We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.

p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief re...

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

We propose statistical systems based on p -adic numbers. In the systems, Hamiltonian is a standard real number which given by map from Therefore we can introduce temperature as and calculate thermodynamical quantities like free energy, entropy, specific heat, etc. Although consider very simple system, corresponds to particle moving in one dimensional space, find that there appear behaviors phas...

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...

We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are p-adic in nature.

The purpose of this paper is to study the arithmetic function f : Z+ → Q ∗ + defined by f(2l) = l (∀k, l ∈ N, l odd). We have, for example, f(1) = 1, f(2) = 1, f(3) = 3, f(12) = 1 3 , f(40) = 1 25 , . . . , so it is clear that f(n) is not always an integer. However, we will show in what follows that f satisfies the property that the product of the f(r) for 1 ≤ r ≤ n is always an integer, and it...