Low Rank Vector Bundles on the Grassmannian G(1,4)

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our notion of $L$-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the classification of rank 2 and rank 3 vector bundles without "inner" cohomology (i.e. H^i_*(E)=H^i(E\otimes\Q)=0 for any $i=2,3,4$) on G(1,4) by studying the associated monads.Comment: 11 pages, no figure

Spacecraft charging and ion wake formation in the near-Sun environment

A three-dimensional (3-D), self-consistent code is employed to solve for the static potential structure surrounding a spacecraft in a high photoelectron environment. The numerical solutions show that, under certain conditions, a spacecraft can take on a negative potential in spite of strong photoelectron currents. The negative potential is due to an electrostatic barrier near the surface of the spacecraft that can reflect a large fraction of the photoelectron flux back to the spacecraft. This electrostatic barrier forms if (1) the photoelectron density at the surface of the spacecraft greatly exceeds the ambient plasma density, (2) the spacecraft size is significantly larger than local Debye length of the photoelectrons, and (3) the thermal electron energy is much larger than the characteristic energy of the escaping photoelectrons. All of these conditions are present near the Sun. The numerical solutions also show that the spacecraft's negative potential can be amplified by an ion wake. The negative potential of the ion wake prevents secondary electrons from escaping the part of spacecraft in contact with the wake. These findings may be important for future spacecraft missions that go nearer to the Sun, such as Solar Orbiter and Solar Probe Plus.Comment: 25 pages, 7 figures, accepted for publication in Physics of Plasma

The Planck-LFI instrument: analysis of the 1/f noise and implications for the scanning strategy

We study the impact of the 1/f noise on the PLANCK Low Frequency Instrument (LFI) osbervations (Mandolesi et al 1998) and describe a simple method for removing striping effects from the maps for a number of different scanning stategies. A configuration with an angle between telescope optical axis and spin-axis just less than 90 degrees (namely 85 degress) shows good destriping efficiency for all receivers in the focal plane, with residual noise degradation < 1-2 %. In this configuration, the full sky coverage can be achieved for each channel separately with a 5 degrees spin-axis precession to maintain a constant solar aspect angle.Comment: submitted to Astronomy and Astrophysics, 12 pages, 15 PostSript figure

La ley nueva y la nueva evangelización. La tradición tomista y la perspectiva moral de Evangelii gaudium

The Pope’s pastoral guidelines in Evangelii gaudium offer the opportunity to rediscover the value of the category law under the guidance of the thomistic tradition present in the papal document. The moral proposal of the Gospel or new law, following the synonymy used by Aquinas, cannot be reduced to a precept or a set of rules; quite the contrary, revisiting the doctrine of the Common Doctor, we may discover the need for wisdom and biblical interpretation of the pillars of Christian morality. In the way of pastoral conversion, the return to the thomist sources illuminates theological reflection again with renewed fertility.Las indicaciones pastorales del Papa Francisco en Evangelii gaudium ofrecen la oportunidad para redescubrir el valor de la categoría ley bajo la guía de la tradición tomista recogida en el documento pontificio. La propuesta moral del Evangelio o ley nueva, siguiendo la sinonimia utilizada por santo Tomás de Aquino, no puede ser reducida a un precepto o una serie de normas; muy por el contrario, revisitando la doctrina del Doctor Común podemos descubrir la necesidad de una hermenéutica sapiencial y profundamente bíblica de uno de los pilares de la moral cristiana. En el camino de la conversión pastoral, el retorno a las fuentes tomistas vuelve a iluminar la reflexión teológica con fecundidad renovada

OH-bearing planar defects in olivine produced by the breakdown of Ti-rich humite minerals from Dabie Shan (China)

The partial breakdown of Ti-chondrodite and Ti-clinohumite during exhumation from ultra-high pressure to amphibolite facies conditions in garnet-pyroxenites from Dabie Shan (China) produces coronas of olivine coexisting with ilmenite blebs. Fourier transform infrared (FTIR) spectra of this newly formed olivine exhibit absorption bands in the hydroxyl-stretching region. Two intense peaks were observed at 3,564 and 3,394 cm-1, identical in energy to peaks in Ti-clinohumite. Transmission electron microscopy (TEM) of the same olivine domains revealed the presence of a complex (001) planar intergrowth. These interlayers have a 1.35 nm repeat distance, which is characteristic of clinohumite. Such interlayers are also enriched in Ti with respect to the adjacent olivine as shown by energy dispersive spectrometry. The combined evidence from FTIR spectroscopy and TEM indicates that OH is incorporated along Ti-clinohumite planar defects. This study provides evidence that the nominally anhydrous phase olivine may contain OH as a humite-type defect beyond the breakdown of the hydrous humite minerals and confirms earlier suggestions that Ti plays a key role in OH incorporation in mantle olivine. We suggest that olivine containing Ti-clinohumite defects is an important phase for water transport in subduction zones and for the storage of water in cold subcontinental mantle. However, these defects are unlikely to be stable in hotter parts of the oceanic mantle such as where basaltic magmas are generated