBN: 0-691-11385-8
392 pp. | 6 x 9 | 64 line illus.
With this second volume, we enter the intriguing world of complex
analysis. From the first theorems on, the elegance and sweep of
the results is evident. The starting point is the simple idea of
extending a function initially given for real values of the
argument to one that is defined when the argument is complex.
From there, one proceeds to the main properties of holomorphic
functions, whose proofs are generally short and quite
illuminating: the Cauchy theorems, residues, analytic
continuation, the argument principle.
With this background, the reader is ready to learn a wealth of
additional material connecting the subject with other areas of
mathematics: the Fourier transform treated by contour
integration, the zeta function and the prime number theorem, and
an introduction to elliptic functions culminating in their
application to combinatorics and number theory.
Thoroughly developing a subject with many ramifications, while
striking a careful balance between conceptual insights and the
technical underpinnings of rigorous analysis, Complex Analysis
will be welcomed by students of mathematics, physics, engineering
and other sciences.
The Princeton Lectures in Analysis represents a sustained effort
to introduce the core areas of mathematical analysis while also
illustrating the organic unity between them. Numerous examples
and applications throughout its four planned volumes, of which
Complex Analysis is the second, highlight the far-reaching
consequences of certain ideas in analysis to other fields of
mathematics and a variety of sciences. Stein and Shakarchi move
from an introduction addressing Fourier series and integrals to
in-depth considerations of complex analysis; measure and
integration theory, and Hilbert spaces; and, finally, further
topics such as functional analysis, distributions and elements of
probability theory.
Paper | June 2003 |ISBN: 0-691-11522-2
536 pp. | 6 x 9
In the past three decades, local search has grown from a simple
heuristic idea into a mature field of research in combinatorial
optimization that is attracting ever-increasing attention. Local
search is still the method of choice for NP-hard problems as it
provides a robust approach for obtaining high-quality solutions
to problems of a realistic size in reasonable time. Local Search
in Combinatorial Optimization covers local search and its
variants from both a theoretical and practical point of view,
each topic discussed by a leading authority. This book is an
important reference and invaluable source of inspiration for
students and researchers in discrete mathematics, computer
science, operations research, industrial engineering, and
management science.
In addition to the editors, the contributors are Mihalis
Yannakakis, Craig A. Tovey, Jan H. M. Korst, Peter J. M. van
Laarhoven, Alain Hertz, Eric Taillard, Dominique de Werra, Heinz
Muhlenbein, Carsten Peterson, Bo Soderberg, David S. Johnson,
Lyle A. McGeoch, Michel Gendreau, Gilbert Laporte, Jean-Yves
Potvin, Gerard A. P. Kindervater, Martin W. P. Savelsbergh,
Edward J. Anderson, Celia A. Glass, Chris N. Potts, C. L. Liu,
Peichen Pan, Iiro Honkala, and Patric R. J. Ostergard.
Emile Aarts is Vice-President and Scientific Program Director of
the Philips Research Laboratories, Eindhoven, and a Professor of
Computer Science at Eindhoven University of Technology. Jan Karel
Lenstra is the John P. Hunter Chair and Professor of Industrial
and Systems Engineering at the Georgia Institute of Technology.
Reviews:
"A truly remarkable and unique collection of work. . . .
Invaluable."--Informs
"The world of local search has changed dramatically in the
last decade and Aarts and Lenstra's book is a tribute to this
development. . . . A very useful source."--Optima
Paper | June 2003 | ISBN: 0-691-11543-5
Cloth | June 2003 | ISBN: 0-691-11542-7
280 pp. | 6 x 9
Kiyosi Ito's greatest contribution to probability theory may be
his introduction of stochastic differential equations to explain
the Kolmogorov-Feller theory of Markov processes. Starting with
the geometric ideas that guided him, this book gives an account
of Ito's program.
The modern theory of Markov processes was initiated by A. N.
Kolmogorov. However, Kolmogorov's approach was too analytic to
reveal the probabilistic foundations on which it rests. In
particular, it hides the central role played by the simplest
Markov processes: those with independent, identically distributed
increments. To remedy this defect, Ito interpreted Kolmogorov's
famous forward equation as an equation that describes the
integral curve of a vector field on the space of probability
measures. Thus, in order to show how Ito's thinking leads to his
theory of stochastic integral equations, Stroock begins with an
account of integral curves on the space of probability measures
and then arrives at stochastic integral equations when he moves
to a pathspace setting. In the first half of the book, everything
is done in the context of general independent increment processes
and without explicit use of Ito's stochastic integral calculus.
In the second half, the author provides a systematic development
of Ito's theory of stochastic integration: first for Brownian
motion and then for continuous martingales. The final chapter
presents Stratonovich's variation on Ito's theme and ends with an
application to the characterization of the paths on which a
diffusion is supported.
The book should be accessible to readers who have mastered the
essentials of modern probability theory and should provide such
readers with a reasonably thorough introduction to continuous-time,
stochastic processes.
Daniel W. Stroock is a Simons Professor of Mathematics at the
Massachusetts Institute of Technology and the author of several
books, including A Concise Introduction to the Theory of
Integration and Probability Theory, an Analytic View.
Series: Annals of Mathematics Studies