Non Archimedean Analysis Quantum Paradoxes Dynamical Systems And Biological Models

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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models

Andrei Y. Khrennikov
Non Archimedean Analysis Quantum Paradoxes Dynamical Systems and Biological Models Book PDF

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 45,5 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789400914834

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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models by Andrei Y. Khrennikov Pdf

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

Andrei Y. Khrennikov
Non Archimedean Analysis Quantum Paradoxes Dynamical Systems and Biological Models Book PDF

Author : Andrei Y. Khrennikov
Publisher : Springer
Page : 376 pages
File Size : 51,5 Mb
Release : 1997-09-30
Category : Science
ISBN : 9780792348009

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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models by Andrei Y. Khrennikov Pdf

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

M. Berz,Khodr Shamseddine
Advances in p adic and Non Archimedean Analysis Book PDF

Author : M. Berz,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 47,9 Mb
Release : 2010-02-17
Category : Mathematics
ISBN : 9780821847404

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Advances in $p$-adic and Non-Archimedean Analysis by M. Berz,Khodr Shamseddine Pdf

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

Helge Glöckner,Alain Escassut,Khodr Shamseddine
Advances in Non Archimedean Analysis Book PDF

Author : Helge Glöckner,Alain Escassut,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 43,5 Mb
Release : 2016-05-20
Category : Functional analysis
ISBN : 9781470419882

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Advances in Non-Archimedean Analysis by Helge Glöckner,Alain Escassut,Khodr Shamseddine Pdf

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.

P-adic Deterministic and Random Dynamics

Andrei Y. Khrennikov,Marcus Nilsson
P adic Deterministic and Random Dynamics Book PDF

Author : Andrei Y. Khrennikov,Marcus Nilsson
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 55,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781402026607

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P-adic Deterministic and Random Dynamics by Andrei Y. Khrennikov,Marcus Nilsson Pdf

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.

Advances in Non-Archimedean Analysis and Applications

W. A. Zúñiga-Galindo,Bourama Toni
Advances in Non Archimedean Analysis and Applications Book PDF

Author : W. A. Zúñiga-Galindo,Bourama Toni
Publisher : Springer Nature
Page : 326 pages
File Size : 41,9 Mb
Release : 2021-12-02
Category : Mathematics
ISBN : 9783030819767

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Advances in Non-Archimedean Analysis and Applications by W. A. Zúñiga-Galindo,Bourama Toni Pdf

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.

Derivatives

Espen Gaarder Haug
Derivatives Book PDF

Author : Espen Gaarder Haug
Publisher : John Wiley & Sons
Page : 400 pages
File Size : 45,7 Mb
Release : 2013-10-18
Category : Business & Economics
ISBN : 9781118836828

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Derivatives by Espen Gaarder Haug Pdf

Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models

Gibbs Measures In Biology And Physics: The Potts Model

Utkir A Rozikov
Gibbs Measures In Biology And Physics The Potts Model Book PDF

Author : Utkir A Rozikov
Publisher : World Scientific
Page : 367 pages
File Size : 41,8 Mb
Release : 2022-07-28
Category : Mathematics
ISBN : 9789811251252

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Gibbs Measures In Biology And Physics: The Potts Model by Utkir A Rozikov Pdf

This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds

A.K. Prykarpatsky,I.V. Mykytiuk
Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds Book PDF

Author : A.K. Prykarpatsky,I.V. Mykytiuk
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 40,5 Mb
Release : 2013-04-09
Category : Science
ISBN : 9789401149945

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,I.V. Mykytiuk Pdf

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

Quantum Bio-informatics III

Luigi Accardi,Wolfgang Freudenberg,Masanori Ohya
Quantum Bio informatics III Book PDF

Author : Luigi Accardi,Wolfgang Freudenberg,Masanori Ohya
Publisher : World Scientific
Page : 512 pages
File Size : 53,8 Mb
Release : 2010
Category : Science
ISBN : 9789814304054

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Quantum Bio-informatics III by Luigi Accardi,Wolfgang Freudenberg,Masanori Ohya Pdf

The purpose of this proceedings volume is to look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigms for information and life sciences on the basis of quantum theory. The main areas in this volume are all related to one of the following subjects: (1) quantum information, (2) bio-informatics and (3) the interrelation between (1) and (2).

