Andrei Khrennikov

Linnaeus University

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Vladimir Anashin

Lomonosov Moscow State University

Warren Siegel

Stony Brook University

Steven Duplij

University of Münster

Antoine Van Proeyen

KU Leuven

Jian-zu Zhang

South China Agricultural University

Dimitry Leites

Stockholm University

François Gieres

Université Claude Bernard Lyon 1

Howard J. Schnitzer

Brandeis University

Rabindra N. Mohapatra

University of Maryland, College Park

Bernard de Wit

National Institute for Subatomic Physics

Cooperative Institutions

Linnaeus University

European Organization for Nuclear Research

The Abdus Salam International Centre for Theoretical Physics (ICTP)

Centre National de la Recherche Scientifique

State University of New York

Växjö Kommun

Max Planck Institute for Physics

The University of Tokyo

Johns Hopkins University

Harvard University

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p-Adic Superanalysis

Springer eBooks (1994)

Andrei Khrennikov

Ultrametric space

10.1007/978-94-015-8356-5_9

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Criteria of measure-preserving for p -adic dynamical systems in terms of the van der Put basis

Journal of Number Theory (2012)

Andrei Khrennikov Ekaterina Yurova

Basis (linear algebra)

Haar measure

Dynamical system (definition)

Representation

10.1016/j.jnt.2012.08.013

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Citations (38)

P-ADIC DYNAMICAL SYSTEMS AND NEURAL NETWORKS

Mathematical Models and Methods in Applied Sciences (1999)

Sergio Albeverio Andrei Khrennikov B. Tirozzi

A p-adic model which describes a large class of neural networks is presented. In this model the states of neurons are described by digits in the canonical expansion of a p-adic number. Thus each p-adic number represents a configuration of firing and non firing neurons. The process of recognition of patterns is investigated in the P-adic framework. We study heteroassociative and autoassociative nets. P-adic dynamical systems are used to describe a feedback process for autoassociative nets.

Dynamical system (definition)

10.1142/s0218202599000634

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Citations (15)

Superschwarzian

Springer eBooks (2004)

Yolanda Lozano Steven Duplij Malte Henkel Malte Henkel Euro Spallucci

Particle (ecology)

10.1007/1-4020-4522-0_590

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P-adic Dynamical Representation of Gene Expression

AIP conference proceedings (2007)

Andrei Khrennikov

We perform geometrization of genetics by representing genetic information by points of the 4‐adic information space. By well known theorem of number theory this space can also be represented as the 2‐adic space. The process of DNA‐reproduction is described by the action of a 4‐adic (or equivalently 2‐adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem..

Genetic Code

Representation

Dynamical system (definition)

Code (set theory)

10.1063/1.2713475

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Physics Beyond The Set-Theoretic Axiom of Foundation

AIP conference proceedings (2009)

Andrei Khrennikov Andrew Schumann Luigi Accardi Guillaume Adenier Christopher A. Fuchs

Classical mechanics implicitly use Archimedes' axiom, according to that everything may be measured by a rigid scale. Uncertainty in quantum mechanics shows the limits of applying Archimedes' axiom. The negation of Archimedes' axiom is derivative from the negation of the set‐theoretic axiom of foundation. The latter postulates that the set‐membership relation is well‐founded: for every set there exists no infinitely descending chain. Denying the foundation axiom in number systems implies setting a non‐Archimedean ordering structure. The main claim of our paper is that physical reality may be regarded as non‐well‐founded in the framework of probabilities distributed on non‐Archimedean ordering structures, in particular, distributed on p‐adic numbers.

Constructive set theory

Negation

Urelement

Zermelo–Fraenkel set theory

Foundation (evidence)

10.1063/1.3109965

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Citations (7)

Supersymmetric Quantum Chromodynamics, electric realization

Springer eBooks (2004)

Yolanda Lozano Steven Duplij Malte Henkel Malte Henkel Euro Spallucci

10.1007/1-4020-4522-0_604

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Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

Russian Journal of Mathematical Physics (2017)

Klaudia Oleschko Andrei Khrennikov

Ultrametric space

10.1134/s1061920817040094

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Citations (3)

Analysis on a Superspace over Banach Superalgebras

Springer eBooks (1999)

Andrei Khrennikov

10.1007/978-94-011-4609-8_2

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Harmonic, Wavelet and P-Adic Analysis

WORLD SCIENTIFIC eBooks (2007)

Nguyen Minh Chuong Yu. V. Egorov Andrei Khrennikov Yves Meyer D. Mumford

Wavelets and Harmonic Analysis: Wavelets and Other Tools: Wavelets and Expectations: A Different Path to Wavelets (K E Gustafson) Multiwavelets. Some Approximations. Theoretic Properties. Samping on the Interval and Translational Invariance (P Massopust) Harmonic Analysis: On Multiple Solutions for the Elliptic Boundary Value Problem with Two Critical Exponents (Yu V Egorov & Y Ilyasov) Some Singular Perturbation Problems Related to the Navier-Stokes Equations (M Hamouda & R Temam) p-Adic and Stochastic Analysis: Over p-Adic Fields: p-Adic and Group-Valued Probabilities (A Khrennikov) Archimedean Stochastic Analysis: Infinite-Dimensional Harmonic Analysis from the Viewpoint of White Noise Theory (T Hida) Stochastic Integral Equations of Fredholm Type (S Ogawa) and other papers.

Harmonic

10.1142/6373

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Citations (40)