Claude Brezinski

Computational Aspects of Linear Control

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.

Sergey Fomin

Symmetric Functions 2001: Surveys of Developments and Perspectives

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.

Pavel S. Knopov, Evgeniya J. Kasitskaya

Empirical Estimates in Stochastic Optimization and Identification

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.

Anne Bourlioux, Martin J. Gander, Gert Sabidussi

Modern Methods in Scientific Computing and Applications

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

Andrea Cappelli, Giuseppe Mussardo

Statistical Field Theories

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.