Hermann Haken – författare
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46 produkter
46 produkter
Inbunden, Engelska, 2020
5 923 kr
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This volume of the “Encyclopedia of Complexity and Systems Science, Second Edition” (ECSS), introduces the fundamental physical and mathematical concepts underlying the theory of complex physical, chemical, and biological systems.
Inbunden, Engelska, 2019
1 115 kr
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This book describes an encompassing modeling approach to psychotherapy, created with the most recent research in the field.
Häftad, Engelska, 2020
880 kr
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This book describes an encompassing modeling approach to psychotherapy, created with the most recent research in the field.
Inbunden, Engelska, 2021
1 835 kr
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The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior.From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning.An important consequence of “the 21st century as the age of cities”, is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers andstudents of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.
Häftad, Engelska, 2022
1 835 kr
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The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior.From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning.An important consequence of “the 21st century as the age of cities”, is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers andstudents of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.
Häftad, Engelska, 2014
545 kr
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This monograph demonstrates the interplay between Shannon information and semantic information in cognition. It shows that Shannon’s information acts as driving force for the formation of semantic information; and vice versa, namely, that semantic information participates in the formation of Shannonian information. The authors show that in cognition, Shannonian and semantic information are interrelated as two aspects of a cognitive process termed as information adaptation. In the latter the mind/brain adapts to the environment by the deflating and/or inflating of the information conveyed by the environment. In the process of information adaptation, quantitative variations in Shannon’s information entail different meanings while different meanings affect the quantity of information. The book illustrates the above conceptually and mathematically by reference to three cognitive processes: pattern recognition, face learning and the recognition of a moving object.
Häftad, Tyska
509 kr
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Inbunden, Tyska, 2003
912 kr
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Atom- und Quantenphysik führt sorgfältig und leicht verständlich in die Ergebnisse und Methoden der empirischen Atomphysik ein, wobei auch das Rüstzeug der Quantentheorie vermittelt und besonders die Wechselwirkung zwischen Experiment und Theorie herausgearbeitet wird. Die vorliegende achte Auflage enthält neben umfangreichen Aktualisierungen neue Abschnitte zur quantenmechanischen Behandlung des Atoms im Magnetfeld und im elektrischen Feld. Weiter finden sich in dem Kapitel "Fortschritte der Quantenphysik: Tieferes Verständnis und neue Anwendungen" genaue Erläuterungen zur Verschränkung von Wellenfunktionen, dem Einstein-Podolsky-Rosen Paradoxon, den Bellschen Ungleichungen, dem Paradoxon der Schrödingerschen Katze und dem Konzept der Dekohärenz. Das letzte Kapitel führt in die Grundlagen der Quantentheorie der chemischen Bindung ein, welche im zweiten Band der Autoren "Molekülphysik und Quantenchemie" ihre Fortsetzung findet. 177 Übungen mit vollständigen Lösungen runden das Buch ab und dienen der Vertiefung.
Häftad, Engelska, 1983
1 620 kr
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This book, written by one of the pioneers of laser theory, is now considered a classic by many laser physicists. Originally published in the prestigious Encyclopedia of Physics series, it is now being republished in paperback to make it available not only to professors and scientists, but also to students. It presents a thorough treatment of the theory of laser resonators, the quantum theory of coherence, and the quantization of electromagnetic fields. Especial emphasis is placed on the quantum-mechanical treatment of laser light by means of quantum-mechanical Langevin equations, the density matrix equation, and the Fokker-Planck equation. The semiclassical approach and the rate equa tion approach are also presented. The principles underlying these approaches are used to derive the relevant equations, from which, in turn, the various properties of laser light are derived. Preface. The concept of the laser came into existence more than a decade ago when SCHAWLOW and TOWNES showed that the maser principle could be extended to the optical region. Since then this field has developed at an incredible pace which hardly anybody could have foreseen. The laser turned out to be a meeting place for such different disciplines as optics (e. g. spectroscopy). optical pumping, radio engineering, solid state physics, gas discharge physics and many other fields. The underlying structure of the laser theory is rather simple.
