Abstract Let X be a compact Kähler manifold. $$T_1, \ldots , T_m$$ T 1 , … m closed positive currents of bi-degree (1, 1) on and T an arbitrary current . We introduce the non-pluripolar product re...

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s R-trees (R+-trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and ...

In this paper we describe the equations defining multi-Rees algebra $k[x_1,\dots,x_n][I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where ideals are generated by subsets of $x_1,\dots,x_n$. We also show that a family binomials whose leading terms squrefree, form Gr\"{o}bner basis for with lexicographic order. if remove include $x$'s, then remaining toric ideal associated to multi-fiber ring. However binom...

It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete R-tree; (ii) M is hyperconvex and has unique metric segments.

We present a new spatial index belonging to R-tree family. Since our new index comes out from the R-tree and holds the concept of nonoverlapping nodes we call it R-tree. The original R-tree was designed for both point and spatial data. Using R-tree for indexing spatial data is very inefficient. In our research we face the problem of indexing product catalogues data that can be represented as po...

R-tree based access methods for moving objects are hardly applicable in practice, due mainly to excessive space requirements and high management costs. To overcome the limitations of such R-tree based access methods, we propose a new index structure called AIM (Adaptive cell-based Index for Moving objects). The AIM is a cell-based multiversion access structure adopting an overlapping technique....

We study the structure of a $3-$Leibniz algebra $T$ graded by an arbitrary abelian group $G,$ which is considered dimension and over base field $\bbbf.$ show that form $T=\uu\oplus\sum_jI_j,$ with $\uu$ linear subspace $T_1,$ homogeneous component associated to unit element $1$ in any $I_j$ well described ideal $T,$ satisfying $$ [I_j, T, I_k] = I_k, T] [T, I_j, 0, if $j\neq k.$ In case being m...

A polymorph of RuI$_3$ synthesized under high pressure was found to have a two-layered honeycomb structure. The resistivity exhibits semimetallic behavior, in contrast insulating properties $\alpha$-RuCl$_3$. In addition, Pauli paramagnetic behavior observed the temperature dependence magnetic susceptibility and nuclear spin-lattice relaxation rate 1/$T_1$. band structure calculations indicate ...

A new dynamic multi-dimensional index structure called RSR-tree is proposed, in which splitting operations of leaf nodes and non-leaf nodes are performed separatively. RSR-tree retains the sequence ordering of index records in a leaf node of RS-tree and thus reduces the addressing time cost of disk access while reading data files. In addition, it integrates the characteristic of reducing the ov...