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Cover: 9780792363309 | Maximum Entropy, Information Without Probability and Complex Fractals
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Maximum Entropy, Information Without Probability and Complex Fractals
Classical and Quantum Approach
Buch von Guy Jumarie
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
1. Introduction.- 2. Summary of Information Theory.- 3. Path Entropies of Non Random Functions.- 4. Path Entropies of Random Functions and of Non-Random Distributed Functions.- 5. Quantum Entropies of Non-Probabilistic Square Matrices.- 6. Complex-Valued Fractional Brownian Motion of Order n. Part I.- 7. Complex-Valued Fractional Brownian Motion of Order n. Part II.- 8. Information Thermodynamics and Complex-Valued Fractional Brownian motion of Order n.- 9. Fractals, Path Entropy, and Fractional Fokker-Planck Equation.- 10. Outline of Applications.
Details
Erscheinungsjahr: 2000
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Fundamental Theories of Physics
Inhalt: xix
270 S.
ISBN-13: 9780792363309
ISBN-10: 0792363302
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Jumarie, Guy
Hersteller: Springer Netherland
Springer Netherlands
Fundamental Theories of Physics
Maße: 241 x 160 x 21 mm
Von/Mit: Guy Jumarie
Erscheinungsdatum: 31.05.2000
Gewicht: 0,612 kg
Artikel-ID: 102550026
Inhaltsverzeichnis
1. Introduction.- 2. Summary of Information Theory.- 3. Path Entropies of Non Random Functions.- 4. Path Entropies of Random Functions and of Non-Random Distributed Functions.- 5. Quantum Entropies of Non-Probabilistic Square Matrices.- 6. Complex-Valued Fractional Brownian Motion of Order n. Part I.- 7. Complex-Valued Fractional Brownian Motion of Order n. Part II.- 8. Information Thermodynamics and Complex-Valued Fractional Brownian motion of Order n.- 9. Fractals, Path Entropy, and Fractional Fokker-Planck Equation.- 10. Outline of Applications.
Details
Erscheinungsjahr: 2000
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Fundamental Theories of Physics
Inhalt: xix
270 S.
ISBN-13: 9780792363309
ISBN-10: 0792363302
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Jumarie, Guy
Hersteller: Springer Netherland
Springer Netherlands
Fundamental Theories of Physics
Maße: 241 x 160 x 21 mm
Von/Mit: Guy Jumarie
Erscheinungsdatum: 31.05.2000
Gewicht: 0,612 kg
Artikel-ID: 102550026
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