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

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

A fitness model for the Italian Interbank Money Market

We use the theory of complex networks in order to quantitatively characterize the formation of communities in a particular financial market. The system is composed by different banks exchanging on a daily basis loans and debts of liquidity. Through topological analysis and by means of a model of network growth we can determine the formation of different group of banks characterized by different business strategy. The model based on Pareto's Law makes no use of growth or preferential attachment and it reproduces correctly all the various statistical properties of the system. We believe that this network modeling of the market could be an efficient way to evaluate the impact of different policies in the market of liquidity.Comment: 5 pages 5 figure

Cryogenic light detectors with enhanced performance for rare events physics

We have developed and tested a new way of coupling bolometric light detectors to scintillating crystal bolometers based upon simply resting the light detector on the crystal surface, held in position only by gravity. This straightforward mounting results in three important improvements: (1) it decreases the amount of non-active materials needed to assemble the detector, (2) it substantially increases the light collection efficiency by minimizing the light losses induced by the mounting structure, and (3) it enhances the thermal signal induced in the light detector thanks to the extremely weak thermal link to the thermal bath. We tested this new technique with a 16 cm$^2$ Ge light detector with thermistor readout sitting on the surface of a large TeO$_2$ bolometer. The light collection efficiency was increased by greater than 50\% compared to previously tested alternative mountings. We obtained a baseline energy resolution on the light detector of 20~eV RMS that, together with increased light collection, enabled us to obtain the best $\alpha$ vs $\beta/\gamma$ discrimination ever obtained with massive TeO$_2$ crystals. At the same time we achieved rise and decay times of 0.8 and 1.6 ms, respectively. This superb performance meets all of the requirements for the CUPID (CUORE Upgrade with Particle IDentification) experiment, which is a 1-ton scintillating bolometer follow up to CUORE.Comment: 6 pages, 4 figure

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

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

When the associated graded ring of a semigroup ring is Complete Intersection

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and gamma-rectangular Ap\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterisation for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection.Comment: 24 page

A comparison of high-frequency cross-correlation measures

On a high-frequency scale the time series are not homogeneous, therefore standard correlation measures can not be directly applied to the raw data. There are two ways to deal with this problem. The time series can be homogenised through an interpolation method [1] (linear or previous tick) and then the Pearson correlation statistic computed. Recently, methods that can handle raw non-synchronous time series have been developed [2,4]. This paper compares two traditional methods that use interpolation with an alternative method applied directly to the actual time series

Patterns on the numerical duplication by their admissibility degree

We develop the theory of patterns on numerical semigroups in terms of the admissibility degree. We prove that the Arf pattern induces every strongly admissible pattern, and determine all patterns equivalent to the Arf pattern. We study patterns on the numerical duplication $S \Join^d E$ when $d \gg0$. We also provide a definition of patterns on rings

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.