Capture Probability in the 3:1 Mean Motion Resonance with Jupiter

We study the capture and crossing probabilities into the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the averaged planar restricted three-body problem based on the symplectic mapping of Hadjidemetriou (1993), adding the secular variations of the orbit of Jupiter and non-symplectic terms to simulate the migration. We found that, for fast migration rates, the captures occur at discrete windows of initial eccentricities whose specific locations depend on the initial resonant angles, indicating that the capture phenomenon is not probabilistic. For slow migration rates, these windows become narrower and start to accumulate at low eccentricities, generating a region of mutual overlap where the capture probability tends to 100%, in agreement with the theoretical predictions for the adiabatic regime. Our simulations allow to predict the capture probabilities in both the adiabatic and non-adiabatic cases, in good agreement with results of Gomes (1995) and Quillen (2006). We apply our model to the case of the Vesta asteroid family in the same context as Roig et al. (2008), and found results indicating that the high capture probability of Vesta family members into the 3:1 mean motion resonance is basically governed by the eccentricity of Jupiter and its secular variations

Minimal Resolution of Relatively Compressed Level Algebras

A relatively compressed algebra with given socle degrees is an Artinian quotient $A$ of a given graded algebra R/\fc, whose Hilbert function is maximal among such quotients with the given socle degrees. For us \fc is usually a ``general'' complete intersection and we usually require that $A$ be level. The precise value of the Hilbert function of a relatively compressed algebra is open, and we show that finding this value is equivalent to the Fr\"oberg Conjecture. We then turn to the minimal free resolution of a level algebra relatively compressed with respect to a general complete intersection. When the algebra is Gorenstein of even socle degree we give the precise resolution. When it is of odd socle degree we give good bounds on the graded Betti numbers. We also relate this case to the Minimal Resolution Conjecture of Mustata for points on a projective variety. Finding the graded Betti numbers is essentially equivalent to determining to what extent there can be redundant summands (i.e. ``ghost terms'') in the minimal free resolution, i.e. when copies of the same $R(-t)$ can occur in two consecutive free modules. This is easy to arrange using Koszul syzygies; we show that it can also occur in more surprising situations that are not Koszul. Using the equivalence to the Fr\"oberg Conjecture, we show that in a polynomial ring where that conjecture holds (e.g. in three variables), the possible non-Koszul ghost terms are extremely limited. Finally, we use the connection to the Fr\"oberg Conjecture, as well as the calculation of the minimal free resolution for relatively compressed Gorenstein algebras, to find the minimal free resolution of general Artinian almost complete intersections in many new cases. This greatly extends previous work of the first two authors.Comment: 31 page

A multi-domain approach to asteroid families identification

Previous works have identified families halos by an analysis in proper elements domains, or by using Sloan Digital Sky Survey-Moving Object Catalog data, fourth release (SDSS-MOC4) multi-band photometry to infer the asteroid taxonomy, or by a combination of the two methods. The limited number of asteroids for which geometric albedo was known until recently discouraged in the past the extensive use of this additional parameter, which is however of great importance in identifying an asteroid taxonomy. The new availability of geometric albedo data from the Wide-field Infrared Survey Explorer (WISE) mission for about 100,000 asteroids significantly increased the sample of objects for which such information, with some errors, is now known. In this work we proposed a new method to identify families halos in a multi-domain space composed by proper elements, SDSS-MOC4 (a*,i-z) colors, and WISE geometric albedo for the whole main belt (and the Hungaria and Cybele orbital regions). Assuming that most families were created by the breakup of an undifferentiated parent body, they are expected to be homogeneous in colors and albedo. The new method is quite effective in determining objects belonging to a family halo, with low percentages of likely interlopers, and results that are quite consistent in term of taxonomy and geometric albedo of the halo members.Comment: 23 pages, 18 figures, 6 tables. Accepted for publication in MNRA