Häftad, Engelska, 1987
545 kr
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Atomic physics and its underlying quantum theory are the point of departure for many modern areas of physics, astrophysics, chemistry, biology, and even electrical engineering. This textbook provides a careful and eminently readable introduction to the results and methods of empirical atomic physics. The student will acquire the tools of quantum physics and at the same time learn about the interplay between experiment and theory. A chapter on the quantum theory of the chemical bond provides the reader with an introduction to molecular physics. Plenty of problems are given to elucidate the material. The authors also discuss laser physics and nonlinear spectroscopy, incorporating latest experimental results and showing their relevance to basic research. Extra items in the second edition include solutions to the exercises, derivations of the relativistic Klein-Gordon and Dirac equations, a detailed theoretical derivation of the Lamb shift, a discussion of new developments in the spectroscopy of inner shells, and new applications of NMR spectroscopy, for instance tomography.
Häftad, Tyska, 1987
610 kr
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Dieses Lehrbuch wendet sich an Studenten der Physik, der Naturwissenschaften oder der Elektrotechnik ab 3. Semester. Die Atomphysik und die dazugehörige Quantenphysik bilden die Grundlage für viele moderne Gebiete der Physik, der Chemie, Biologie wie auch der Elektrotechnik. Es führt sorgfältig und leicht verständlich in die Ergebnisse und Methoden der empirischen Atomphysik ein. Gleichzeitig wird dem Leser das Rüstzeug der Quantentheorie vermittelt, wobei die Wechselwirkung zwischen Experiment und Theorie besonders herausgearbeitet wird. Die Autoren haben die neuesten Resultate mit berücksichtigt und behandeln insbesondere auch die für Grundlagenforschung und Anwendung gleichermaßen wichtige Laserphysik und nichtlineare Spektroskopie. Verbesserungen und Ergänzungen in der vorliegenden 3. Auflage beziehen sich u.a. auf die Behandlung der relativistischen Klein-Gordon und Dirac-Gleichungen, eine theoretische Ableitung der Lamb-Verschiebung, neue Entwicklungen in der Spektroskopie innerer Schalen, neue Anwendungen der NMR-Spektroskopie, z.B. Tomographie. Außerdem enthält diese Auflage eine große Anzahl von Übungsaufgaben einschließlich der Lösungen zur Vertiefung und zum Selbststudium.
Inbunden, Engelska, 2005
1 298 kr
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The Physics of Atoms and Quanta is a thorough introduction to experiments and theory in this field. Every classical and modern aspect is included and discussed in detail. The new edition is completely revised, new sections on atoms in strong electric fields and high magnetic fields complete the comprehensive coverage of all topics related to atoms and quanta.All new developments, such as new experiments on quantum entanglement, the quantum computer, quantum information, the Einstein-Podolsky-Rosen paradoxon, Bell's inequality, Schrodinger's cat, decoherence, Bose-Einstein-Condensation and the atom laser are discussed. Over 170 problems and their solutions help deepen the insight in this subject area and make this book a real study text. The second and more advanced book by the same authors entitled Molecular Physics and Elements of Quantum Chemistry is the completion of this unique textbook.
Inbunden, Tyska, 2006
912 kr
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Molekülphysik und Quantenchemie führt systematisch und leicht zugänglich in die Grundlagen der beiden Gebiete ein, wie es zum Verständnis der physikalischen Eigenschaften von Molekülen und der chemischen Bindung erforderlich ist. Aufbauend auf Grundkenntnissen aus der Atom- und Quantenphysik (von den gleichen Autoren) vermittelt es den Studenten der Physik, der Physikalischen Chemie und der Theoretischen Chemie die experimentellen und theoretischen Grundlagen und deren Wechselwirkung. Die vorliegende fünfte Auflage wurde um wesentliche aktuelle Entwicklungen experimenteller Methoden und theoretischer Ansätze erweitert. Neu: Abschnitte zu Molekularen Funktionseinheiten, zu Optischer Spektroskopie und Elektrolumineszenz. Durchgehende überarbeitete Neuauflage. 133 Aufgaben vervollständigen das Buch. Die dazugehörigen Lösungen können im Internet abgerufen werden.
