This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: * optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. * emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. * gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. * auxiliary function, generalized penalty function, modified Lagrange func tion. * convexity, quasiconvexity, abstract convexity.

Devoted to information security, this volume begins with a short course on cryptography, mainly based on lectures given by Rudolf Ahlswede at the University of Bielefeld in the mid 1990s. It was the second of his cycle of lectures on information theory which opened with an introductory course on basic coding theorems, as covered in Volume 1 of this series. In this third volume, Shannon's historical work on secrecy systems is detailed, followed by an introduction to an information-theoretic model of wiretap channels, and such important concepts as homophonic coding and authentication. Once the theoretical arguments have been presented, comprehensive technical details of AES are given. Furthermore, a short introduction to the history of public-key cryptology, RSA and El Gamal cryptosystems is provided, followed by a look at the basic theory of elliptic curves, and algorithms for efficient addition in elliptic curves. Lastly, the important topic of "oblivious transfer" is discussed, which is strongly connected to the privacy problem in communication. Today, the importance of this problem is rapidly increasing, and further research and practical realizations are greatly anticipated. This is the third of several volumes serving as the collected documentation of Rudolf Ahlswede's lectures on information theory. Each volume includes comments from an invited well-known expert. In the supplement to the present volume, Rudiger Reischuk contributes his insights. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.

Although the monograph Progress in Optimization I: Contributions from Aus tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization. The intention is to publish a similar book annually, following each Optimization Day. The idea of having an annual Optimization Day was conceived by Barney Glover; the first of these Optimization Days was held in 1994 at the University of Ballarat. Barney hoped that such a yearly event would bring together the many, but widely dispersed, researchers in Australia who were publishing in optimization and related areas such as control. The first Optimization Day event was followed by similar conferences at The University of New South Wales (1995), The University of Melbourne (1996), the Royal Melbourne Institute of Technology (1997), and The University of Western Australia (1998). The 1999 conference will return to Ballarat University, being organized by Barney's long-time collaborator Alex Rubinov. In recent years the Optimization Day has been held in conjunction with other locally-held national or international conferences. This has widened the scope of the monograph with contributions not only coming from researchers in Australia and neighboring regions but also from their collaborators in Europe and North America."

Over the last two decades there has been a great deal of research into nonlinear dynamic models in economics, finance and the social sciences. This book contains twenty papers that range over very recent applications in these areas. Topics covered include structural change and economic growth, disequilibrium dynamics and economic policy as well as models with boundedly rational agents. The book illustrates some of the most recent research tools in this area and will be of interest to economists working in economic dynamics and to mathematicians interested in seeing ideas from nonlinear dynamics and complexity theory applied to the economic sciences.

Materials sciences relate the macroscopic properties of materials to their microscopic structure and postulate the need for holistic multiscale research. The investigation of shape memory alloys is a prime example in this regard. This particular class of materials exhibits strong coupling of temperature, strain and stress, determined by solid state phase transformations of their metallic lattices. The present book presents a collection of simulation studies of this behaviour. Employing conceptually simple but comprehensive models, the fundamental material properties of shape memory alloys are qualitatively explained from first principles. Using contemporary methods of molecular dynamics simulation experiments, it is shown how microscale dynamics may produce characteristic macroscopic material properties. The work is rooted in the materials sciences of shape memory alloys and covers thermodynamical, micro-mechanical and crystallographical aspects. It addresses scientists in these research fields and their students.

We are rarely asked to. make decisions based on only one criterion; most often, decisions are based on several usually confticting, criteria. In nature, if the design of a system evolves to some final, optimal state, then it must include a balance for the interaction of the system with its surroundings certainly a design based on a variety of criteria. Furthermore, the diversity of nature's designs suggests an infinity of such optimal states. In another sense, decisions simultaneously optimize a finite number of criteria, while there is usually an infinity of optimal solutions. Multicriteria optimization provides the mathematical framework to accommodate these demands. Multicriteria optimization has its roots in mathematical economics, in particular, in consumer economics as considered by Edgeworth and Pareto. The critical question in an exchange economy concerns the "equilibrium point" at which each of N consumers has achieved the best possible deal for hirnself or herself. Ultimately, this is a collective decision in which any further gain by one consumer can occur only at the expense of at least one other consumer. Such an equilibrium concept was first introduced by Edgeworth in 1881 in his book on mathematical psychics. Today, such an optimum is variously called "Pareto optimum" (after the Italian-French welfare economist who continued and expanded Edgeworth's work), "effi. cient," "nondominated," and so on."

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction.

Volume III concentrates on the "classical aspects "of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles." "This must be supplemented by the crucial, but elusive quantization procedure.

The book is arranged in four sections, devoted to realizing the universal principle "force equals curvature: "

Part I: The Euclidean Manifold as a Paradigm

Part II: Ariadne's Thread in Gauge Theory

Part III: Einstein's Theory of Special Relativity

Part IV: Ariadne's Thread in Cohomology

For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.

"Quantum Field Theory" builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

"

Unifying topics that are scattered throughout the literature, this book offers a definitive review of mathematical aspects of quantization and quantum field theory. It presents both basic and advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. It begins with a discussion of the mathematical structures underlying free bosonic or fermionic fields: tensors, algebras, Fock spaces, and CCR and CAR representations. Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in mathematics and physics. This title, first published in 2013, has been reissued as an Open Access publication on Cambridge Core.

This second edition of "A Beginner's Guide to Finite Mathematics" takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. This new edition includes chapters on game theory and financial mathematics. Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors.

