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...

In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures is the overlap of the bounding boxes in the directory, which increases with growing dimension. To avoid this p...

We propose a spatio-temporal access method for objects that move through a set of fixed and disjoint regions. The proposal is based on an R-tree, on a temporal access method and on a hashing scheme. With our method it is possible to respond to queries of the timeslice and interval types as well as queries about the trajectory that an object has followed. It is also possible to process spatio-te...