In the paper we describe basin of attraction of the p-adic dynamical system f(x) = x + ax. Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs. Mathematics Subject Classification: 37E99, 37B25, 54H20, 12J12.

In the paper we describe basin of attraction p-adic dynamical system G(x) = (ax)(x+ 1). Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs. Mathematics Subject Classification: 37E99, 37B25, 54H20, 12J12.

In this paper, we present a new image denoising method for removing Gaussian noise from corrupted image by using shearlet transform and nonlinear diffusion. The image is decomposed by the shearlet transform to obtain the shearlet coefficients in each subband; then a diffusion scheme based on statistical property of shearlet coefficients is used to shrink noisy shearlet coefficients. The test sh...

Abstract. Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the utilization of parabolic scaling. One prominent example is the shearlet system. Our objective in this paper is three-fold: We firstly de...

We describe an algorithm for solving systems of univariate p-adic constraints. In analogy with univariate real constraints, we formalize univariate p-adic constraints as univariate polynomial equations and order comparisons between p-adic values of univariate polynomials. Systems of constraints are arbitrary boolean combinations of such constraints. Our method combines techniques of Presburger ...

In this paper, we first develop a digital shearlet theory which is rationally designed in the sense that it is the digitalization of the existing shearlet theory for continuum data. This shows that shearlet theory indeed provides a unified treatment for the continuum and digital realm. Secondly, we discuss our implementation of the associated digital shearlet transform. This software package ca...

The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...

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 ...

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...