Enzyme kinetics, binding kinetics and pharmacological dose-response curves are currently analyzed by a few standard methods. Some of these, like Michaelis-Menten enzyme kinetics, use plausible approximations, others, like Hill equations for dose-response curves, are outdated. Calculating realistic reaction schemes requires numerical mathematical routines which usually are not covered in the curricula of life science. This textbook will give a step-by-step introduction to numerical solutions of non-linear and differential equations. It will be accompanied with a set of programs to calculate any reaction scheme on any personal computer. Typical examples from analytical biochemistry and pharmacology can be used as versatile templates. When a reaction scheme is applied for data fitting, the resulting parameters may not be unique. Correlation of parameters will be discussed and simplification strategies will be offered.

The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla- bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con- trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza- tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control- lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac- cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Grobner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family.In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels.

This book is intended for statisticians with minimal backgrounds in algebra.As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field."

This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this 2008 book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts are applied to research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. This self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics. It has been reissued as an Open Access publication on Cambridge Core.

This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.

This book offers a comprehensive report on the state-of-the art in the broadly-intended field of "intelligent systems". After introducing key theoretical issues, it describes a number of promising models for data and system analysis, decision making, and control. It discusses important theories, including possibility theory, the Dempster-Shafer theory, the theory of approximate reasoning, as well as computing with words, together with novel applications in various areas, such as information aggregation and fusion, linguistic data summarization, participatory learning, systems modeling, and many others. By presenting the methods in their application contexts, the book shows how granular computing, soft computing and fuzzy logic techniques can provide novel, efficient solutions to real-world problems. It is dedicated to Professor Ronald R. Yager for his great scientific and scholarly achievements, and for his long-lasting service to the fuzzy logic, and the artificial and computational intelligence communities. It has been motivated by the authors' appreciation of his original thinking and groundbreaking ideas, with a special thought to his valuable research on the computerized implementation of various aspects of human cognition for decision-making and problem-solving.

FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch'iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.

This book addresses the acoustic signal analysis and spectral dynamics of the tanpura, an Indian plucked string instrument. In addition, it strives to provide a logical and objective explanation of Indian classical musicians' cognitive experience. Issues of relevance in this regard include the rich, mellifluous sound; the undulation of the loudness; the somewhat cyclical variation of the timbre, which is strongly related to these undulations; and the occasional perception of virtual notes to which no strings are tuned. The book analyses the materials used in the tanpura, the instrument's simple structure, the intricacies of the lower bridge, and the theory of string vibration with variable string length. Cognitive experiments to provide the basis for perceptual quality assessment, as well as a methodology for ranking, are described. This is followed by acoustic analyses, both temporal and spectral, for sounds produced by male and female tanpuras, for each individual string and the combined one. An important aspect related to the naturalness of perceived sound, namely the intrinsically associated random perturbations, is also discussed. The apparent irregularities perceived in the acoustic signal produced by the tanpura reveal the importance of examining the signal from the perspective of non-linear analysis, an aspect that is also covered in the book. Given its scope, the book will appeal to students and researchers in the fields of music acoustics, artificial intelligence, and cognitive science, as well as musicians and musicologists around the world.

This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

In these volumes, the most significant of the collected papers of the Chinese-American theoretical physicist Tsung-Dao Lee are printed. A complete list of his published papers, in order of publication, appears in the Bibliography of T.D. Lee. The papers have been arranged into ten categories, in most cases according to the subject matter. At the beginning of each of the first eight categories of papers, there is a commentary on the content and significance of all of the papers in the category. The two short final categories do not have any commentaries. The editor would like to thank Dr. Richard Friedberg for his assistance in the early stages of the editorial work on this project, as well as for writing commentaries on the papers of Categories III and IV. I would also like to thank Dr. Norman Christ for writing the commentary on the papers of Category VII. The assistance of Irene Tramm was in valuable in many aspects of preparing this collection, including locating copies of Lee's p pers. GERALD FEINBERG List of Categories of T.D. Lee's Papers Volume 1 I. Weak Interactions II. Early Papers on Astrophysics and Hydrodynamics III. Statistical Mechanics IV. Polarons and Solitons Volume 2 V. Quantum Field Theory VI. Symmetry Principles Volume 3 VII. Discrete Physics VIII. Strong Interaction Models IX. Historical Papers X. Gravity (Continuum Theory) Contents (Volume 3)* Introduction (by G. Feinberg) ............................................................ ix Bibliography of T.D. Lee ................................................................. xiii VII. Discrete Physics Commentary ................................................................ ."

This is a book on Linear-Fractional Programming (here and in what follows we will refer to it as "LFP"). The field of LFP, largely developed by Hungarian mathematician B. Martos and his associates in the 1960's, is concerned with problems of op timization. LFP problems deal with determining the best possible allo cation of available resources to meet certain specifications. In particular, they may deal with situations where a number of resources, such as people, materials, machines, and land, are available and are to be combined to yield several products. In linear-fractional programming, the goal is to determine a per missible allocation of resources that will maximize or minimize some specific showing, such as profit gained per unit of cost, or cost of unit of product produced, etc. Strictly speaking, linear-fractional programming is a special case of the broader field of Mathematical Programming. LFP deals with that class of mathematical programming problems in which the relations among the variables are linear: the con straint relations (i.e. the restrictions) must be in linear form and the function to be optimized (i.e. the objective function) must be a ratio of two linear functions."

* Recommended by T.Basar, SC series ed.

* This text addresses a new, active area of research and fills a gap in the literature.

* Bridges mathematics, engineering, and computer science; considers stochastic and optimization aspects of congestion control in Internet data transfers.

* Useful as a supplementary text & reference for grad students with some background in control theory; also suitable for researchers.