To describe the true behavior of most real-world systems with sufficient accuracy, engineers have to overcome difficulties arising from their lack of knowledge about certain parts of a process or from the impossibility of characterizing it with absolute certainty. Depending on the application at hand, uncertainties in modeling and measurements can be represented in different ways. For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments.

The goal of this Special Volume on "Modeling, Design, and Simulation of Systems with Uncertainties" is to cover modern methods for dealing with the challenges presented by imprecise or unavailable information. All contributions tackle the topic from the point of view of control, state and parameter estimation, optimization and simulation.

Thematically, this volume can be divided into two parts. In the first we present works highlighting the theoretic background and current research on algorithmic approaches in the field of uncertainty handling, together with their reliable software implementation. The second part is concerned with real-life application scenarios from various areas including but not limited to mechatronics, robotics, and biomedical engineering.

On August 1997 a conference titled "From Local to Global Optimiza- tion" was held at Storgarden in Rimfor.sa near the Linkoping Institute of Technology, Sweden. The conference gave us the opportunity to cel- ebrate Hoang Thy's achievements in Optimization during his 70 years of life. This book consists of a collection of research papers based on results presented during the conference and are dedicated to Professor Hoang Thy on the occasion of his 70th birthday. The papers cover a wide range of recent results in Mathematical Pro- gramming. The work of Hoang Thy, in particular in Global Optimiza- tion, has provided directions for new algorithmic developments in the field. We are indebted to the Kluwer Academic Publishers for inviting us to publish this volume, and the Center for Industrial Information Transfer (CENIIT) for financial support. We wish to thank the referees for their help and the authors for their papers. We also wish to join all contributors of this book in expressing birthday wishes and gratitude to Hoang Thy for his inspiration, support, and friendship to all of us. Athanasios Migdalas, Panos M. Pardalos, and Peter Varbrand November 1998 xv Hoang Tuy: An Appreciation Its a pleasure for me as colleague and friend to take this opportunity to celebrate Hoang 'I\lY'S numerous contributions to the field of mathemat- ical programming.

The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.

This volume consists of eight papers on new advances in interpolation theory for matrix functions and completion theory for matrices and operators. Much emphasis is placed on different interpolation and completion problems when the interpolant is estimated in two different norms. The book also focusses on the study of the spectra of different completions of 2 x 2 block matrices when originally all entries are specified except the lower left corner. A third theme concerns two-sided tangential interpolation problems for real rational matrix functions, and also for the time varying case. A tangential moment problem is also analyzed. All papers deal with related problems of modern matrix analysis, operator theory, complex analysis and system theory and will appeal to a wide group of mathematicians and engineers. The material can be used for advance courses and seminars. Contents: Editorial Introduction ? D. Alpay/P. Loubaton: The tangential trigonometric moment problem on an interval and related topics ? M. Bakonyi/V.G. Kaftal/G. Weiss/H.J. Woerdeman: Maximum entropy and joint norm bounds for operator extensions ? J.A. Ball/I. Gohberg/M.A. Kaashoek: Bitangential interpolation for input-output operators of time varying systems: the discrete time case ? J.A. Ball/I. Gohberg/L. Rodman: Two-sided tangential interpolation of real rational matrix functions ? H. Du/C. Gu: On the spectra of operator completion problems ? C. Foias/A.E. Frazho/W.S. Li: The exact H2 estimate for the central H interpolant ? A.E. Frazho/s.M. Kherat: On mixed H2 - H tangential interpolation ? I. Gohberg/C.Gu: On a completion problem for matrices

This volume of papers presented at the conference in honor of Calixto P. Calderon by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

The past decade has witnessed the rapid development of a new mathematical tool, called wavlet analysis, for analyzing complex signals. It has begin to play a serious role in applications ranging from communications to geophysics, and from simulations to image processing. Like Fourier analysis (of which it is a generalization), or musical notation, wavelet analysis provides a method for representing a set of complex phenomena in a simpler, more compact, and thus more efficient manner. This text introduces the ideas and methods of wavelet analysis, relates them to previously known methods in mathematics and engineering, and shows how to apply wavelet analysis to digital signal processing. It begins by describing the multiscale (sometimes called "fractal") nature of information in many aspects of thereal world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functins on a space. The discussion then turns from the continuous to the discrete and shows how a properly selected set of wavelets can be used to represent -- and even differentiate -- a wide range of signls efficiently and effectively. The last part of the book presents a wide variety of applications of wavelets to probllems in data compression and telecommunications.

