Although the study of dynamical systems is mainly concerned with single trans formations and one-parameter flows (i. e. with actions of Z, N, JR, or JR+), er godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-dimensional sym metry groups. However, the wealth of concrete and natural examples, which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. A remarkable exception is provided by a class of geometric actions of (discrete subgroups of) semi-simple Lie groups, which have led to the discovery of one of the most striking new phenomena in multi-dimensional ergodic theory: under suitable circumstances orbit equivalence of such actions implies not only measurable conjugacy, but the conjugating map itself has to be extremely well behaved. Some of these rigidity properties are inherited by certain abelian subgroups of these groups, but the very special nature of the actions involved does not allow any general conjectures about actions of multi-dimensional abelian groups. Beyond commuting group rotations, commuting toral automorphisms and certain other algebraic examples (cf. [39]) it is quite difficult to find non-trivial smooth Zd-actions on finite-dimensional manifolds. In addition to scarcity, these examples give rise to actions with zero entropy, since smooth Zd-actions with positive entropy cannot exist on finite-dimensional, connected manifolds. Cellular automata (i. e.

Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions."

Companies and institutions depend more than ever on the availability of their Information Technology, and most mission critical business processes are IT-based. Business Continuity is the ability to do business under any circumstances and is an essential requirement faced by modern companies. Both concepts - High Availability and Disaster Recovery - are realized by redundant systems. This book presents requirements, concepts, and realizations of redundant systems on all abstraction levels, and all given examples refer to UNIX and Linux Systems.

This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrodinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.

Companies and other organizations depend more than ever on the availability of their Information Technology, and most mission critical business processes are IT-based processes. Business Continuity is the ability to do business under any circumstances and is an essential requirement modern companies are facing. "High Availability and Disaster Recovery" are contributions of the IT to fulfill this requirement. And companies will be confronted with such demands to an even greater extent in the future, since their credit ratings will be lower without such precautions. Both, "High Availability and Disaster Recovery," are realized by redundant systems. Redundancy can and should be implemented on different abstraction levels: from the hardware, the operating system and middleware components up to the backup computing center in case of a disaster. This book presents requirements, concepts, and realizations of redundant systems on all abstraction levels, and all given examples refer to UNIX and Linux Systems.

Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schroedinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others. The contributors to the volume are the leading experts in the area. The book will provide a valuable source both for active researchers and graduate students in the respective fields.

Klaus Schmidt has been a pioneer in the concept and process of inclusive, or holistic, branding as an integral - indeed leading - element in corporate strategy. This book explains the genesis and characteristics of the holistic approach, including its dimensions, structure and methodology, then demonstrates its startling relevance to today's pressing global business issues. Compelling case studies from leading organisations in a variety of industries show the practical necessity of holistic brand thinking, and its results.

Dieses Buch bietet eine erste Einfuhrung in die mathematische Theorie der dynamischen Systeme, die fur Studierende des letzten Studienjahres des Bachelor Studiums und fur das Master Studium geeignet ist. Aufbauend auf den Grundbegriffen der Topologischen Dynamik und der Ergodentheorie in den ersten beiden Kapiteln behandelt das dritte Kapitel den fur die Ergodentheorie zentralen Begriff der Entropie, der seinen Ursprung in der statistischen Physik und der Informationstheorie hat, und der die Komplexitat eines masstheoretischen dynamischen Systems quantifiziert. Das vierte Kapitel ist ebenfalls der Entropie gewidmet, diesmal aber im Rahmen der topologischen Dynamik, bei derEntropie einen quantitativen Ausdruck fur die Verformung eines kompakten metrischen Raumes durch eine stetige Transformation darstellt. Das funfte und letzte Kapitel gibt einen kleinen Einblick in aktuelle Entwicklungen der Theorie der dynamischen Systeme mit ihren mehrparametrischen Verallgemeinerungen des klassischen Konzepts der Zeitentwicklung und den daraus entspringenden und zum Teil uberraschenden Querverbindungen zu anderen mathematischen Disziplinen.
Das in Vorlesungen erprobte Material dieses Buches kann durch eine den Interessen der Studierenden angepasste Themenauswahl wahlweise fur eine ein- oder zweisemestrige Vorlesung eingesetzt werden. "

The excavation of Gobekli Tepe has revealed the hitherto unknown religion of the Neolithic Revolution." This book offers an archaeological starter basis for interpreting that ancient religion. Other fresh perspectives affect our understanding of civilization, human sacrifice, cannibalism, warfare, and imperialism. Fresh contextual perspectives are presented on ancient Egypt and Greece, on Abraham, the Scapegoat question, as well as on the teaching strategies of Confucius in China-all these are remotely linked to Gobekli Tepe. The author is a former student of Mircea Eliade (University of Chicago) and the family resemblance in his orientation shows. His earlier innovations in the History of Religions field include: (1) a historical interpretation of Navajo hunter mythology; (2) recording the nine-night Navajo Coyoteway Ceremonial in 1974, which had been declared extinct in 1910; (3) identification of the Serpent as primary deity of ancient Middle American Civilization, thereby rejecting the primacy of the Jaguar totem; (4) identifying Neo-Platonism as a bridge leading from ancient Egyptian theology at Heliopolis to orthodox Christian theology.

Excavation of Goebekli Tepe has revealed the hitherto unknown religion of the "Neolithic Revolution." Almost twelve millennia ago the cult was established, at the northern end of the Fertile Crescent, by priests who were hunter-shamans, miners of flint and weapon-makers. Progress in weapon manufacture resulted in overhunting, a temporary surplus of meat, too many human hunters, and a decline in prey animal populations. Shortages of prey animals elicited a priestly cult that specialized in the regeneration of life. Priestly minds rationalized taking control of plants and animals and thereby encouraged domestication--which led to "hyper-domestication," or, what evolved as our history of civilization and our history of religions.

The origin of this volume and the symposium proceedings it records can be traced to the deliberations of the National Academy of Sciences' Animal Orientation and Tracking Committee of the 1969 Space Biology Summer Study at Santa Cruz, California, whose members pointed to the potential role of satellites and recent bioengineering developments as a means of gaining information about the many questions of animal travel, particularly the mechanisms involved in long-distance navigational ability. Coming several years since its predecessor conferences, at a time of a new popularization of ecology and a growing availability of advanced technology, the Wallops Station symposium reflected its temporal and geographic setting. The papers and discussions of this volume contrast the classical approaches to phenomena of ancient interest, the beginnings made in applying satellite technology, and the conceptual and methodological advances in experimental biology which have taken place in the past few years. The range of species, sensory modalities, and methodologies provide the reader with a substantial sample of the developments in this field and with the basis for predicting, to some degree, its future course. Already apparent is the combining of field observations made under highly variable natural conditions with analytic, manipulative laboratory methods. A greater precision in the experimental questions now being posed is making their solution increasingly susceptible to neurophysiological and behavioral techniques for isolating the variables, both internal and environmental, which control this class of behavior. Whether the mechanisms of orientation and navigation will yield to the current array of approaches addressed to specific questions or must await a more general understanding of brain function, there is little doubt that this symposium will have had a significant effect on the research to be reported whenever the participants in this field again assemble to assess their progress. Richard E. Belleville Bioscience Programs