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 ...

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....

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...

In this article, we study a class of stochastic partial differential equations with fractional operators subject to some time-independent multiplicative Gaussian noise. We derive sharp conditions, under which unique global $$L^p(\Omega )$$ -solution exists for all $$p\ge 2$$ . case, exact moment asymptotics following the same strategy as that in recent work by Balan et al. (Inst Henri Poincaré ...

We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths quantum scalar fields at different temperature $T_1$ and $T_2$ bilinear couplings between them. particularly focus on entanglement or inseparability property states. The critical temperatures respective oscillators, $T_{1c}$ $T_{2c}$, higher than which disappears, can be determined. It is foun...