Agent-Based Computer Simulation of Dichotomous Economic Growth reports a project in agent-based computer stimulation of processes of economic growth in a population of boundedly rational learning agents. The study is an exercise in comparative simulation. That is, the same family of growth models will be simulated under different assumptions about the nature of the learning process and details of the production and growth processes. The purpose of this procedure is to establish a relationship between the assumptions and the simulation results. The study brings together a number of theoretical and technical developments, only some of which may be familiar to any particular reader. In this first chapter, some issues in economic growth are reviewed and the objectives of the study are outlined. In the second chapter, the simulation techniques are introduced and illustrated with baseline simulations of boundedly rational learning processes that do not involve the complications of dealing with long-run economic growth. The third chapter sketches the consensus modern theory of economic growth which is the starting point for further study. In the fourth chapter, a family of steady growth models are simulated, bringing the simulation, growth and learning aspects of the study together. In subsequent chapters, variants on the growth model are explored in a similar way. The ninth chapter introduces trade, with a spacial trading model that is combined with the growth model in the tenth chapter. The book returns again and again to the key question: to what extent can the simulations explain' the puzzles of economic growth, and particularly the key puzzle of dichotomization, by constructing growth and learning processes that produce the puzzling results? And just what assumptions of the simulations are most predictable associated with the puzzling results?

This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics.This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.

Subrahmanyan Chandrasekhar - known simply as Chandra throughout the scientific world - has become a legendary figure for his prolific contributions to physics, astrophysics, and applied mathematics. Before his death in 1995, Chandra had forbidden a memorial of the conventional sort, celebrating his life. This book, which contains some thirty articles by his former students, his associates, and his colleagues, is in a sense a memorial volume. It says little about Chandra's great scientific achievements, but shows his human side and the various facets of his brilliant personality, his incredible memory, his wit, and the breadth of his knowledge of art, music, literature, and the humanities in general. The contributors to this highly interesting book are among the few who broke the seemingly forbidden barrier surrounding the very private Chandra and came to know him well in one context or another. They include Lalitha Chandrasekhar, Roger Penrose, Richard H Dalitz, J W Cronin, Robert G Sachs, Abhay Ashtekar, and Robert Wald.

The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-oriented design.

Statistical methods have become an increasingly important and integral part of research in the health sciences. Many sophisticated methodologies have been developed for specific applications and problems. This self-contained volume, an outgrowth of an International Conference on Statistics in Health Sciences, covers a wide range of topics pertaining to new statistical methods in the health sciences. The chapters, written by leading experts in their respective fields, are thematically divided into the following areas: prognostic studies and general epidemiology, pharmacovigilance, quality of life, survival analysis, clustering, safety and efficacy assessment, clinical design, models for the environment, genomic analysis, and animal health. This comprehensive volume will serve the health science community as well as practitioners, researchers, and graduate students in applied probability, statistics, and biostatistics.

The book deals with the numerical simulation of noise in semiconductor devices operating in linear (small-signal) and nonlinear (large-signal) conditions. The main topics of the book are: An overview of the physical basis of noise in semiconductor devices, a detailed treatment of numerical noise simulation in small-signal conditions, and a presentation of innovative developments in the noise simulation of semiconductor devices operating in large-signal quasi-periodic conditions. The main benefit that the reader will derive from the book is the ability to understand, and, if needed, replicate the development of numerical, physics-based noise simulation of semiconductor devices in small-signal and large-signal conditions.

This and the previous volume of the OT series contain the proceedings of the Workshop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems."

The "Turbulence and Interactions 2006" (TI2006) conference was held on the island of Porquerolles, France, May 29-June 2, 2006. The scientific sponsors of the conference were * Association Francaise de Mecanique, * CD-adapco, * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * FLUENT, * The French Ministery of Foreign Affairs, * Laboratoire de Modelisation en Mecanique, Paris 6, * ONERA. The conference was a unique event. Never before have so many organisations concerned with turbulence works come together in one conference. As the title "Turbulence and Interactions" anticipated, the workshop was not run with parallel sessions but instead of one united gathering where people had strong interactions and discussions. Many of the 85 or so attendants were veterans of previous ERCOFTAC conferences. Some young researchers attended their very first int- national meeting. The organisers were fortunate in obtaining the presence of the following - vited speakers: N. Adams (TUM, Germany), C. Cambon (ECL, France), J.-P. Dussauge (Polytech Marseille, France), D.A. Gosman (Imperial College, UK), Y. Kaneda (Nagoya University, Japan), O. Simonin (IMFT, France), G. Tryggvason (WPI, USA), D. Veynante (ECP, France), F. Waleffe (University of Wisconsin, USA), Y.K. Zhou (University of California, USA). The topics covered by the 59 papers ranged from experimental results through theory to computations. The papers of the conference went through the usual - viewing process for two special issues of international journals : Computers and Fluids, and Flow, Turbulence and Combustion.

In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.

