Andrei Yu Khrennikov's Books

Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

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Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.

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Page Count

255

Publisher

Cambridge University Press

Published Date

ISBN 10

1108100104

ISBN 13

9781108100106

P-adic Deterministic and Random Dynamics

By: Andrei Y. Khrennikov,Marcus Nilsson

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P-adic Deterministic and Random Dynamics

By: Andrei Y. Khrennikov,Marcus Nilsson

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

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Page Count

279

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402026609

ISBN 13

9781402026607

Interpretations of Probability

By: Andrei Khrennikov

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Interpretations of Probability

By: Andrei Khrennikov

This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

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Page Count

241

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110213192

ISBN 13

9783110213195

p-Adic Valued Distributions in Mathematical Physics

By: Andrei Y. Khrennikov

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p-Adic Valued Distributions in Mathematical Physics

By: Andrei Y. Khrennikov

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

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271

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401583560

ISBN 13

9789401583565

Quantum Methods In Social Science: A First Course

By: Emmanuel Haven,Andrei Yu Khrennikov,Terry R Robinson

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Quantum Methods In Social Science: A First Course

By: Emmanuel Haven,Andrei Yu Khrennikov,Terry R Robinson

Shown here is how basic concepts of physics can be used to improve models in finance, economics, psychology and biology. Readers are introduced to how physical theory can inform non-physical phenomena in the social sciences, thereby improving decision making and modeling capabilities in research-based and professional settings.Consisting of three parts, the first part deals with the application of quantum operator methods to financial transactions and population dynamics. Part two develops physical concepts, working from classical Lagrangian and Hamiltonian mechanics and leading to an introduction of quantum information and its application to decision making. The final part treats classical and quantum probability theory in some detail and deals, at a more advanced level, with the impact of quantum probabilities on common knowledge and common beliefs between agents in systems.Quantum Methods in Social Science is a high level textbook for advanced undergraduate or graduate students of economics, finance and business, while also being of interest to those with a background in physics.

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276

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1786342790

ISBN 13

9781786342799

Applied Algebraic Dynamics

By: Vladimir Anashin,Andrei Khrennikov

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Applied Algebraic Dynamics

By: Vladimir Anashin,Andrei Khrennikov

This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.

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Page Count

558

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110203014

ISBN 13

9783110203011

Probability And Randomness: Quantum Versus Classical

By: Andrei Yu Khrennikov

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Probability And Randomness: Quantum Versus Classical

By: Andrei Yu Khrennikov

Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level.

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299

Publisher

World Scientific

Published Date

ISBN 10

1783267984

ISBN 13

9781783267989

Quantum Social Science

By: Emmanuel Haven,Andrei Khrennikov

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Quantum Social Science

By: Emmanuel Haven,Andrei Khrennikov

Written by world experts in the foundations of quantum mechanics and its applications to social science, this book shows how elementary quantum mechanical principles can be applied to decision-making paradoxes in psychology and used in modelling information in finance and economics. The book starts with a thorough overview of some of the salient differences between classical, statistical and quantum mechanics. It presents arguments on why quantum mechanics can be applied outside of physics and defines quantum social science. The issue of the existence of quantum probabilistic effects in psychology, economics and finance is addressed and basic questions and answers are provided. Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way.

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Page Count

305

Publisher

Cambridge University Press

Published Date

ISBN 10

1139851497

ISBN 13

9781139851497

Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

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Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

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255

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Cambridge University Press

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1108100104

ISBN 13

9781108100106

Ubiquitous Quantum Structure

From Psychology to Finance

By: Andrei Y. Khrennikov

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Ubiquitous Quantum Structure

From Psychology to Finance

By: Andrei Y. Khrennikov

Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.

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Page Count

226

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642051014

ISBN 13

9783642051012

Probability And Randomness: Quantum Versus Classical

By: Andrei Yu Khrennikov

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Probability And Randomness: Quantum Versus Classical

By: Andrei Yu Khrennikov

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Page Count

299

Publisher

World Scientific

Published Date

ISBN 10

1783267984

ISBN 13

9781783267989

Quantum Methods In Social Science: A First Course

By: Emmanuel Haven,Andrei Yu Khrennikov,Terry R Robinson

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Quantum Methods In Social Science: A First Course

By: Emmanuel Haven,Andrei Yu Khrennikov,Terry R Robinson

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Solve jigsaw puzzle

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Page Count

276

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1786342790

ISBN 13

9781786342799

Book's by Andrei Yu Khrennikov

Ultrametric Pseudodifferential Equations and Applications

Ultrametric Pseudodifferential Equations and Applications

P-adic Deterministic and Random Dynamics

P-adic Deterministic and Random Dynamics

Interpretations of Probability

Interpretations of Probability

p-Adic Valued Distributions in Mathematical Physics

p-Adic Valued Distributions in Mathematical Physics

Quantum Methods In Social Science: A First Course

Quantum Methods In Social Science: A First Course

Applied Algebraic Dynamics

Applied Algebraic Dynamics

Probability And Randomness: Quantum Versus Classical

Probability And Randomness: Quantum Versus Classical

Quantum Social Science

Quantum Social Science

Ultrametric Pseudodifferential Equations and Applications

Ultrametric Pseudodifferential Equations and Applications

Ubiquitous Quantum Structure

Ubiquitous Quantum Structure

Probability And Randomness: Quantum Versus Classical

Probability And Randomness: Quantum Versus Classical

Quantum Methods In Social Science: A First Course

Quantum Methods In Social Science: A First Course

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