A metric condition for a closed circular set to be a set of uniqueness

H$^*$-condition on the set of submodules of a module

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

A necessary condition for a Shearlet system to be a frame via admissibility

    Necessary conditions for  shearlet  and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

Coupled coincidence point theorems for maps under a new invariant set in ordered cone metric spaces

 In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.

A RELATION BETWEEN THE CATEGORIES Set * , SetT, Set AND SetT

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

A minimum data set for chronic venous disease