e-Skeletons®

semigroups with inverse skeletons and zappa-sz'{e}p products

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green's relations $mbox{$...

Semigroups with inverse skeletons and Zappa-Sz$acute{rm e}$p products

The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ Esubseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${mathc...

Implementation Skeletons in Eden : Low - E ort Parallel Programming ?

Ultrametric Skeletons

We prove that for every ε ∈ (0, 1) there exists Cε ∈ (0,∞) with the following property. If (X, d) is a compact metric space and μ is a Borel probability measure on X then there exists a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and a probability measure ν supported on S satisfying ν (Bd(x, r)) 6 (μ(Bd(x,Cεr)) 1−ε for all x ∈ X and r ∈ (0,∞). The dependen...

Electrostatic skeletons

Let u be the equilibrium potential of a compact set K in R. An electrostatic skeleton of K is a positive measure μ such that the closed support S of μ has connected complement and no interior, and the Newtonian (or logarithmic, when n = 2) potential of μ is equal to u near infinity. We prove the existence of an electrostatic skeleton for every convex polytope. Our proof raises several interesti...