Criteria of measure-preserving for pp-adic dynamical systems in terms of the van der Put basis

This paper is devoted to (discrete) $p$-adic dynamical systems, an important domain of algebraic and arithmetic dynamics. We consider the following open problem from theory of $p$-adic dynamical systems. Given continuous function $f:Z_p > Z_p.$ Let us represent it via special convergent series, namely van der Put series. How can one specify whether this function is measure-preserving or not for an arbitrary $p$? In this paper, for any prime $p$ we present a complete description of all compatible measure-preserving functions in the additive form representation. In addition we prove the criterion in terms of coefficients with respect to the van der Put basis determining whether a compatible function $f:Z_p > Z_p$ preserves the Haar measure

Layered nanomaterials for renewable energy generation and storage

This study focuses on potential applications of two-dimensional (2D) materials in renewable energy research.</jats:p

T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these

Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure $\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F : Z2 -&gt; Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.Bibliografiskt granskad</p

Nafion/Surface Modified Ceria Hybrid Membranes for Fuel Cell Application

Low chemical durability of proton exchange membranes is one the main factors limiting their lifetime in fuel cells. Ceria nanoparticles are the most common free radical scavengers. In this work, hybrid membranes based on Nafion-117 membrane and sulfonic or phosphoric acid functionalized ceria synthesized from various precursors were prepared by the in situ method for the first time. Ceria introduction led to a slight decrease in conductivity of hybrid membranes in contact with water. At the same time, conductivity of membranes containing sulfonic acid modified ceria exceeded that of the pristine Nafion-117 membrane at 30% relative humidity (RH). Hydrogen permeability decreased for composite membranes with ceria synthesized from cerium (III) nitrate, which correlates with their water uptake. In hydrogen-air fuel cells, membrane electrode assembly fabricated with the hybrid membrane containing ceria synthesized from cerium (IV) sulfate exhibited a peak power density of 433 mW/cm2 at a current density of 1080 mA/cm2, while operating at 60 °C and 70% RH. It was 1.5 times higher than for the pristine Nafion-117 membrane (287 mW/cm2 at a current density of 714 mA/cm2)