Inbunden, Engelska, 2006
542 kr
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The widespread interest this book has found among professors, scientists and stu dents working in a variety of fields has made a new edition necessary. I have used this opportunity to add three new chapters on recent developments. One of the most fascinating fields of modern science is cognitive science which has become a meet ing place of many disciplines ranging from mathematics over physics and computer science to psychology. Here, one of the important links between these fields is the concept of information which, however, appears in various disguises, be it as Shan non information or as semantic information (or as something still different). So far, meaning seemed to be exorcised from Shannon information, whereas meaning plays a central role in semantic (or as it is sometimes called "pragmatic") information. In the new chapter 13 it will be shown, however, that there is an important interplay between Shannon and semantic information and that, in particular, the latter plays a decisive role in the fixation of Shannon information and, in cognitive processes, al lows a drastic reduction of that information. A second, equally fascinating and rapidly developing field for mathematicians, computer scientists and physicists is quantum information and quantum computa tion. The inclusion of these topics is a must for any modern treatise dealing with in formation. It becomes more and more evident that the abstract concept of informa tion is inseparably tied up with its realizations in the physical world.
Inbunden, Engelska, 2004
1 083 kr
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This textbook introduces the molecular physics and quantum chemistry needed to understand the physical properties of molecules and their chemical bonds. It follows the authors' earlier textbook "The Physics of Atoms and Quanta" and presents both experimental and theoretical fundamentals for students in physics and physical and theoretical chemistry. The new edition treats new developments in areas such as high-resolution two-photon spectroscopy, ultrashort pulse spectroscopy, photoelectron spectroscopy, optical investigation of single molecules in condensed phase, electroluminescence, and light-emitting diodes.
Inbunden, Engelska, 2004
1 173 kr
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This book is a reprint edition that comprises two titles, namely "Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology" and ''Advanced Synergetics. Instability Hierarchies of Self Organizing Systems and Devices". The reason for this publication is two-fold: Since synergetics is a new type of interdisciplinary field, initiated by the author in 1969, the basic ideas developed in these volumes are of considerable theoretical interest. But much more than this, the methods and even the concrete examples presented in these books are still highly useful for graduate students, professors, and even for researchers in this fascinating field. The reason lies in the following facts: Synergetics deals with complex systems, i. e. systems that are composed of many individual parts that are able to spontaneously form spatial, temporal or functional structures by means of self-organization. Such phenomena occur in many fields ranging from physics, chemistry and biology to economy and sociology. More recent areas of application have been found in medicine and psychology, where the great potential of the basic principles of synergetics can be unearthed. Further applications have become possible in informatics, for instance the designing of new types of computers, and in other fields of engineering.
Inbunden, Engelska, 2004
561 kr
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This book presents a novel approach to neural nets and thus offers a genuine alternative to the hitherto known neuro-computers. This approach is based on the author's discovery of the profound analogy between pattern recognition and pattern formation in open systems far from equilibrium. Thus the mathematical and conceptual tools of synergetics can be exploited, and the concept of the synergetic computer formulated. A complete and rigorous theory of pattern recognition and learning is presented. The resulting algorithm can be implemented on serial computers or realized by fully parallel nets whereby no spurious states occur. Explicit examples (e.g. recognition of faces and city maps) are provided. The recognition process is made invariant with respect to simultaneous translation, rotation, and scaling, and allows the recognition of complex scenes. Oscillations and hysteresis in the perception of ambiguous patterns are treated, as well as the recognition of movement patterns. A comparison between the recognition abilities of humans and the synergetic computer sheds new light on possible models of mental processes.The synergetic computer can also perform logical steps such as the XOR operation. The new edition includes a section on transformation properties of the equations of the synergetic computer and on the invariance properties of the order parameter equations. Further additions are a new section on stereopsis and recent developments in the use of pulse-coupled neural nets for pattern recognition.
