Maximum Entropy Information Without Probability And Complex Fractals
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Maximum Entropy Information Without Probability And Complex Fractals
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Author : Guy Jumarie
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Maximum Entropy Information Without Probability And Complex Fractals written by Guy Jumarie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Computers categories.
Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.
Maximum Entropy Information Without Probability And Complex Fractals
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Author : Guy Jumarie
language : en
Publisher:
Release Date : 2014-01-15
Maximum Entropy Information Without Probability And Complex Fractals written by Guy Jumarie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Entropy Measures Maximum Entropy Principle And Emerging Applications
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Author : Karmeshu
language : en
Publisher: Springer
Release Date : 2012-10-01
Entropy Measures Maximum Entropy Principle And Emerging Applications written by Karmeshu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-01 with Technology & Engineering categories.
The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.
Factorization Method In Quantum Mechanics
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Author : Shi-Hai Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-01
Factorization Method In Quantum Mechanics written by Shi-Hai Dong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-01 with Science categories.
This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader’s disposal. For this purpose, the text provides a comprehensive description of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in quantum mechanics textbooks.
Hierarchical Methods
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Author : V. Kulish
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Hierarchical Methods written by V. Kulish and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Science categories.
The book consists of two Volumes. The first (the preceding volume) is devoted to the general nonlinear theory of the hierarchical dynamic oscillative–wave systems. This theory has been called the theory of hi- archical oscillations and waves. Here two aspects of the proposed theory are discussed. The first aspects concern the fundamental nature and the basic c- cepts and ideas of a new hierarchical approach to studying hierarchical dynamic systems. A new hierarchical paradigm is proposed as a - sis of a new point of view of such types of systems. In turn, a set of hierarchical principles is formulated as the fundamental basis of this paradigm. Therein the self-resemblance (holographic) principle plays a key role here. An adequate mathematic description (factorization) of the proposed paradigm is carried out. The concepts of structural and dynamic (functional) operators are put into the basis of this descr- tion. Electrodynamics is chosen as a convenient basis for an obvious demonstration of some key points of the proposed new theory. The second aspect has a purely mathematical nature. It is related to the form of factorization (i.e., mathematical description) of hier- chical types of dynamic models, and discussion of the methods of their mathematical analysis. A set of the hierarchical asymptotic analytical– numerical methods is given as an evidence of the practical effectiveness of the proposed version of hierarchical theory.
Foundations Of Quantum Mechanics An Empiricist Approach
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Author : W.M. de Muynck
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Foundations Of Quantum Mechanics An Empiricist Approach written by W.M. de Muynck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Science categories.
Taking a new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures, this book views old and new problems of the foundations of quantum mechanics. It demonstrates the crucial role of the generalized formalism in fundamental issues and practical applications.
Cosmological Pattern Of Microphysics In The Inflationary Universe
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Author : Maxim Y. Khlopov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-20
Cosmological Pattern Of Microphysics In The Inflationary Universe written by Maxim Y. Khlopov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-20 with Science categories.
Modern cosmology is a quickly developing ?eld of research. New technical devices and tools supply the community with new experimental data measured with high accuracy. The self-consistent explanation of these data needs t- oretical models that are based on hypothetical predictions of particle theory. In their turn, such predictions imply cosmology for their probe. Speci?c st- ies of the cosmological consequences of particle theory, linking them to their observable signatures, are actual. This boiling kettle of theoretical research and experimental efforts produces ideas that will be preserved for following generations. The aim of this book is to acquaint the reader with some of these ideas, - fering nontrivial ways to probe the physical basis of modern cosmology. An extensive review of the newest ideas in modern cosmology, e. g. , related with the development of the M-brane theory, lies beyond the scope of our book, which is aimed at providing a ?rmly established system of probes for these ideas, linking their predictions to their possible experimental test. We use the framework of in?ationary paradigm to reveal the phenomena that can shed light on the physical origin of the observed Universe, of its matter content and large-scale structure. The crucial role of quantum ?uctuations in creation of our Universe and in possible features, re?ecting cosmological impact of microphysics, is discussed. These features are shown to be accessible to - perimental test in the near future.
Relativity In Rotating Frames
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Author : G. Rizzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Relativity In Rotating Frames written by G. Rizzi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
Even if the subject is a long-standing one, this is the first monograph on this field. On the one hand, this book is intended to give a rather wide review on this field, both in a historical and pedagogical perspective; on the other hand, it aims at critically re-examining and discussing the most controversial issues. For instance, according to some authors the celebrated Sagnac effect is a disproval of the theory of relativity applied to rotating frames; according to others, it is an astonishing experimental evidence of the relativistic theory. In order to give the reader a deeper insight into this research field, the contributing authors discuss their opinions on the main subjects in an enthralling virtual round table: in this way, the reader can get a direct comparison of the various viewpoints on the most controversial and interesting topics. This is particularly expedient, since the differences in the various approaches are often based upon subtleties that can be understood only by a direct comparison of the underlying hypotheses.
Relativity And The Dimensionality Of The World
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Author : Vesselin Petkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-08
Relativity And The Dimensionality Of The World written by Vesselin Petkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-08 with Science categories.
All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space. But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given ‘at once', which means that physical bodies are four-dimensional worldtubes containing the whole histories in time of the three-dimensional bodies of our everyday experience. The implications of a real Minkowski world for physics itself and especially for our world view are enormous. The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? It contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it.
The Geometry Of Hamilton And Lagrange Spaces
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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
The Geometry Of Hamilton And Lagrange Spaces written by R. Miron and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Mathematics categories.
The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many international conferences were devoted to debate this subject, proceedings and monographs were published [10], [18], [112], [113],... A large area of applicability of this geometry is suggested by the connections to Biology, Mechanics, and Physics and also by its general setting as a generalization of Finsler and Riemannian geometries. The concept of Hamilton space, introduced in [105], [101] was intensively studied in [63], [66], [97],... and it has been successful, as a geometric theory of the Ham- tonian function the fundamental entity in Mechanics and Physics. The classical Legendre’s duality makes possible a natural connection between Lagrange and - miltonspaces. It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.