We prove that the only non-Archimedean strictly convex spaces are zero space and one-dimensional linear over $\, \mathbb{Z}/3\mathbb{Z}$, with any of its trivial norms.

The automaton transformation of infinite words over alphabet Fp = {0, 1, . . . , p− 1}, where p is a prime number, coincide with the continuous transformation (with respect to the p-adic metric) of a ring Zp of p-adic integers. The objects of the study are non-Archimedean dynamical systems generated by automata mappings on the space Zp. Measure-preservation (with the respect to the Haar measure...

It is well known [4] that the non-Archimedean residue class fields K of the ring of continuous real valued functions on a space are realclosed and 7/i-sets. It does not appear to be known that the exponential function in the reals induces an exponential function in K (definitions to follow) ; thus K is exponentially closed. The property of being exponentially closed is a new invariant which wil...

An Archimedean graph in R 2 is any finite subgraph of the vertices and edges of one of the 11 Archimedean tilings of R E shown in Figures 1-3. Archimedean filings are commonly characterized (as in Figures 1-3) by the order in which regular polygons (with unit edges) occur around each vertex of the tiling; see Grtinbaum and Shephard [3]. We use the same description for Archimedean subgraphs. Whe...

Abstract. In this paper we are concentrated on a problem of linear chanceconstrained programming where the constraint matrix is considered random with a known distribution of the matrix rows. The rows are not considered to be independent; instead, we make use of the copula notion to describe the dependence of the matrix rows. In particular, the distribution of the rows is driven by so-called Ar...

We introduce an arithmetic functional equation f(x2+y2)=f(x2)+f(y2) and then investigate stability estimates of the by using Brzdȩk fixed point theorem on a non-Archimedean fuzzy metric space normed space. To apply theorem, proof uses linear relationship between two variables, x y.

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

Purpose Spiral k-space trajectories allow for rapid data acquisition, leading to reduced motion artifacts, and facilitating the imaging of dynamic objects. The spiral trajectory is effective in coronary artery imaging (1). Either numerical (2) or approximate analytic (3) methods were used to calculate the sampling of the trajectory. Improved performance was observed with variable density spiral...