Inbunden, Engelska, 2008
545 kr
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Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and computational neurosciences. Some of the advanced chapters will also be of interest to the specialists. The book approaches the subject through pulse-coupled neural networks, with at their core the lighthouse and integrate-and-fire models, which allow for the highly flexible modelling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. Topics also include pulse-averaged equations and their application to movement coordination. The book closes with a short analysis of models versus the real neurophysiological system.The second edition has been thoroughly updated and augmented by two extensive chapters that discuss the interplay between pattern recognition and synchronization. Further, to enhance the usefulness as textbook and for self-study, the detailed solutions for all 34 exercises throughout the text have been added.
Häftad, Engelska, 2010
921 kr
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The Physics of Atoms and Quanta is a thorough introduction to experiments and theory in this field. Every classical and modern aspect is included and discussed in detail. The new edition is completely revised, new sections on atoms in strong electric fields and high magnetic fields complete the comprehensive coverage of all topics related to atoms and quanta. All new developments, such as new experiments on quantum entanglement, the quantum computer, quantum information, the Einstein-Podolsky-Rosen paradoxon, Bell's inequality, Schrodinger's cat, decoherence, Bose-Einstein-Condensation and the atom laser are discussed. Over 170 problems and their solutions help deepen the insight in this subject area and make this book a real study text. The more advanced book by the same authors entitled Molecular Physics and Elements of Quantum Chemistry coplements this unique textbook.
Häftad, Engelska, 2010
545 kr
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This book presents the concepts needed to deal with self-organizing complex systems from a unifying point of view that uses macroscopic data. The various meanings of the concept "information" are discussed and a general formulation of the maximum information (entropy) principle is used. With the aid of results from synergetics, adequate objective constraints for a large class of self-organizing systems are formulated and examples are given from physics, life and computer science. The relationship to chaos theory is examined and it is further shown that, based on possibly scarce and noisy data, unbiased guesses about processes of complex systems can be made and the underlying deterministic and random forces determined. This allows for probabilistic predictions of processes, with applications to numerous fields in science, technology, medicine and economics. The extensions of the third edition are essentially devoted to an introduction to the meaning of information in the quantum context.Indeed, quantum information science and technology is presently one of the most active fields of research at the interface of physics, technology and information sciences and has already established itself as one of the major future technologies for processing and communicating information on any scale. This book addresses graduate students and nonspecialist researchers wishing to get acquainted with the concept of information from a scientific perspective in more depth. It is suitable as a textbook for advanced courses or for self-study.
Häftad, Engelska, 2010
867 kr
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Since the publication of the first edition of this book, there have been many im portant new developments in the field of molecular physics. The new methods and results which are most significant for students are treated extensively in this second edition. Among these are in particular single-molecule spectroscopy and the field of molecular electronics, which is in a stage of rapid development, including the areas of electroluminescence and organic light-emitting diodes. In addition, we have ex tended and corrected the earlier material in a number of places. We have also included exercises in this new edition; they will allow students to deepen their understanding and offer a basis for further individual study. The complete solutions to the exercises can be found on the Internet under www. springeronline. com/3-540-40792-S. We are grateful to Mr. C. -D. Bachem and Dr. Th. Schneider of the Springer Verlag for their continuous and very agreeable cooperation during the preparation of the book. We thank our colleague Prof. W. D. Brewer for his competent translation. Stuttgart, February 2004 H. Haken . H. C. Wolf Preface to the First Edition This textbook is intended for use by students of physics, physical chemistry, and theoretical chemistry. The reader is presumed to have a basic knowledge of atomic and quantum physics at the level provided, for example, by the first few chapters in our book The Physics of Atoms and Quanta.
