Michele Zorzi and Ramesh R. Rao Abstract—In this paper, we consider the slotted ALOHA protocol with capture, in a mobile communication environment, in the presence of Rayleigh fading and log-normal shadowing. The capture probabilities and their asymptotic value, as the number of colliding packets tends to infinity, are computed. A sufficient condition, under which this limit is positive, is ide...

Let $G$ be a countable monoid and let $A$ an Artinian group (resp. module). $\Sigma \subset A^G$ closed subshift which is also subgroup submodule) of $A^G$. Suppose that $\Gamma$ finitely generated consisting pairwise commuting cellular automata \to \Sigma$ are homomorphisms groups modules) with binary operation given by composition maps. We show the valuation action on $\Sigma$ satisfies natur...

Abstract In this article we study dynamical behaviour of generic Lebesgue measure-preserving interval maps. We show that for each k ⩾ 1 the set periodic points period at least is a Cantor Hausdorff dimension zero and upper box one. Moreover, obtain analogous results also in context circle Furthermore, building on former results, there dense collection transitive maps whose have full measure pos...

Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual trajectories computed in molecular dynamics are accurate for only short time intervals, whereas apparently reliable information can be extracted from very long-tim...

A raster-based computer graphics method of imaging volumetric data (data sampled on a three-dimensional grid) has been added to an existing molecular rendering program. Any molecular property expressed as a 30 grid of scalar data values can be displayed around and inside of the molecular van der Waals surface as a collection of colored clouds and transparent surfaces. Different antical properti...