This book provides a self-contained introduction to typical properties of volume preserving homeomorphisms, examples of which include transitivity, chaos and ergodicity. The authors make the first part of the book very concrete by focusing on volume preserving homeomorphisms of the unit n-dimensional cube. They also prove fixed point theorems (Conley-Zehnder-Franks). This is done in a number of short self-contained chapters that would be suitable for an undergraduate analysis seminar or a graduate lecture course. Parts Two and Three consider compact manifolds and sigma compact manifolds respectively, describing the work of the two authors in extending the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.

This book presents a fresh, new approach to systems analysis and modeling with a systems science flavor that stimulates systems thinking. After introducing systems modeling principles, the ensuing wide selection of examples aptly illustrate that anything which changes over time can be modeled as a system. Each example begins with a knowledge base that displays relevant information obtained from systems analysis. The diversity of examples clearly establishes a new protocol for synthesizing systems models.

Everyone makes decisions, but not everyone is a decision analyst. A decision analyst uses quantitative models and computational methods to formulate decision algorithms, assess decision performance, identify and evaluate options, determine trade-offs and risks, evaluate strategies for investigation, and so on. This book is written for decision analysts.

The present text offers a graduate level treatment of time dependent phenomena in condensed matter physics. Conventional ideas of linear response theory and kinetic theory are treated in detail. The general emphasis, however, in on the development of generalized Langevin equations for treating nonlinear behaviour in a wide variety of systems. A full treatment is given for the underpinnings of hydrodynamics for fluids.

Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning.

Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.

A new approach to understanding nonlinear dynamics and strange attractors. The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question. In a significant evolution of the field of Nonlinear Dynamics, The Topology of Chaos responds to the fundamental challenge of chaotic systems by introducing a new analysis method-Topological Analysis-which can be used to extract, from chaotic data, the topological signatures that determine the stretching and squeezing mechanisms which act on flows in phase space and are responsible for generating chaotic data.

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.

In diesem Buch finden Sie ausführliche Tipps zum rationellen, verhaltens- und behaltensorientierten Lesen, zum aktiven Zuhören und Mitschreiben, zum zielführenden Arbeiten in der Gruppe, zur mündlichen Präsentation wissenschaftlicher Arbeiten, zur effizienten Vorbereitung auf Prüfungen sowie zur erfolgsgerichteten Studienplanung und -organisation.

Fiber Reinforced Plastics (FRP) are widely used for the design of load-bearing structures. Life time prediction based on failure analysis is therefore essential for many applications in Aeronautics, Automotive and Civil Engineering. Analysis of Failure in Fiber Polymer Laminates presents Alfred Puck´s failure model, which, among several other theories, predicts fracture limits best and describes the failure phenomena in FRP most realistically – as confirmed within the “World-wide Failure Exercise”. Using Puck´s model the composite engineer can follow the gradual failure process in a laminate and deduce from the results of the analysis how to improve the laminate design. This capability distinguishes the model from other phenomenological and global models. It thus reduces the number of required component tests and iteration loops in the design process and paves the way to sorely needed software for crash-simulation of FRP-structures.