Häftad, Engelska, 2012
1 190 kr
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This book is a reprint edition that comprises two titles, namely "Synergetics. The reason for this publication is two-fold: Since synergetics is a new type of interdisciplinary field, initiated by the author in 1969, the basic ideas developed in these volumes are of considerable theoretical interest.
Del 50 - Springer Series in Synergetics
Synergetic Computers and Cognition
A Top-Down Approach to Neural Nets
Häftad, Engelska, 2010
545 kr
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The first edition of this book has found great interest among scientists and en gineers dealing with pattern recognition and among psychologists working on psychophysics or Gestalt psychology. This book also proved highly useful for graduate students of informatics. The concept of the synergetic computer offers an important alternative to the by now more traditional neural nets. I just mention a few advantages: There are no ghost states so that time-consuming methods such as simulated annealing can be avoided; the synaptic strengths are explicitly determined by the prototype patterns to be stored, but they can equally well be learned, and the learning procedure allows a classification. Also a precise meaning and function can be attributed to "hidden variables". The synergetic computer has found a number of important practical applications in industry. I use the opportunity of this second edition to include a new section on transfor mation properties of the equations of the synergetic computer and on the invariance properties of its order parameter equations. A new section is devoted to the problem of stereopsis that is dealt with by the basic concept of the synergetic computer. Finally, attention is paid to a recent de velopment, namely to the use of pulse-coupled neural nets for pattern recognition.
Häftad, Engelska, 2010
545 kr
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Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and computational neurosciences. Some of the advanced chapters will also be of interest to the specialists. The book approaches the subject through pulse-coupled neural networks, with at their core the lighthouse and integrate-and-fire models, which allow for the highly flexible modelling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. Topics also include pulse-averaged equations and their application to movement coordination. The book closes with a short analysis of models versus the real neurophysiological system.The second edition has been thoroughly updated and augmented by two extensive chapters that discuss the interplay between pattern recognition and synchronization. Further, to enhance the usefulness as textbook and for self-study, the detailed solutions for all 34 exercises throughout the text have been added.
Del 20 - Springer Series in Synergetics
Advanced Synergetics
Instability Hierarchies of Self-Organizing Systems and Devices
Häftad, Engelska, 2012
545 kr
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This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.
Del 45 - Springer Series in Synergetics
Synergetics of Cognition
Proceedings of the International Symposium at Schloß Elmau, Bavaria, June 4–8, 1989
Häftad, Engelska, 2013
1 083 kr
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This book presents the invited lectures given at the International Symposium on Synergetics of Cognition held at SchloB Elmau, Bavaria (Fed. Rep. of Germany), June 4-8, 1989. The understanding of the processes underlying cognition is certainly one of the most challenging and difficult problems confronting the human mind. It is an enterprise that requires the cooperation of scientists from fields ranging from the neurosciences and psychology through biology to the computer sciences, physics and mathematics. The papers included in this volume reflect this joint effort. As will be evident, there is a remarkable convergence of ideas stemming from various fields, for instance, the earlier ideas on Gestalt theory celebrate a come back and remarkable analogies are being established with modem concepts of self-organization as dealt with in the interdisciplinary field of synergetics. The individual topics range from the "microscopic level", where new exciting results on specific oscillations of neural activity are reported, to computer simulations of perception, and finally psychological experiments at the "macroscopic level". We hope that this book will convey to its readers the same enthusiasm that was felt by the participants of the symposium. We wish to thank Mrs. U. Funke for the excellent organisation of the sym posium, and the Volkswagen-Stiftung, Hannover, for its financial support. We are furthermore grateful to Christoph Stadler and Zora Franko for their help in com piling the name and subject indexes. Finally we wish to thank Springer-Verlag, in particular Dr. Angela Lahee, for the excellent cooperation.
