The difficulties associated with the appraisal of the determinacy properties of a three-dimensional sy em are circumvented by the introdu ion of a new geometrical argument. It brings about a complete typology of the eigenvalues moduli in discrete time three-dimensional dynamical sy ems and then provides a new apparatus for assessing from a geometrical andpoint the emergence of local bifurcation...

− The influence of IR radiation diffraction upon geometrical resolution of the IR line scanner has been analysed in the paper. Analysis of IR line scanner properties in band 3 – 5 μm and 8 – 12 μm proved that when applying the aperture diaphragms the influence of the radiant diffraction upon geometrical resolution may be significant. This influence is stronger for larger fnumbers N in the appli...

Topological energy bands have important geometrical properties described by the Berry curvature. We show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field. Using...

Modern data analysis tools have to work on high-dimensional data, whose components are not independently distributed. High-dimensional spaces show surprising, counter-intuitive geometrical properties that have a large influence on the performances of data analysis tools. Among these properties, the concentration of the norm phenomenon results in the fact that Euclidean norms and Gaussian kernel...

We describe the geometrical properties of solid's shadows projected onto a flat plane by point-light sources. Even though the shape and position of each element are arbitrary and unknown, we indicate that there exists a certain constraint between three shadows on the plane; i.e., three cross points determined by pairs of tangential lines must sit on a straight line. This property is considered ...

We study the geometrical properties of the subgroups of the mutliplicative group of a "nite extension of a "nite "eld endowed with its vector space structure and we show that in some cases the associated projective space has a natural group structure. We construct some cyclic codes related to Reed}Muller codes by evaluating polynomials on these subgroups. The geometrical properties of these gro...

This paper proposes a new geometrical structure for stereoscopic vision using omnidirectional cameras. The motivation of this work comes from the desire to equip a small hopping robot with an efficient and robust vision system to perform self localization during exploration missions. Because of size and weight constraints, we selected the Panoramic Annular Lens, for which no geometric model of ...