The purpose of this paper is to contribute the theory profinite semigroups by considering special class consisting those all whose finitely generated closed subsemigroups are countable, which said be locally countable. We also call countable a pseudovariety V (of finite semigroups) for pro-V investigate operations preserving local countability pseudovarieties and show that, in contrast with fin...

We model the societal task of redistricting political districts as a partitioning problem: Given set n points in plane, each belonging to one two parties, and parameter k, our goal is compute partition P plane into regions so that region contains roughly s = n/k points. should satisfy notion "local" fairness, which related core, well-studied concept cooperative game theory. A associated with ma...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...