A family of quotients of the Rees algebra

A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.Comment: 17 pages. To appear on "Communications in Algebra

The dynamics of social interaction with agents’ heterogeneity

We analyze a class of binary dynamic models inspired by [4] on agents’ choices and social interaction. The main feature of our analysis is that agents are heterogeneous, in particular their attitude to interact with the choices of the other agents changes over time endogenously. Although dynamic approaches to the study of models with heterogeneous agents have been already applied in different fields, to our knowledge a complete study of an endogenously varying population of agents has not yet been pursued. As observed in [3], the main problem is given by the fact that with heterogeneous agents the system may be non reversible. We address these problems, we describe the (possible multiple) steady states of the processes involved, we analyze local and global stability and we discuss the similarities and the differences with respect to the literature. Applications are also provided.heterogeneous agent models, intensity-based models, mean field interactions, random utilities, social interactions.

Complete integral closure and strongly divisorial prime ideals

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without {\em prime} strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.Comment: 18 page

Colors and taxonomy of Centaurs and Trans-Neptunian Objects

The study of the surface properties of Centaurs and Trans-Neptunian Objects (TNOs) provides essential information about the early conditions and evolution of the outer Solar System. Due to the faintness of most of these distant and icy bodies, photometry currently constitutes the best technique to survey a statistically significant number of them. Our aim is to investigate color properties of a large sample of minor bodies of the outer Solar System, and set their taxonomic classification. We carried out visible and near-infrared photometry of Centaurs and TNOs, making use, respectively, of the FORS2 and ISAAC instruments at the Very Large Telescope (European Southern Observatory). Using G-mode analysis, we derived taxonomic classifications according to the Barucci et al. (2005a) system. We report photometric observations of 31 objects, 10 of them have their colors reported for the first time ever. 28 Centaurs and TNOs have been assigned to a taxon. We combined the entire sample of 38 objects taxonomically classified in the framework of our programme (28 objects from this work; 10 objects from DeMeo et al. 2009a) with previously classified TNOs and Centaurs, looking for correlations between taxonomy and dynamics. We compared our photometric results to literature data, finding hints of heterogeneity for the surfaces of 4 objects.Comment: 7 pages, 4 figures. To be published in Astronomy and Astrophysic

Aqueous alteration on main belt primitive asteroids: results from visible spectroscopy

This work focuses on the study of the aqueous alteration process which acted in the main belt and produced hydrated minerals on the altered asteroids. The aqueous alteration is particularly important for unraveling the processes occurring during the earliest times of the Solar System history, as it can give information both on the asteroids thermal evolution and on the localization of water sources in the asteroid belt. We present new spectral observations in the visible region of 80 asteroids belonging to the primitive classes C, G, F, B and P. We combine the present observations with the visible spectra of asteroids available in the literature for a total of 600 primitive main belt asteroids. Our analysis shows that the aqueous alteration sequence starts from the P-type objects, practically unaltered, and increases through the F, B, C, and G asteroids. Around 50% of the observed C-type asteroids show absorption features in the vis. range due to hydrated silicates, implying that more than 70% of them will have a 3 $\mu$m absorption band and thus hydrated minerals on their surfaces. The process dominates in primitive asteroids located between 2.3 and 3.1 AU, that is at smaller heliocentric distances than previously suggested. The aqueous alteration process dominates in the 50--240 km sized primitive asteroids, while it is less effective for bodies smaller than 50 km. No correlation is found between the aqueous alteration process and the asteroids albedo or orbital elements. Comparing the $\sim$ 0.7 $\mu$m band parameters of hydrated silicates and CM2 carbonaceous chondrites, we see that the band center of meteorites is at longer wavelengths than that of asteroids. This difference on center positions may be attributed to different minerals abundances, and to the fact that CM2 available on Earth might not be representative of the whole aqueous altered asteroids population.Comment: Icarus, accepted for publication on 28 January 2014 Manuscript pages: 38; Figures: 13 ; Tables:

Identity, reputation and social interaction with an application to sequential voting

We analyze binary choices in a random utility model assuming that the agent's preferences are affected by conformism (with respect to the behavior of the society) and coherence (with respect to his identity). We apply the analysis to sequential voting when voters like to win.identity; reputation; social interaction; random utility models; voting system.

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Arf characters of an algebroid curve

Two algebroid branches are said to be equivalent if they have the same multiplicity sequence. It is known that two algebroid branches $R$ and $T$ are equivalent if and only if their Arf closures, $R'$ and $T'$ have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch. We extend the above equivalence to algebroid curves with $d>1$ branches. An equivalence class is described, in this more general context, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of $\mathbb N^d$. We express this semigroup in terms of a finite set of information, a set of characters of the curve, and apply this result to determine other curves equivalent to a given one.Comment: 17 page