Covering based Rough Sets are an important generalization of Rough Set Theory. Basically, they replace the partition generated from an equivalence relation by a covering. In this context many approximation operators can be defined [16, 26, 27, 28, 34]. In this paper we want to discover relationships among approximation operators defined from neighborhoods. We use the concepts of duality, adjoin...

We show that a mod-ℓ-representation of p-adic group arising from the analogue Yu's construction is supercuspidal if and only it arises representation finite reductive group. This has been previously shown by Henniart Vigneras under assumption second adjointness holds.

Strong and Markov uniqueness problems in L 2 for Dirichlet operators on rigged Hilbert spaces are studied. An analytic approach based on a{priori estimates is used. The extension of the problem to the L p-setting is discussed. As a direct application essential self{ adjointness and strong uniqueness in L p is proved for the generator (with initial domain the bounded smooth cylinder functions) o...