P Adic Deterministic And Random Dynamics

Author: Andrei Y. Khrennikov
Editor: Springer Science & Business Media
ISBN: 1402026609
Size: 15,71 MB
Format: PDF, Docs
Read: 752
Download

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.

The Arithmetic Of Dynamical Systems

Author: J.H. Silverman
Editor: Springer Science & Business Media
ISBN: 038769904X
Size: 19,29 MB
Format: PDF, ePub, Mobi
Read: 726
Download

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.

Theory Of P Adic Distributions

Author: S. Albeverio
Editor: Cambridge University Press
ISBN: 0521148561
Size: 11,61 MB
Format: PDF, Mobi
Read: 612
Download

A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.

Mathematical Reviews

Author:
Editor:
ISBN:
Size: 20,88 MB
Format: PDF, Docs
Read: 394
Download


P Adic Mathematical Physics

Author: Andreĭ I︠U︡rʹevich Khrennikov
Editor: Amer Inst of Physics
ISBN: 9780735403185
Size: 20,18 MB
Format: PDF, ePub, Mobi
Read: 820
Download

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.

Information Dynamics In Cognitive Psychological Social And Anomalous Phenomena

Author:
Editor: Springer Science & Business Media
ISBN: 9781402018688
Size: 17,13 MB
Format: PDF, ePub, Mobi
Read: 521
Download

In this book we develop various mathematical models of information dynamics, I -dynamics (including the process of thinking), based on methods of classical and quantum physics. The main aim of our investigations is to describe mathematically the phenomenon of consciousness. We would like to realize a kind of Newton-Descartes program (corrected by the lessons of statistical and quantum mechanics) for information processes. Starting from the ideas of Newton and Descartes, in physics there was developed an adequate description of the dynamics of material systems. We would like to develop an analogous mathematical formalism for information and, in particular, mental processes. At the beginning of the 21st century it is clear that it would be impossible to create a deterministic model for general information processes. A deterministic model has to be completed by a corresponding statistical model of information flows and, in particular, flows of minds. It might be that such an information statistical model should have a quantum-like structure.

Meromorphic Functions Over Non Archimedean Fields

Author: Pei-Chu Hu
Editor: Springer Science & Business Media
ISBN: 9780792365327
Size: 18,74 MB
Format: PDF, ePub, Docs
Read: 537
Download

This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.

Topological Geometrodynamics

Author: Matti Pitkanen
Editor: Bentham Science Publishers
ISBN: 1681081792
Size: 14,61 MB
Format: PDF, ePub, Docs
Read: 463
Download

Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.

An Introduction To G Functions

Author: Bernard M. Dwork
Editor: Princeton University Press
ISBN: 9780691036816
Size: 10,16 MB
Format: PDF, ePub, Mobi
Read: 927
Download

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.

Non Archimedean Analysis Quantum Paradoxes Dynamical Systems And Biological Models

Author: Andrei Y. Khrennikov
Editor: Springer Science & Business Media
ISBN: 9400914830
Size: 16,95 MB
Format: PDF, Kindle
Read: 488
Download

N atur non facit saltus? This book is devoted to the fundamental problem which arises contin uously in the process of the human investigation of reality: the role of a mathematical apparatus in a description of reality. We pay our main attention to the role of number systems which are used, or may be used, in this process. We shall show that the picture of reality based on the standard (since the works of Galileo and Newton) methods of real analysis is not the unique possible way of presenting reality in a human brain. There exist other pictures of reality where other num ber fields are used as basic elements of a mathematical description. In this book we try to build a p-adic picture of reality based on the fields of p-adic numbers Qp and corresponding analysis (a particular case of so called non-Archimedean analysis). However, this book must not be considered as only a book on p-adic analysis and its applications. We study a much more extended range of problems. Our philosophical and physical ideas can be realized in other mathematical frameworks which are not obliged to be based on p-adic analysis. We shall show that many problems of the description of reality with the aid of real numbers are induced by unlimited applications of the so called Archimedean axiom.