1,976 research outputs found
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 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 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 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
Water quality monitoring: a ‘toolbox’ in response to the EU’s Water Framework Directive requirements
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, -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 -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
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