In the framework of adelic approach we consider real and p-adic properties of dynamical system given by linear fractional map f(x) = (ax + b)/(cx + d), where a, b, c, and d are rational numbers. In particular, we investigate behavior of this adelic dynamical system when fixed points are rational. It is shown that any of rational fixed points is p-adic indifferent for all but a finite set of pri...

The discrete Lotka–Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natura...

In this work we describe the use of truncated p-adic expansion for handling rational numbers by parallel algorithms for symbolic computation. As a case study we propose a parallel implementation for solving linear systems over the rationals. The parallelization is based on a multiple homomorphic image technique and the result is recovered by a parallel version of the Chinese remainder algorithm...

The aim of this manuscript is to examine and survey various formulae for Fubini type numbers polynomials with application the p-adic integrals some special polynomials. Relations related polynomials, Bernoulli numbers, Euler Stirling combinatorial are given. Moreover, by using generating functions their functional equations, new including Hermite Lah Finally, remarks on results presented.

We study and investigate the p-adic arithmetic along with analysis of exact solution of linear equation systems over rational numbers. Initially we study the basic concepts involving the p-adic numbers and why they form a better representation. After that we describe a parallel implementation of an algorithm for solving systems of linear equations over the field of rational number based on the ...

The so-called essential matrix relates corresponding points of two images from the same scene in 3D, and allows to solve the relative pose problem for the two cameras up to a global scaling factor, if the camera calibrations are known. We will discuss how Hensel’s lemma from number theory can be used to find geometric approximations to solutions of the equations describing the essential matrix....

The aim of this short review is to attract the attention of the pseudo-differential community to possibilities in the development of operator calculus for symbols (depending on p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of this calculus were presented in works of the authors of this paper in order to perform p-adic valued quantization. Unfortunately, this ...