The idea of a discrete space-time has been introduced by physicists in the past in several different ways. Heisenberg advocated a fundamental length, Snyder has proposed a position operator with discrete spectrum, Ahmavaara has carried out a physical model on a cubic lattice, which is embedded in a finite linear space over a Galois field. Recently the use of discrete space-time variables in Lat...

BACKGROUND Posterior mapping is an increasingly popular hierarchical Bayesian based method used to infer character histories and reconstruct ancestral states at nodes of molecular phylogenies, notably of morphological characters. As for all Bayesian analyses specification of prior values is an integrative and important part of the analysis. He we provide an example of how alternative prior choi...

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.

We answer a question of I. Juhasz by showing that MA +¬ CH does not imply that every compact ccc space of countable π-character is separable. The space constructed has the additional property that it does not map continuously onto Iω1 .

In particle-in-cell (PIC) simulation, errors in space charge forces are of random character. It results in an unphysical increase of effective beam emittance, even while symplectic integrator is used. To establish quantitative measure of this effect on beam dynamics, an analytical model of equilibrium beam affected by random errors in space charge field calculations is considered. An explicit e...