Ultrametric Functional Analysis

Bertin Diarra
Ultrametric Functional Analysis Book PDF

Author : Bertin Diarra
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 40,6 Mb
Release : 2005
Category : Topological fields
ISBN : 9780821836842

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Ultrametric Functional Analysis by Bertin Diarra Pdf

With contributions by leading mathematicians, this proceedings volume reflects the program of the Eighth International Conference on $p$-adic Functional Analysis held at Blaise Pascal University (Clermont-Ferrand, France). Articles in the book offer a comprehensive overview of research in the area. A wide range of topics are covered, including basic ultrametric functional analysis, topological vector spaces, measure and integration, Choquet theory, Banach and topological algebras,analytic functions (in particular, in connection with algebraic geometry), roots of rational functions and Frobenius structure in $p$-adic differential equations, and $q$-ultrametric calculus. The material is suitable for graduate students and researchers interested in number theory, functionalanalysis, and algebra.

Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems

Masanori Ohya,I. Volovich
Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano and Bio systems Book PDF

Author : Masanori Ohya,I. Volovich
Publisher : Springer Science & Business Media
Page : 768 pages
File Size : 40,6 Mb
Release : 2011-01-15
Category : Science
ISBN : 9789400701717

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Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems by Masanori Ohya,I. Volovich Pdf

This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.

Probability and Randomness

Andrei Khrennikov
Probability and Randomness Book PDF

Author : Andrei Khrennikov
Publisher : World Scientific
Page : 300 pages
File Size : 43,9 Mb
Release : 2016-03-04
Category : Mathematics
ISBN : 9781783267989

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Probability and Randomness by Andrei Khrennikov Pdf

' 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. Contents:Foundations of ProbabilityRandomnessSupplementary Notes on Measure-theoretic and Frequency ApproachesIntroduction to Quantum FormalismQuantum and Contextual ProbabilityInterpretations of Quantum Mechanics and ProbabilityRandomness: Quantum Versus ClassicalProbabilistic Structure of Bell''s ArgumentQuantum Probability Outside of Physics: from Molecular Biology to Cognition Readership: Researchers in mathematical physics, probability and statistics. Keywords:Kolmogorov Axiomataics;Randomness;Independence;Quantum Probability'

Advances in Physarum Machines

Andrew Adamatzky
Advances in Physarum Machines Book PDF

Author : Andrew Adamatzky
Publisher : Springer
Page : 839 pages
File Size : 47,6 Mb
Release : 2016-01-09
Category : Technology & Engineering
ISBN : 9783319266626

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Advances in Physarum Machines by Andrew Adamatzky Pdf

This book is devoted to Slime mould Physarum polycephalum, which is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralized actuation. The ease of culturing and experimenting with Physarum makes this slime mould an ideal substrate for real-world implementations of unconventional sensing and computing devices The book is a treatise of theoretical and experimental laboratory studies on sensing and computing properties of slime mould, and on the development of mathematical and logical theories of Physarum behavior. It is shown how to make logical gates and circuits, electronic devices (memristors, diodes, transistors, wires, chemical and tactile sensors) with the slime mould. The book demonstrates how to modify properties of Physarum computing circuits with functional nano-particles and polymers, to interface the slime mould with field-programmable arrays, and to use Physarum as a controller of microbial fuel cells. A unique multi-agent model of slime is shown to serve well as a software slime mould capable for solving problems of computational geometry and graph optimization. The multiagent model is complemented by cellular automata models with parallel accelerations. Presented mathematical models inspired by Physarum include non-quantum implementation of Shor's factorization, structural learning, computation of shortest path tree on dynamic graphs, supply chain network design, p-adic computing and syllogistic reasoning. The book is a unique composition of vibrant and lavishly illustrated essays which will inspire scientists, engineers and artists to exploit natural phenomena in designs of future and emergent computing and sensing devices. It is a 'bible' of experimental computing with spatially extended living substrates, it spanstopics from biology of slime mould, to bio-sensing, to unconventional computing devices and robotics, non-classical logics and music and arts.

Theory of P-adic Distributions

S. Albeverio,V. M. Shelkovich
Theory of P adic Distributions Book PDF

Author : S. Albeverio,V. M. Shelkovich
Publisher : Cambridge University Press
Page : 369 pages
File Size : 47,8 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 9780521148566

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Theory of P-adic Distributions by S. Albeverio,V. M. Shelkovich Pdf

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