July 2002, ISBN 1-4020-0711-6, Hardbound
Book Series: NUMERICAL METHODS AND ALGORITHMS
: Volume 1
The main objective of this volume is to create
a bridge between
control theory and its numerical analysis
aspects. It is unique
because it presents both subjects in a single
volume. The book
combines an exposition of linear control
theory and the
corresponding modern relevant computational
techniques such as
orthogonal polynomials, Pade approximation,
numerical linear
algebra, and some topics on nonlinear differential
equations. It
can be considered as an introduction to control
theory for
numerical analysts looking for a wide area
of applications and as
an introduction to recent numerical methods
for control
specialists.
Audience: Aimed at advanced students at a
doctoral or post-doctoral
level, engineers, and researchers in control
theory and numerical
analysis.
Contents
Introduction. 1. Control of linear systems.
2. Formal orthogonal
polynomials. 3. Pade approximations. 4. Transform
inversion. 5.
Linear algebra issues. 6. Lanczos tridiagonalization
process. 7.
Systems of linear algebraic equations. 8.
Regularization of ill-conditioned
systems. 9. Sylvester and riccati equations.
10. Topics on
nonlinear differential equations. 11. Appendix:
the mathematics
of model reduction. Index.
July 2002, ISBN 1-4020-0774-4, Paperback
July 2002, ISBN 1-4020-0773-6, Hardbound
Book Series: NATO SCIENCE SERIES: II: Mathematics,
Physics and
Chemistry : Volume 74
This book surveys recent developments and
outlines research
prospects in various fields, the fundamental
questions of which
can be stated in the language of symmetric
functions.
Interdisciplinary interconnections are emphasized.
Contents and Contributors
Preface. List of contributors. List of invited
NATO ASI
participants. Notes on Macdonald polynomials
and the geometry of
Hilbert schemes; H. Haiman. The Laplacian
method; P. Hanlon.
Kerov's central limit theorem for the Plancherel
measure on Young
diagrams; V. Ivanov, G. Olshanski. Symmetric
functions and the
Fock space; B. Leclerc. An introduction to
birational Weyl group
actions; M. Noumi. Symmetric functions and
random partitions;
Okounkov. From Littlewood-Richardson coefficients
to cluster
algebras in three lectures; A. Zelevinsky.
July 2002, ISBN 1-4020-0707-8, Hardbound
Book Series: APPLIED OPTIMIZATION : Volume
71
This book contains problems of stochastic
optimization and
identification. Results concerning uniform
law of large numbers,
convergence of approximate estimates of extremal
points, as well
as empirical estimates of functionals with
probability 1 and in
probability are presented. It is shown that
the investigation of
asymptotic properties of approximate estimates
and estimates of
unknown parameters in various regression
models can be carried
out by using general methods, which are presented
by the authors.
The connection between stochastic programming
methods and
estimation theory is described. It was assumed
to use the methods
of asymptotic stochastic analysis for investigation
of extremal
points, and on the other hand to use stochastic
programming
methods to find optimal estimates.
Audience: Specialists in stochastic optimization
and estimations,
postgraduate students, and graduate students
studying such topics.
Contents:
Preface. 1. Introduction. 2. Parametric Empirical
Methods. 3.
Parametric Regression Models. 4. Periodogram
Estimates for Random
Processes and Fields. 5. Nonparametric Identification
Problems.
References.
August 2002, ISBN 1-4020-0782-5, Paperback
August 2002, ISBN 1-4020-0781-7, Hardbound
Book Series: NATO SCIENCE SERIES: II: Mathematics,
Physics and
Chemistry : Volume 75
The influence of scientific computing has
become very wide over
the last few decades: almost every area science
and engineering
is greatly influenced by simulations - image
processing, thin
films, mathematical finance, electrical engineering,
moving
interfaces and combustion, to name but a
few.
One half of this book focuses on the techniques
of scientific
computing: domain decomposition, the absorption
of boundary
conditions and one-way operators, convergence
analysis of multi-grid
methods and other multi-grid techniques,
dynamical systems, and
matrix analysis.
The remainder of the book is concerned with
combining techniques
with concrete applications: stochastic differential
equations,
image processing, thin films, and asymptotic
analysis for
combustion problems.
Contents :
Preface. Key to group picture. Participants.
Contributors.
Computation of large-scale quadratic forms
and transfer functions
using the theory of moments, quadrature and
Pade approximation; Z.
Bai, G.H. Golub. Thin film dynamics: theory
and applications; A.L.
Bertozzi, M. Bowen. Numerical turbulent combustion:
an asymptotic
view via an idealized test-case; A. Bourlioux.
Multigrid methods:
from geometrical to algebraic versions; G.
