Analytically unramified one-dimensional semilocal rings and their value semigroups

AbstractIn a one-dimensional local ring R with finite integral closure each nonzerodivisor has a value in Nd, where d is the number of maximal ideals in the integral closure. The set of values constitutes a semigroup, the value semigroup of R. We investigate the connection between the value semigroup and the ring. There is a particularly close connection for some classes of rings, e.g. Gorenstein rings, Arf rings, and rings of small multiplicity. In many respects, the Arf rings and the Gorenstein rings turn out to be opposite extremes. We give applications to overrings, intersection numbers, and multiplicity sequences in the blow-up sequences studied by Lipman

Puzzling asteroid 21 Lutetia: our knowledge prior to the Rosetta fly-by

A wide observational campaign was carried out in 2004-2009 aimed to complete the ground-based investigation of Lutetia prior to the Rosetta fly-by in July 2010. We have obtained BVRI photometric and V-band polarimetric measurements over a wide range of phase angles, and visible and infrared spectra in the 0.4-2.4 micron range. We analyzed them together with previously published data to retrieve information on Lutetia's surface properties. Values of lightcurve amplitudes, absolute magnitude, opposition effect, phase coefficient and BVRI colors of Lutetia surface seen at near pole-on aspect have been determined. We defined more precisely parameters of polarization phase curve and showed their distinct deviation from any other moderate-albedo asteroid. An indication of possible variations both in polarization and spectral data across the asteroid surface was found. To explain features found by different techniques we propose that (i) Lutetia has a non-convex shape, probably due to the presence of a large crater, and heterogeneous surface properties probably related to surface morphology; (ii) at least part of the surface is covered by a fine-grained regolith with particle size less than 20 microns; (iii) the closest meteorite analogues of Lutetia's surface composition are particular types of carbonaceous chondrites or Lutetia has specific surface composition not representative among studied meteorites

Goto Numbers of a Numerical Semigroup Ring and the Gorensteiness of Associated Graded Rings

The Goto number of a parameter ideal Q in a Noetherian local ring (R,m) is the largest integer q such that Q : m^q is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x^{a_1}, x^{a_2},..., x_{a_{\nu}}]] are characterized using the semigroup of R. This helps in computing them for classes of numerical semigroup rings, as well as on a case-by-case basis. The minimal Goto number of R and its connection to other invariants is explored. Necessary and sufficient conditions for the associated graded rings of R and R/x^{a_1}R to be Gorenstein are also given, again using the semigroup of R.Comment: 36 pages, corrected typos and improved exposition throughout. To appear in Communications in Algebr

Low delta-V near-Earth asteroids: A survey of suitable targets for space missions

In the last decades Near-Earth Objects (NEOs) have become very important targets to study, since they can give us clues to the formation, evolution and composition of the Solar System. In addition, they may represent either a threat to humankind, or a repository of extraterrestrial resources for suitable space-borne missions. Within this framework, the choice of next-generation mission targets and the characterisation of a potential threat to our planet deserve special attention. To date, only a small part of the 11,000 discovered NEOs have been physically characterised. From ground and space-based observations one can determine some basic physical properties of these objects using visible and infrared spectroscopy. We present data for 13 objects observed with different telescopes around the world (NASA-IRTF, ESO-NTT, TNG) in the 0.4 - 2.5 um spectral range, within the NEOSURFACE survey (http://www.oa-roma.inaf.it/planet/NEOSurface.html). Objects are chosen from among the more accessible for a rendez-vous mission. All of them are characterised by a delta-V (the change in velocity needed for transferring a spacecraft from low-Earth orbit to rendez-vous with NEOs) lower than 10.5 km/s, well below the Solar System escape velocity (12.3 km/s). We taxonomically classify 9 of these objects for the first time. 11 objects belong to the S-complex taxonomy; the other 2 belong to the C-complex. We constrain the surface composition of these objects by comparing their spectra with meteorites from the RELAB database. We also compute olivine and pyroxene mineralogy for asteroids with a clear evidence of pyroxene bands. Mineralogy confirms the similarity with the already found H, L or LL ordinary chondrite analogues.Comment: 9 pages, 7 figures, to be published in A&A Minor changes by language edito

Ultraviolet and visible photometry of asteroid (21) Lutetia using the Hubble Space Telescope

The asteroid (21) Lutetia is the target of a planned close encounter by the Rosetta spacecraft in July 2010. To prepare for that flyby, Lutetia has been extensively observed by a variety of astronomical facilities. We used the Hubble Space Telescope (HST) to determine the albedo of Lutetia over a wide wavelength range, extending from ~150 nm to ~700 nm. Using data from a variety of HST filters and a ground-based visible light spectrum, we employed synthetic photometry techniques to derive absolute fluxes for Lutetia. New results from ground-based measurements of Lutetia's size and shape were used to convert the absolute fluxes into albedos. We present our best model for the spectral energy distribution of Lutetia over the wavelength range 120-800 nm. There appears to be a steep drop in the albedo (by a factor of ~2) for wavelengths shorter than ~300 nm. Nevertheless, the far ultraviolet albedo of Lutetia (~10%) is considerably larger than that of typical C-chondrite material (~4%). The geometric albedo at 550 nm is 16.5 +/- 1%. Lutetia's reflectivity is not consistent with a metal-dominated surface at infrared or radar wavelengths, and its albedo at all wavelengths (UV-visibile-IR-radar) is larger than observed for typical primitive, chondritic material. We derive a relatively high FUV albedo of ~10%, a result that will be tested by observations with the Alice spectrograph during the Rosetta flyby of Lutetia in July 2010.Comment: 14 pages, 2 tables, 8 figure

Coordinated thermal and optical observations of Trans-Neptunian object (20000) Varuna from Sierra Nevada

