NA60 results on phi production in the hadronic and leptonic channels in In-In collisions at 158 GeV

The NA60 experiment at the CERN SPS studied phi meson production in In-In collisions at 158 A GeV via muon and kaon decay channels. Results in the hadronic channel are presented for the first time. These are discussed in the framework of the so-called phi puzzle through the comparison with the previous NA60 measurements in the muon channel. The yield and inverse m_T slopes observed in the two channels are compatible within errors, showing that the large discrepancies seen in Pb-Pb collisions between NA50 (muon pairs) and NA49 (kaon pairs) are not seen in the NA60 In-In data.Comment: 4 pages, 4 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

On Certain Classes of Curve Singularities with Reduced Tangent Cone

We study a class of rational curves with an ordinary singular point, which was introduced in [Geramita and Orecchia, Minimally Generating Ideals Defining Certain Tangent Cones, J. of Algebra 78, No. 1 (1982), 36 – 57]. We find some conditions under which the tangent cone is reduced and we show that the tangent cone is not always reduced. We construct another class of rational curves with an ordinary singular point satisfying the condition required in [Ibid.] and whose tangent cone is always reduced

GLAST, the Gamma-ray Large Area Space Telescope

GLAST, a detector for cosmic gamma rays in the range from 20 MeV to 300 GeV, will be launched in space in 2005. Breakthroughs are expected in particular in the study of particle acceleration mechanisms in space and of gamma ray bursts, and maybe on the search for cold dark matter; but of course the most exciting discoveries could come from the unexpected.Comment: 6 pages, 3 figures. Invited talk at the hird International Workshop "New Worlds in Astroparticle Physics", September 2000, University of the Algarve. Faro, Portugal. To be published in the Proceeding

A remark on Waring decompositions of some special plane quartics

This work concerns Waring decompositions of a certain kind of plane quartics of high rank. The main result is the following. Let x, l_1, ...., l_7 be linear forms and q a quadratic form on a vector space of dimension 3. If x^2q=l_1^4+...+l_7^4 and the lines l_1=0, ..., l_7=0 in P^2 intersect x=0 in seven distinct points, then the line x=0 is (possibly improperly) tangent to the conic q=0

Products of ideals may not be Golod

We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak Golodness of monomial ideals. Along the way, we ask some related questions.Comment: 18 pages, minor changes from first versio

The asymptotic leading term for maximum rank of ternary forms of a given degree

Let $\operatorname{r_{max}}(n,d)$ be the maximum Waring rank for the set of all homogeneous polynomials of degree $d>0$ in $n$ indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when $n,d\ge 3$, the value of $\operatorname{r_{max}}(n,d)$ is known only for $(n,d)=(3,3),(3,4),(3,5),(4,3)$. We prove that $\operatorname{r_{max}}(3,d)=d^2/4+O(d)$ as a consequence of the upper bound $\operatorname{r_{max}}(3,d)\le\left\lfloor\left(d^2+6d+1\right)/4\right\rfloor$.Comment: v1: 10 pages. v2: extended introduction and some mistakes correcte

Stochastic models associated to a Nonlocal Porous Medium Equation

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation. In particular, we focus our attention on the interpretation of the weak solution of the nonlinear diffusion equation by means of random flights.Comment: Published at https://doi.org/10.15559/18-VMSTA112 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/