Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models write by Andrei Y. Khrennikov. This book was released on 2013-03-07. Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models available in PDF, EPUB and Kindle. 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.
Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models write by Andrei Y. Khrennikov. This book was released on 1997-09-30. Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models available in PDF, EPUB and Kindle. 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.
Advances in $p$-adic and Non-Archimedean Analysis
Advances in $p$-adic and Non-Archimedean Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in $p$-adic and Non-Archimedean Analysis write by M. Berz. This book was released on 2010-02-17. Advances in $p$-adic and Non-Archimedean Analysis available in PDF, EPUB and Kindle. This volume contains the proceedings of the Tenth International Conference on $p$-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008. This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.
Advances in Non-Archimedean Analysis
Advances in Non-Archimedean Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Non-Archimedean Analysis write by Helge Glöckner. This book was released on 2016-05-20. Advances in Non-Archimedean Analysis available in PDF, EPUB and Kindle. This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Advances in Non-Archimedean Analysis and Applications
Advances in Non-Archimedean Analysis and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Non-Archimedean Analysis and Applications write by W. A. Zúñiga-Galindo. This book was released on 2021-12-02. Advances in Non-Archimedean Analysis and Applications available in PDF, EPUB and Kindle. This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role – a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems – for instance, proteins – asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