Chemical abundances and kinematics of barium stars

In this paper we present an homogeneous analysis of photospheric abundances based on high-resolution spectroscopy of a sample of 182 barium stars and candidates. We determined atmospheric parameters, spectroscopic distances, stellar masses, ages, luminosities and scale height, radial velocities, abundances of the Na, Al, $alpha$-elements, iron-peak elements, and s-process elements Y, Zr, La, Ce, and Nd. We employed the local-thermodynamic-equilibrium model atmospheres of Kurucz and the spectral analysis code {\sc moog}. We found that the metallicities, the temperatures and the surface gravities for barium stars can not be represented by a single gaussian distribution. The abundances of $alpha$-elements and iron peak elements are similar to those of field giants with the same metallicity. Sodium presents some degree of enrichment in more evolved stars that could be attributed to the NeNa cycle. As expected, the barium stars show overabundance of the elements created by the s-process. By measuring the mean heavy-element abundance pattern as given by the ratio [s/Fe], we found that the barium stars present several degrees of enrichment. We also obtained the [hs/ls] ratio by measuring the photospheric abundances of the Ba-peak and the Zr-peak elements. Our results indicated that the [s/Fe] and the [hs/ls] ratios are strongly anti-correlated with the metallicity. Our kinematical analysis showed that 90% of the barium stars belong to the thin disk population. Based on their luminosities, none of the barium stars are luminous enough to be an AGB star, nor to become self-enriched in the s-process elements. Finally, we determined that the barium stars also follow an age-metallicity relation.Comment: 30 pages, 26 figures, 18 tables, accepted for publication in MNRA

Risk analysis of biodeterioration in contemporary art collections: the poly-material challenge

[EN] Biodeterioration is one of the most common alteration factors affecting cultural heritage, and its appear-ance responds to numerous factors. Awareness of the risk it poses to heritage material and the study of its development is essential. With the mass production evolution of widely accessible materials, the cri-teria for choosing the constituents of a work of art no longer respond to traditional premises, associating the conservation of these new materials with the flawed expectation of longevity and stable resistance to biological attack.This work aims to update the contemporary preventive conservation practice through the review of the biodeterioration risk of indoor poly-material artworks. It also means analyzing the potential incidence of biological agents deteriorating contemporary materials stored in art collections, characterized by their industrial origin, and frequently used in the pieces produced in the current art scene. Due to their char-acteristic agglomeration of components, the artistic object is subjected to complicated surveillance and problematic biological control and eradication, which can often be contraindicated for some constituents.The study encompasses four main points that make up the risk review analysis sequence: a brief art history exposition to understand poly-material creative values; a general definition of terms surrounding biodeterioration; a selection of most used contemporary materials and a study of their biodeterioration risks; and the basic preventive conservation considerations regarding biological attacks. The review con-cludes with a critical analysis of the complicated issue of preventive treatment compatibility, as well as a proposed model of action and consideration towards heritage pieces endangered or affected by biological attacks.The author of the work would like to thank the Universitat Politècnica de València (UPV) and the Department of Conservation and Restoration of Cultural Heritage for their widely accessible resources that made this thorough exploration possible, as well as artist Sarah Meyers Brent (Fig. 6 right), book publisher house Akal (Fig. 2 right) and blog site AITIMinforma (Fig. 7) for granting photographic use permission.Bosch-Roig, P.; Zmeu, CN. (2022). Risk analysis of biodeterioration in contemporary art collections: the poly-material challenge. Journal of Cultural Heritage. 58:33-48. https://doi.org/10.1016/j.culher.2022.09.01433485

Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type

In this paper we show a partial answer the a question of C. Huneke and G. Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded countable Cohen-Macaulay representation type, and assume that R has an isolated singularity. Is R then necessarily of graded finite Cohen-Macaulay representation type? In particular, this question has an affirmative answer for standard graded non-Gorenstein rings as well as for standard graded Gorenstein rings of minimal multiplicity. Along the way, we obtain a partial classification of graded Cohen-Macaulay rings of graded countable Cohen-Macaulay type.Comment: 15 Page