We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that cla...

Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...

The Genocchi numbers and polynomials possess many interesting properties and are arising in many areas of mathematics and physics. Recently, many mathematicians have studied in the area of the q-Genocchi numbers and polynomials see 1–13 . In this paper, we construct a new type of q-Genocchi numbers G α,β n,q and polynomials G α,β n,q x with weight α and weak weight β. Throughout this paper, we ...

It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring of P−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebr...

Let p be a fixed prime number. Throughout this paper, p, p , and p will denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of the algebraic closure of p , respectively. Let be the set of natural numbers, and let ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Let q be regarded as either a complex number q ∈ or a p-adic n...

Let p be a fixed odd prime. Throughout this paper Zp, Qp, C and Cp will respectively, denote the ring of p−adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of the algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p −νp(p) = 1 p . When one talks of q-extension, q is variously considered as an indeter...

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using padic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim’s h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question ...

Let p be a fixed odd prime. Throughout this paper Zp,Qp,C, andCp, will, respectively, denote the ring of p-adic rational integers, the field, of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z N ∪ {0}. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1 see 1–14 . When one speaks of ...

Let p be a fixed odd prime number. Throughout this paper, Zp,Qp,C, and Cp denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. Let vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks of q-ext...

Donnay et al. (2019) classified nonsingular quadratic forms Q with integral coefficients and prime numbers p such that the set of quotients values attained for integer arguments is dense in field p-adic numbers. The aim this note to give another proof classification.