Haase, U. Langer. One-way
operators, absorbing boundary conditions
and domain decomposition
for wave propagation; L. Halpern, A. Rahmouni.
Deterministic and
random dynamical systems: theory and numerics;
A.R. Humphries, A.M.
Stuart. Optimal investment problems and volatility
homogenization
approximations; M. Jonsson, R. Sircar. Image
processing with
partial differential equations; K. Mikula.
Interface connections
in domain decomposition methods; F. Nataf.
A review of level set
and fast marching methods for image processing;
J.A. Sethian.
Recent developments in the theory of front
propagation and its
applications; P.E. Souganidis. Computing
finite-time
singularities in interfacial flows; T.P.
Witelski. Index
August 2002, ISBN 1-4020-0761-2, Paperback
August 2002, ISBN 1-4020-0760-4, Hardbound
Book Series: NATO SCIENCE SERIES: II: Mathematics, Physics and
Chemistry : Volume 73
Recent developments in theoretical physics include new instances
of the unification of quite different phenomena. The theoretical
community is challenged by the growing interactions between high-energy
physics, statistical physics, and condensed matter physics. The
common language, though, is exact solutions of two-dimensional
and conformable field theories. This volume is a faithful
representation of this interdisciplinary domain. Conformable and
integrable field theories have been active research topics for
several decades. The main recent developments concern the
boundary effects and applications to disordered systems. The
number of applications of the exact methods to condensed-matter
problems has been growing over the years. Nowadays it is widely
recognized that strongly interacting systems in low dimensions
can be successfully described by integrable and conformable
theories. This volume is an indispensable aid to those seeking to
find their way in this domain.
Contents and Contributors
Preface. Part I: Integrable Models and Conformal Field Theories.
Field Theory of Scaling Lattice Models: The Potts
Antiferromagnet; G. Delfino. The ODE/IM Correspondence and PT-symmetric
Quantum Mechanics; P. Dorey, et al. Coupled Models WD3(ƒÏ): Their
Fixed Points; V.S. Dotsenko, et al. The Combinatorics of
Alternating Tangles: From Theory to Computerized Enumeration; J.L.
Jacobsen, P. Zinn-Justin. On the Sine-Gordon One-Point Functions;
R.H. Poghossian. On Vertex Operators and the Normalization of
Form Factors; Y. Pugai. Integrable Chain Models with Staggered R-matrices;
A.G. Sedrakyan. On the Quantization of Affine Jacobi Varieties of
Spectral Curves; F.A. Smirnov. Rational Conformal Field Theory in
Four Dimensions; N.M. Nikolov, et al. Perturbed Conformal Field
Theory on a Sphere; A.B. Zamolodchikov. Part II: Integrable and
Conformal Field Theories With Boundaries. Two-boundary
Integrability and the Josephson Current in a Luttinger Liquid; J.-S.
Caux, et al. Coupling the Sine-Gordon Field Theory to a
Mechanical System at the Boundary P. Baseilhac, et al. Reflection
Amplitudes and Expectation Values of Fields in Integrable
Boundary Theories; V.A. Fateev. Integrable Boundary Conditions
for the O(N) Nonlinear Sigma Model; M. Moriconi. Verlinde Nim-reps
for Charge Conjugate ƒÐƒÇ(N) WZW Theory; V.B. Petkova, J.-B.
Zuber. Open-String Models with Broken Supersymmetry; A. Sagnotti.
Conformal Boundary Conditions and 3D Topological Field Theory; J.
Fuchs, et al. The Spectrum of Boundary Sine-Gordon Theory; Z.
Bajnok, et al. Part III: Disordered Systems. A Classification on
Non-Hermitian Random Matrices; D. Bernard, A. LeClair. The Stress
Tensor in Quenched Random Systems; J. Cardy. Taking N O with S
Matrices; P. Fendley. Scattering in Quantum Field Theories with
Supergroup Invariance; H. Saleur, et al. Nishimori Point in
Random-Bond Ising and Potts Models in 2D; A. Honecker, et al. 2D
Random Dirac Fermions: Large N Approach; D. Serban. Part IV:
Quantum Hall Effect and Condensed Matter Applications. Impurities
in One Dimension; S. Eggert. Axions, Quantum Mechanical Pumping,
and Primeval Magnetic Fields; J. Frohlich, B. Pedrini. Paired and
Clustered Quantum Hall States; K. Schoutens, et al. Integrability
and Conformal Symmetry in the BCS Model; G. Sierra. Wavefunction
Statistics at the Quantum Hall Critical Point; A.M. Tsvelik.
Aharonov-Bohm Effect in the Quantum Hall Regime and Laplacian
Growth Problems; P.B. Wiegmann. Index.