In this article, first we generalize the concept of complete parts in hyperrings by introducing the concept R-parts in hyperrings and then we study R-closures in hyperrings. Finally we characterize R-closures in hyperfields.

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...

An element of a finitely generated non-Abelian free group F (X) is said to be filling if that element has positive translation length in every very small minimal isometric action of F (X) on an R-tree. We give a proof that the set of filling elements of F (X) is exponentially F (X)-generic in the sense of Arzhantseva and Ol’shanskĭı. We also provide an algebraic sufficient condition for an elem...

An A-tree is a metric space in which any two points are joined by a unique arc. Every arc is isometric to a closed interval of R . When a group G acts on a tree (Z-tree) X without inversion, then X/G is a graph. One gets a presentation of G from the quotient graph X/G with vertex and edge stabilizers attached. For a general R-tree X, there is no such combinatorial structure on X/G . But we can ...

We examine the problem of indexing objects in animated movies. We consider an animated movie as consisting of a frame sequence where each frame is described by objects in a 2-dimensional space. The queries of interest are of the form: \\nd the objects that were in area S between frames fi and fj". The straightforward approach to index such objects is to consider the frame sequence as another di...

Several studies have suggested recently that a more dynamic conflict resolution mechanism in the ACT–R cognitive architecture (Anderson & Lebiere, 1998) could improve the decision–making behaviour of cognitive models. This part of ACT–R theory is revisited and a new solution is proposed. The new algorithm (OPTIMIST) has been implemented as an overlay to the ACT–R architecture, and can be used a...