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.

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.

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.

In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems. It begins with a thorough introduction, where the general research domain, the problems, and ways of their solutions are discussed. The book then progresses systematically by first covering the theoretical aspects before tackling the applications. In the application section, a software library is described, which contains discrete EFDS identification methods elaborated during fundamental research of the book.

"Extremal Fuzzy Dynamic Systems" will be of interest to theoreticians interested in modeling fuzzy processes, to researchers who use fuzzy statistics, as well as practitioners from different disciplines whose research interests include abnormal, extreme and monotone processes in nature and society. Graduate students could also find this book useful.

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.

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.

The combined observational power of the multiple earth observing satellites is currently not being harnessed holistically to produce more durable societal benefits. We are not able to take complete advantage of the prolific amount of scientific output and remote sensing data that are emerging rapidly from satellite missions and convert them quickly into decision-making products for users. The current application framework we have appears to be an analog one lacking the absorption bandwidth required to handle scientific research and the voluminous (petabyte-scale) satellite data. This book will tackle this question: "How do we change this course and take full advantage of satellite observational capability for a more sustainable, happier and safer future in the coming decades?"

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses." These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.

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 book discusses the recent techniques in NGS data analysis which is the most needed material by biologists (students and researchers) in the wake of numerous genomic projects and the trend toward genomic research. - The book includes both theory and practice for the NGS data analysis. So, readers will understand the concept and learn how to do the analysis using the most recent programs. - The steps of application workflows are written in a manner that can be followed for related projects. - Each chapter includes worked examples with real data available on the NCBI databases. Programming codes and outputs are accompanied with explanation. - The book content is suitable as teaching material for biology and bioinformatics students. Meets the requirements of a complete semester course on Sequencing Data Analysis Covers the latest applications for Next Generation Sequencing Covers data reprocessing, genome assembly, variant discovery, gene profiling, epigenetics, and metagenomics

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well. Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.

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."

In view of the current and forthcoming observational data on pulsar wind nebulae, this book offers an assessment of the theoretical state of the art of modelling them. The expert authors also review the observational status of the field and provide an outlook for future developments. During the last few years, significant progress on the study of pulsar wind nebulae (PWNe) has been attained both from a theoretical and an observational perspective, perhaps focusing on the closest, more energetic, and best studied nebula: the Crab, which appears in the cover. Now, the number of TeV detected PWNe is similar to the number of characterized nebulae observed at other frequencies over decades of observations. And in just a few years, the Cherenkov Telescope Array will increase this number to several hundreds, actually providing an essentially complete account of TeV emitting PWNe in the Galaxy. At the other end of the multi-frequency spectrum, the SKA and its pathfinder instruments, will reveal thousands of new pulsars, and map in exquisite detail the radiation surrounding them for several hundreds of nebulae. By carefully reviewing the state of the art in pulsar nebula research this book prepares scientists and PhD students for future work and progress in the field.

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.

Covering some of the key areas of optimal control theory (OCT), a rapidly expanding field, the authors use new methods to set out a version of OCT's more refined'maximum principle.' The results obtainedhave applicationsin production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games.

This book" "explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control."

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.

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 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 supplement to the comprehensive series "Encyclopedia of Fluid Mechanics" steps back from the topical approach to fluid mechanics, and embraces the overall subject from an entirely mathematical viewpoint. Within the pure science of mathematics, the motion of particles and fluids is described and studies without the uncertainty that can accompany experimental investigations. This volume addresses the mathematical details of model formation and development, which constitutes the basis for numerical experimentation. It is intended to stimulate and report current and emerging concepts in pure research on flow dynamics.

This book explains music's comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers. The book unfolds in a basic discourse in everyday language that is accessible to everybody who wants to understand what this topic is about. Musical ontology is delayed in its fundamental dimensions: its realities, its meaningful communication, and its embodied utterance from musical creators to an interested audience. The authors' approach is applicable to every musical genre and is scientific, the book is suitable for non-musicians and non-scientists alike.

This book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems. Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Besides, the electromagnetic parameters of complex medium such as the permittivity and conductivity are retrieved by a cascaded framework in Chapter 4. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 5. Finally, in Chapter 6, a series of the latest advanced frameworks and the corresponding physics applications are introduced. As deep learning techniques are experiencing vigorous development in computational physics, more people desire related reading materials. This book is intended for graduate students, professional practitioners, and researchers who are interested in DL for computational physics.

This textbook is a comprehensive introduction to computational mathematics and scientific computing suitable for undergraduate and postgraduate courses. It presents both practical and theoretical aspects of the subject, as well as advantages and pitfalls of classical numerical methods alongside with computer code and experiments in Python. Each chapter closes with modern applications in physics, engineering, and computer science. No previous experience in Python is required Simplified computer code for fast-paced learning and transferable skills development Includes practical problems ideal for project assignments and distance learning Presents both intuitive and rigorous faces of modern scientific computing Provides an introduction to neural networks and machine learning

This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton - Jacobi Equations; and (6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics. Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.