Local refinable finitely generated shift-invariant spaces play a significant role in many areas of approximation theory and geometric design. In this paper we present a new approach to the construction of such spaces. We begin with a refinable function ψ : R → Rm which is supported on [0, 1]. We are interested in spaces generated by a function φ : R → Rn built from the shifts of ψ.

Weakly symmetric spaces are particular Riemannian homogeneous spaces which have been introduced by Selberg [21] in 1956 in the framework of his trace formula. They attracted only little interest until the author and Vanhecke [7] found a simple geometric characterization of weakly symmetric spaces which lead to a large number of new examples. The purpose of this note is to present a survey about...

The size of the experimental enclosure used in a reorientation paradigm appears to have a profound effect on very young children (Learmonth, Newcombe, & Huttenlocher, 2001; Learmonth, Nadel, & Newcombe, 2002) and non-human species (Sovrano, Bisazza, & Vallortigara, 2005; Sovrano, & Vallortigara, 2006; Vallortigara, Feruglio, & Sovrano, 2005). Greater preference has been found for geometric info...

Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context of Thurston’s 3-dimensional geometrization program. The basic problem is for a given topology Σ an...

When operating in dark and confined spaces, the capacity of robots to localise an absolute reference frame is utmost importance. This letter presents localisation system, using deep 3D landmarks, for known spaces. The system estimates robot's relative visual inertial odometry. Local landmarks are extracted from view. Similar are, also, prior map which then registered with local provide via exte...