A compact minimal shadow boundary in Euclidean space is totally geodesic

We prove that a compact minimal shadow boundary of a hypersurface in Euclidean space is totally geodesic. We show that shadow boundaries detect principal directions and umbilical points of a hypersurface. As application we deduce that every shadow boundary of a compact strictly convex surface contains at least two principal direction

Kinematic study of planetary nebulae in NGC 6822

By measuring precise radial velocities of planetary nebulae (which belong to the intermediate age population), H II regions, and A-type supergiant stars (which are members of the young population) in NGC 6822, we aim to determine if both types of population share the kinematics of the disk of H I found in this galaxy. Spectroscopic data for four planetary nebulae were obtained with the high spectral resolution spectrograph Magellan Inamori Kyocera Echelle (MIKE) on the Magellan telescope at Las Campanas Observatory. Data for other three PNe and one H II region were obtained from the SPM Catalog of Extragalactic Planetary Nebulae which employed the Manchester Echelle Spectrometer attached to the 2.1m telescope at the Observatorio Astron\'omico Nacional, M\'exico. In the wavelength calibrated spectra, the heliocentric radial velocities were measured with a precision better than 5-6 km s$^{-1}$. Data for three additional H II regions and a couple of A-type supergiant stars were collected from the literature. The heliocentric radial velocities of the different objects were compared to the velocities of the H i disk at the same position. From the analysis of radial velocities it is found that H II regions and A-type supergiants do share the kinematics of the H I disk at the same position, as expected for these young objects. On the contrary, planetary nebula velocities differ significantly from that of the H I at the same position. The kinematics of planetary nebulae is independent from the young population kinematics and it is closer to the behavior shown by carbon stars, which are intermediate-age members of the stellar spheroid existing in this galaxy. Our results are confirming that there are at least two very different kinematical systems in NGC 6822

On-line identification of seeds in mandarins with magnetic resonance imaging

Mandarins have been inspected using magnetic resonance imaging (MRI) in order to detect the presence of seeds. To enhance contrast between seeds and pulp, effective transverse relaxation time-weighted fast low angle shot images (703 ms acquisition time) were acquired. Stationary fruits were imaged and then the images were segmented to extract several features. The maximum radius of the region containing the seeds and the central axis rmax, and the perimeter of this region P were the most powerful features for discrimination between seedless and seed-containing fruits. Such features were the most robust since they showed the lowest noise-to-signal ratios (N/S). The proportions of correct classification were 88.9% and 86.7% for seedless and seed-containing fruits, respectively, under MRI stationary conditions. The performance under on-line conditions was evaluated by imaging the fruits while conveyed at 54 mm/s. An analysis of variance with the features extracted from the static images and the motion-corrected dynamic images showed that there were statistically indistinguishable. The proportions of correct classification were 92.5% and 79.5% for the seedless and seed-containing category, respectively, under MRI dynamic conditions. Reduction in the distance between categories for rmax was addressed as the main cause for the decrease in discrimination performance. The robustness of the motion correction procedure was highlighted by the low differences in the N/S ratio and the noise-to-measured range ratios between static and dynamic features