In the era of huge datasets, the top-k search becomes an effective way to decrease the search time of top-k objects. The original top-k search requires a monotone combination function and lists of objects ordered by attribute values. Our approach of the top-k search is motivated by complex user preferences over product catalogues. Such user preferences are composed of the local user preferences...

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 ...