We report on coordinated thermal and optical measurements of trans-Neptunian object (20000) Varuna obtained in January-February 2002, respectively from the IRAM 30-m and IAA 1.5 m telescopes. The optical data show a lightcurve with a period of 3.176+/-0.010 hr, a mean V magnitude of 20.37+/-0.08 and a 0.42+/-0.01 magnitude amplitude. They also tentatively indicate that the lightcurve is asymmetric and double-peaked. The thermal observations indicate a 1.12+/-0.41 mJy flux, averaged over the object's rotation. Combining the two datasets, we infer that Varuna has a mean 1060(+180/-220) km diameter and a mean 0.038(+0.022/-0.010) V geometric albedo, in general agreement with an earlier determination using the same technique.Comment: Accepted for publication in Astronomy & Astrophysics (7 pages, including 3 figures

The Color Distribution in the Edgeworth-Kuiper Belt

We have started since 1997 the Meudon Multicolor Survey of Outer Solar System Objects with the aim of collecting a large and homogeneous set of color data for Trans-Neptunian and Centaurs objects [...] We have a combined sample of 52 B-R color measurements for 8 Centaurs, 22 Classicals, 13 Plutinos, 8 Scattered objects and 1 object with unidentified dynamical class. This dataset is the largest single and homogeneous published dataset to date [...]. A strong (color) correlation with mean excitation velocity points toward a space weathering/impact origin for the color diversity. However, thorough modeling of the collisional/dynamical environment in the Edgeworth-Kuiper belt needs to be done in order to confirm this scenario. We found also that the Classical TNOs consist in the superposition of two distinct populations: the dynamically Cold Classical TNOs (red colors, low i, small sizes) and the dynamically Hot Classical TNOs (diverse colors, moderate and high i, larger sizes). [...] Our specific observation strategy [...] permitted us to highlight a few objects suspected to have true compositional and/or texture variation on their surfaces. These are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77 and should be prime targets for further observations [...]. Our survey has also highlighted 1998 SN165 whose colors and dynamical properties puts it in a new dynamical class distinct from the Classicals, its previously assigned dynamical class.Comment: Accepted for publication in Astronomical Journal (38 pages, inc. 11 figures

Physical properties of ESA Rosetta target asteroid (21) Lutetia: Shape and flyby geometry

Aims. We determine the physical properties (spin state and shape) of asteroid (21) Lutetia, target of the ESA Rosetta mission, to help in preparing for observations during the flyby on 2010 July 10 by predicting the orientation of Lutetia as seen from Rosetta. Methods. We use our novel KOALA inversion algorithm to determine the physical properties of asteroids from a combination of optical lightcurves, disk-resolved images, and stellar occultations, although the latter are not available for (21) Lutetia. Results. We find the spin axis of (21) Lutetia to lie within 5 degrees of ({\lambda} = 52 deg., {\beta} = -6 deg.) in Ecliptic J2000 reference frame (equatorial {\alpha} = 52 deg., {\delta} = +12 deg.), and determine an improved sidereal period of 8.168 270 \pm 0.000 001 h. This pole solution implies the southern hemisphere of Lutetia will be in "seasonal" shadow at the time of the flyby. The apparent cross-section of Lutetia is triangular as seen "pole-on" and more rectangular as seen "equator-on". The best-fit model suggests the presence of several concavities. The largest of these is close to the north pole and may be associated with large impacts.Comment: 17 pages, 5 figures, 3 tables, submitted to Astronomy and Astrophysic

Marco Polo: near Earth object sample return mission

Marco Polo is a joint European-Japanese mission of sample return from a Near Earth Object. The Marco Polo proposal was submitted to ESA on July 2007 in the framework of the Cosmic Vision 2015-2025 context, and on October 2007 passed the first evaluation process. The primary objectives of this mission is to visit a primitive NEO, belonging to a class that cannot be related to known meteorite types, to characterize it at multiple scales, and to bring samples back to Earth. Marco Polo will give us the first opportunity for detailed laboratory study of the most primitive materials that formed the planets. This will allow us to improve our knowledge on the processes which governed the origin and early evolution of the Solar System, and possibly of the life on Earth

Optical devices provide unprecedented insights into the laser cleaning of calcium oxalate layers

Abstract Calcium oxalates are insoluble colorless or whitish salts constituting noble patina, on both natural and artificial stone artworks' surfaces, the presence of which is extremely valued. The oxalates are not considered detrimental to the substrate, however, being often accompanied by other substances such as gypsum, silicates, and pigmented particles. They may form very adherent, relatively thick and colored layers creating disfiguring effects and hindering legibility of the pictorial surface. For this reason it may be appropriate to diminish their thickness, but patina's partial preservation is particularly required calling for extremely gradual and controllable cleaning approach. Thinning of calcium oxalate patina from a detached 16th century fresco (from Sansepolcro) was performed through the use of laser (Nd:YAG and Er:YAG) systems and chemical means (Carbogel loaded 5 wt.% of tetrasodium EDTA). Optical coherence tomography (OCT), providing a non-invasive stratigraphic cross-section of the examined surface, allowed to distinguish the oxalate from the underlying original layers and therefore to have an overview about its distribution, to numerically evaluate patina's thickness range and to provide the information on the amount of the material both removed and left on the artwork's surface. Laser scanning conoscopic microprofilometry allowed for a high-density sampling of the artwork's surface providing a three-dimensional model of the surface pattern. The obtained 3D models were used to estimate the amount of material removed and to compare them with those provided by OCT. The successful exploitation of the proposed exceptional cleaning monitoring methodology may be seen as an innovative and valid support for the restorers in the conservation of mural painting or other surfaces covered by oxalate layers and may pilot more targeted, cautious and respectful cleaning intervention