P ADIC DETERMINISTIC AND RANDOM DYNAMICS MATHEMATICS AND ITS APPLICATIONS

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P Adic Deterministic And Random Dynamics

Author : Andrei Y. Khrennikov
ISBN : 9781402026607
Genre : Science
File Size : 85.42 MB
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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.
Category: Science

The Arithmetic Of Dynamical Systems

Author : J.H. Silverman
ISBN : 9780387699042
Genre : Mathematics
File Size : 86.8 MB
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This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
Category: Mathematics

Theory Of P Adic Distributions

Author : S. Albeverio
ISBN : 9780521148566
Genre : Mathematics
File Size : 50.36 MB
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A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Category: Mathematics

Mathematical Reviews

Author :
ISBN : UOM:39015078588624
Genre : Mathematics
File Size : 56.48 MB
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Category: Mathematics

P Adic Mathematical Physics

Author : Andreĭ I︠U︡rʹevich Khrennikov
ISBN : 073540318X
Genre : Mathematics
File Size : 85.51 MB
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The subject of this conference was recent developments in p-adic mathematical physics and related areas. The field of p-Adic mathematical physics was conceived in 1987 as a result of attempts to find non-Archimedean approaches to space-time at the Planck scale as well as to strings. Since then, many applications of p-adic numbers and adeles in physics and related sciences have emerged. Some of them are p-adic and adelic string theory, p-adic and adelic quantum mechanics and quantum field theory, ultrametricity of spin glasses, biological and hierarchical systems, p-adic dynamical systems, p-adic probability theory, p-adic models of cognitive processes and cryptography, as well as p-adic and adelic cosmology.
Category: Mathematics

Information Dynamics In Cognitive Psychological Social And Anomalous Phenomena

Author : Andrei Khrennikov
ISBN : 1402018681
Genre : Computers
File Size : 87.62 MB
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This book develops a new physical/mathematical model for the functioning of the human brain, based, not on the modern Newton-Einstein view of physical reality, but on 'information reality'. The work is devoted to the physical-mathematical modeling of (conscious) cognitive phenomena. The most important distinguishing feature of the theory presented here is a new model of mental space, the so-called p-adic hierarchic tree space, and the development of mental analogs of classical and quantum mechanics. Mental processes and more general information processes are handled as a kind of new physical processes. In particular, the procedure of information quantization and an information analog of Bohmian mechanics are developed. Here, mind is a singularity in the mental pilot wave. Applications to neurophysiology, localization of mental function and brain ablations, and psychology (in particular, Freud's psychoanalysis) are considered.Audience: This book will be of interest to researchers working on physical, mathematical, cognitive, neurophysical, psychological and philosophical aspects of human consciousness.
Category: Computers

An Introduction To G Functions

Author : Bernard M. Dwork
ISBN : 0691036810
Genre : Mathematics
File Size : 82.48 MB
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Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.
Category: Mathematics

Physics Briefs

Author :
ISBN : UOM:39015027837122
Genre : Physics
File Size : 29.46 MB
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Category: Physics

Which Degree 1996

Author : Careers Research and Advisory Centre (Cambridge, England)
ISBN : 1860170528
Genre : Universities and colleges
File Size : 40.85 MB
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Category: Universities and colleges