Associated graded rings of one-dimensional analytically irreducible rings II

Lance Bryant noticed in his thesis that there was a flaw in our paper "Associated graded rings of one-dimensional analytically irreducible rings", J. Algebra 304 (2006), 349-358. It can be fixed by adding a condition, called the BF condition. We discuss some equivalent conditions, and show that they are fulfilled for some classes of rings, in particular for our motivating example of semigroup rings. Furthermore we discuss the connection to a similar result, stated in more generality, by Cortadella-Zarzuela. Finally we use our result to conclude when a semigroup ring in embedding dimension at most three has an associated graded which is a complete intersection.Comment: revised argument for Lemma 1.1, results unchange

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

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

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.

On free resolutions of some semigroup rings

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions.Comment: Revised version, with new title, new author and new result

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

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.

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