In this work an R-tree variant, which uses minimum volume covering ellipsoids instead of usual minimum bounding rectangles, is presented. The most significant aspects, which determine R-tree index structure performance, is an amount of dead space coverage and overlaps among the covering regions. Intuitively, ellipsoid as a quadratic surface should cover data more tightly, leading to less dead s...

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.

The current study has determined the toxicity effects of copper nanoparticles on the some vital organs such as gill, liver and kidney of Caspian Roach; Rutillus rutillus caspicus. For this purpose, 120 fishes were used as experimental samples and exposed to 0.1, 0.2 and 0.5 mg/L of Cu nanoparticles for 21 days, and 30 fishes assumed as the experiment control. The mean water temperature...

The research was accomplished in order to study behavioral and histopathological effects of Copper on Rutilus rutilus caspicus under experimental condition. The study was performed using Water Static Method during 96 hours. 15 fish with averaged weight 2?0.5 g in weight were encountered to different concentrations (0, 0.1, 0.2, 0.3, 0.4 mg/l) of Copper. A group of fish was considered as control...

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...