Del 62 - Springer Series in Synergetics
Interdisciplinary Approaches to Nonlinear Complex Systems
Häftad, Engelska, 2012
1 083 kr
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Nonlinear dynamics is now recognized as playing a crucialrole in a wide variety of disciplines. But what is only justbeginning is the important process of cross fertilizationand transfer of knowledge and expertise from one area toanother. This book is intended to promote this process whichwill undoubtedly contribute greatly to furthering ourunderstanding of complex systems. Contributions areprovided by leading experts from the areas of sociology,cognitive science, chemistry, physiology, ecology,economics, neural networks and physics.
Häftad, Tyska, 2012
652 kr
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Atom- und Quantenphysik führt sorgfältig und leicht verständlich in die Ergebnisse und Methoden der empirischen Atomphysik ein, wobei auch das Rüstzeug der Quantentheorie vermittelt und besonders die Wechselwirkung zwischen Experiment und Theorie herausgearbeitet wird.
Del 2 - Springer Series in Synergetics
Synergetics
A Workshop Proceedings of the International Workshop on Synergetics at Schloss Elmau, Bavaria, May 2–7, 1977
Häftad, Engelska, 2011
545 kr
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This volume contains most of the invited papers presented at the International Work shop on Synergetics, Schloss E1mau, Bavaria, May 2 to.May 7, 1977. This workshop fol lowed an International Symposium on SynergetiGS at Schloss E1mau, 1972, and an Inter national SUl11l1erschoo1 at Erice, Sicily, 1974. Synergetics is a rather new field of interdisciplinary research which studies the self-organized behavior of systems leading to the formation of structures and func tionings. Indeed the whole universe seems to be organized, with pronounced structures starting from spiral galaxies down to living cells. Furthermore, very many of the most interesting phenomena occur in systems which are far from thermal equilibrium. Synergetics in its present form focusses its attention on those phenomena where dra matic changes occur on a macroscopic scale. Here indeed Synergetics was able to re veal profound analogies between systems in different disciplines ranging from physics to sociology. This volume contains contributions from various fields but the reader will easily discover their cOl11J1on goal. Not only in the natural sciences but also in ecology, sociology, and economy, man is confronted with the problems of complex sys tems. The principles and analogies unearthed by Synergetics will certainly be very he1pfu~ to cope with such difficult problems. I use this opportunity to thank the Vo1kswagenwerk Foundation for its support of the project Synergetics and in particular for sponsoring the International Workshop on Synergetics.
Del 5 - Springer Series in Synergetics
Pattern Formation by Dynamic Systems and Pattern Recognition
Proceedings of the International Symposium on Synergetics at Schloß Elmau, Bavaria, April 30 – May 5, 1979
Häftad, Engelska, 2011
545 kr
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This book contains the manuscripts of the papers delivered at the International Sym posium on Synergetics held at SchloB Elmau, Bavaria, Germany, from April 30 until May 5, 1979. This conference followed several previous ones (Elmau 1972, Sicily 1974, Elmau 1977). This time the subject of the symposium was "pattern formation by dynam ic systems and pattern recognition". The meeting brought together scientists from such diverse fields as mathematics, physics, chemistry, biology, history as well as experts in the fields of pattern recognition and associative memory. When I started this type of conference in 1972 it appeared to be a daring enter prise. Indeed, we began to explore virgin land of science: the systematic study of cooperative effects in physical systems far from equi~ibrium and in other disciplines. Though these meetings were attended by scientists from quite different disciplines, a basic concept and even a common language were found from the very beginning. The idea that there exist profound analogies in the behaviour of large classes of complex systems, though the systems themselves may be quite different, proved to be most fruitful. I was delighted to see that over the past one or two years quite similar conferences were now held in various places allover the world. The inclusion of prob lems of pattern recognition at the present meeting is a novel feature, however.