This book is aimed to be both a textbook for graduate students and a starting point for applicationsscientists. It is designedto show how to implementspectral methods to approximate the solutions of partial differential equations. It presents a syst- atic development of the fundamental algorithms needed to write spectral methods codes to solve basic problems of mathematical physics, including steady potentials, transport, and wave propagation. As such, it is meant to supplement, not replace, more general monographs on spectral methods like the recently updated "Spectral Methods: Fundamentals in Single Domains" and "Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics" by Canuto, Hussaini, Quarteroni and Zang, which provide detailed surveys of the variety of methods, their performance and theory. I was motivated by comments that I have heard over the years that spectral me- ods are "too hard to implement." I hope to dispel this view-or at least to remove the "too." Although it is true that a spectral code is harder to hack together than a s- ple ?nite difference code (at least a low order ?nite difference method on a square domain), I show that only a few fundamental algorithms for interpolation, differen- ation, FFT and quadrature-the subjects of basic numerical methods courses-form the building blocks of any spectral code, even for problems in complex geometries. Ipresentthealgorithmsnotonlytosolveproblemsin1D, but2Daswell, toshowthe ?exibility of spectral methods and to make as straightforward as possible the tr- sition from simple, exploratory programs that illustrate the behavior of the methods to application programs.

Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice * J. Frohlich: Mathematical Aspects of the Quantum Hall Effect * M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings * U. Hamenstadt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations * M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology * S.B. Kuksin: KAM-Theory for Partial Differential Equations * M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results * J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations * I. Madsen: The Cyclotomic Trace in Algebraic K-Theory * A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology * J. Nekovar: Values of L-Functions and p-Adic Cohomology * Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups * M.A. Nowak: The Evolutionary Dynamics of HIV Infections * R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons * A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods * A. Schrijver: Paths in Graphs and Curves on Surfaces * B. Silverman: Function Estimation and Functional Data Analysis * V. Strassen: Algebra and Complexity * P. Tukia: Generalizations of Fuchsian and Kleinian Groups * C. Viterbo: Properties of Embedded Lagrange Manifolds * D. Voiculescu: Alternative Entropies in Operator Algebras * M. Wodzicki : Algebraic K-Theory and Functional Analysis * D. Zagier: Values of Zeta Functions and Their Applications

This book presents an operator theoretic approach to robust control analysis for linear time-varying systems. It emphasizes the conceptual similarity with the H control theory for time-invariant systems and at the same time clarifies the major difficulties confronted in the time varying case. The necessary operator theory is developed from first principles and the book is as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input- output operators and the relationship between stabilization and the existance of co-prime factorizations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems. Robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, and the relationship between these types of uncertainties is clarified. The book closes with the solution of the orthogonal embedding problem for time varying contractive systems. This book will be useful to both mathematicians interested in the potential applications of operator theory in control and control engineers who wish to deal with some of the more mathematically sophisticated extension of their work.

This and the next volume of the OT series contain the proceedings of the Work shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

This book offers an essential compendium of astronomical high-resolution techniques. Recent years have seen considerable developments in such techniques, which are critical to advances in many areas of astronomy. As reflected in the book, these techniques can be divided into direct methods, interferometry, and reconstruction methods, and can be applied to a huge variety of astrophysical systems, ranging from planets, single stars and binaries to active galactic nuclei, providing angular resolution in the micro- to tens of milliarcsecond scales. Written by experts in their fields, the chapters cover adaptive optics, aperture masking imaging, spectra disentangling, interferometry, lucky imaging, Roche tomography, imaging with interferometry, interferometry of AGN, AGN reverberation mapping, Doppler- and magnetic imaging of stellar surfaces, Doppler tomography, eclipse mapping, Stokes imaging, and stellar tomography. This book is intended to enable a next generation of astronomers to apply high-resolution techniques. It informs readers on how to achieve the best angular resolution in the visible and near-infrared regimes from diffraction-limited to micro-arcsecond scales.

The theory of practical rationality does not belong to one academic discipline alone. There are quite divergent philosophical, economical, sociological, psychological and politological contributions. Sometimes the disciplinary boundaries impede theoretical progress. On the other hand it is an indication for the high complexity of the subject that so many divergent paradigms compete with one another, or - what is worse - live separately in a kind of splendid isolation. Decision theory in the broader sense, embracing the theory of games and collective choice theory, can help to understand practical reason in philosophical analysis. But there are interesting aspects which cannot be dealt with adequately within a decision-theoretic conceptual framework. To have both of these convictions justifies to neglect dis ciplinary boundaries and poses a problem for the orthodoxies of either sides. All the essays of this volume focus on the relation between economic rationality and practical reason and discuss different aspects of the same problem, i. e. a basic deficiency in the standard economic theory of practical rationality. But philosophical analysis would not be of much help if it just rejected the economic paradigm. It must rather help to integrate economic aspects into a broader view on practical reason."

The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. The eight chapters of the book cover themes and variations on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis. Although the book is primarily intended to serve as a research reference, it will also be useful for graduate and advanced undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors' exposition makes most of the material accessible to readers with a sound foundation in linear algebra.

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23-24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.

From the reviews:

"Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte f r Mathematik