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...

It is shown that if $A \subseteq \mathbb{R}^3$ a Borel set of Hausdorff dimension $\dim A \in (3/2,5/2)$, then for a.e. $\theta [0,2\pi)$ the projection $\pi_{\theta}(A)$ $A$ onto 2-dimensional plane orthogonal to $\frac{1}{\sqrt{2}}(\cos \theta, \sin 1)$ satisfies \pi_{\theta}(A) \geq \max\left\{\frac{4\dim A}{9} + \frac{5}{6},\frac{2\dim A+1}{3} \right\}$. This improves bound Oberlin and Ober...

An “automatic continuity” question has naturally occurred since Roger Howe established the local theta correspondence over R: Does the algebraic version of local theta correspondence over R agree with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.

Abstract In this paper, we mainly consider the real interpolation spaces for variable Lebesgue defined by decreasing rearrangement function and corresponding martingale Hardy spaces. Let $$0&lt;q\le \infty $$ 0 &lt; q ≤ ∞ </mml:mat...

The reflectance of an absorbing substrate Rtheta(?) is considered as a function of the angle of incidence ? and an incident polarization parameter theta, where cos(2)theta and sin(2)theta give the power fractions of incident radiation that are p-and s-polarized, respectively. Taking GaAs as an example, we find that at certain wavelengths (e.g., 0.248 and 0.620 microm), the R(theta) vs ? curve b...

Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...

The Historical R-tree is a spatio-temporal access method aimed at the retrieval of window queries in the past. The concept behind the method is to keep an R-tree for each timestamp in history, but allow consecutive trees to share branches when the underlying objects do not change. New branches are only created to accommodate updates from the previous timestamp. Although existing implementations...