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Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.

Ergodic theory. Information theory --- Partial differential equations --- Differential equations --- Mathematics --- Classical mechanics. Field theory --- differentiaalvergelijkingen --- wiskunde --- dynamica --- informatietheorie

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For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as a chapter on perturbation methods and a section in Chapter 3 that shows how to solve differential equations using Mathematica codes. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0, and all Mathematica codes are in the book itself. This new edition also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many further enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.

Ergodic theory. Information theory --- Differential equations --- Mathematical analysis --- Mathematics --- Classical mechanics. Field theory --- differentiaalvergelijkingen --- analyse (wiskunde) --- wiskunde --- dynamica --- informatietheorie

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Cryptography is an area that traditionally focused on secure communication, authentication and integrity. In recent times though, there is a wealth of novel fine-tuned cryptographic techniques that sprung up as cryptographers focused on the specialised problems that arise in digital content distribution. These include fingerprinting codes, traitor tracing, broadcast encryption and others. This book is an introduction to this new generation of cryptographic mechanisms as well as an attempt to provide a cohesive presentation of these techniques. Encryption for Digital Content details the subset cover framework (currently used in the AACS encryption of Blu-Ray disks), fingerprinting codes, traitor tracing schemes as well as related security models and attacks. It provides an extensive treatment of the complexity of the revocation problem for multi-receiver (subscriber) encryption mechanisms, as well as the complexity of the traceability problem. Pirate evolution type of attacks are covered in depth. This volume also illustrates the manner that attacks affect parameter selection, and how this impacts implementations. The authors gratefully acknowledge the support of the National Science Foundation under Grant No. 0447808.

Ergodic theory. Information theory --- Mathematical control systems --- Computer science --- Programming --- Computer architecture. Operating systems --- Information systems --- Computer. Automation --- coderen --- cryptografie --- informatica --- database management --- informatietechnologie --- programmatielogica --- computerbeveiliging --- computernetwerken --- informatietheorie

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The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presented here are the outgrowth of very recent studies by the authors, including a number of new original results here in print for the first time authors have provided a comprehensive and reasonably self-contained exposition of the general topic outlined above. This includes supplying all the functional analytic framework along with the function space theory as pertinent in the study of nonlinear plate models and more generally second order in time abstract evolution equations. While von Karman evolutions are the object under considerations, the methods developed transcendent this specific model and may be applied to many other equations, systems which exhibit similar hyperbolic or ultra-hyperbolic behavior (e.g. Berger's plate equations, Mindlin-Timoschenko systems, Kirchhoff-Boussinesq equations etc). In order to achieve a reasonable level of generality, the theoretical tools presented in the book are fairly abstract and tuned to general classes of second-order (in time) evolution equations, which are defined on abstract Banach spaces. The mathematical machinery needed to establish well-posedness of these dynamical systems, their regularity and long-time behavior is developed at the abstract level, where the needed hypotheses are axiomatized. This approach allows to look at von Karman evolutions as just one of the examples of a much broader class of evolutions. The generality of the approach and techniques developed are applicable (as shown in the book) to many other dynamics sharing certain rather general properties. Extensive background material provided in the monograph and self-contained presentation make this book suitable as a graduate textbook.

Ergodic theory. Information theory --- Partial differential equations --- Mathematical analysis --- Mathematics --- Classical mechanics. Field theory --- Applied physical engineering --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde --- economie --- wiskunde --- dynamica --- informatietheorie

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This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems. The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrange and Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics. The new edition is completely revised and updated. New exercises and new sections in canonical transformation and Hamiltonian theory have been added.

Ergodic theory. Information theory --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Physics --- Applied physical engineering --- toegepaste wiskunde --- toegepaste mechanica --- economie --- wiskunde --- fysica --- mechanica --- dynamica --- informatietheorie