The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

The contribution of hyperspectral remote sensing to identify vegetation characteristics necessary to assess the fate of Persistent Organic Pollutants (POPs) in the environment

During recent years hyperspectral remote sensing data were successfully used to characterise the state and properties of vegetation. The information on vegetation cover and status is useful for a range of environmental modelling studies. Recent works devoted to the understanding of the fate of Persistent Organic Pollutants (POPs) in the environment showed that forests and vegetation in general act as a «sponge» for chemicals present in air and the intensity of this «capture» effect depends on some vegetation parameters such as surface area, leaf composition, turnover etc. In the framework of the DARFEM experiment conducted in late June 2001, different airborne hyperspectral images were acquired and analysed to derive some vegetation parameters of relevance for multimedia models, such as the spatial distribution of plant species and their relative foliage biomass. The study area, south west of Milan, encompasses a range of land cover types typical of Northern Italy, including intensive poplar plantations and natural broad-leaf forest. An intensive field campaign was accomplished during the aerial survey to collect vegetation parameters and radiometric measurements. Results obtained from the analysis of hyperspectral images, map of vegetation species, Leaf Area Index (LAI) and foliage biomass are presented and discussed

Hilbert functions of schemes of double and reduced points

It remains an open problem to classify the Hilbert functions of double points in P2. Given a valid Hilbert function Hof a zero-dimensional scheme in P2, we show how to construct a set of fat points Z⊆P2of double and reduced points such that HZ, the Hilbert function of Z, is the same as H. In other words, we show that any valid Hilbert function Hof a zero-dimensional scheme is the Hilbert function of a set a positive number of double points and some reduced points. Fo r some families of valid Hilbert functions, we are also able to show that His the Hilbert function of only double points. In addition, we give necessary and sufficient conditions for the Hilbert function of a scheme of a double points, or double points plus one additional reduced point, to be the Hilbert function of points with support on a star configuration of lines

Steiner configurations ideals: Containment and colouring

Given a homogeneous ideal I ⊆ k[x0, …, xn ], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m, r ∈ N, I(m) ⊆ Ir holds. In the last years, several conjectures have been posed on this problem, creating an active area of current interests and ongoing investigations. In this paper, we investigated the Stable Harbourne Conjecture and the Stable Harbourne–Huneke Conjecture, and we show that they hold for the defining ideal of a Complement of a Steiner configuration of points in Pnk. We can also show that the ideal of a Complement of a Steiner Configuration of points has expected resurgence, that is, its resurgence is strictly less than its big height, and it also satisfies Chudnovsky and Demailly’s Conjectures. Moreover, given a hypergraph H, we also study the relation between its colourability and the failure of the containment problem for the cover ideal associated to H. We apply these results in the case that H is a Steiner System

Anisotropic flows and shear viscosity of the Quark-Gluon plasma within a transport approach

In this talk we discuss the build up of elliptic flow v2 and high order harmonics v3, v4 and v5 for a fluid at fixed η/s by mean of an event-by-event transport approach. We discuss the effect of the η/s ratio on the build up of the vn(pT). In particular we study the effect of a temperature dependent η/s for two different beam energies: RHIC for Au+Au at p s = 200GeV and LHC for Pb+ Pb at p s = 2.76 TeV. We find that for the two different beam energies considered t he suppression of the vn(pT) due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. In ultra-central collisions the vn(pT) show a strong sensitivity to the η/s ratio in the QGP phase and this sensitivity increase with the increase of the order of the harmonic

Entrepreneurial intention studies: A hybrid bibliometric method to identify new directions for theory and research

Fragmentation is the main obstacle to scientific progress on entrepreneurial intention. To address this issue, we systematise the current literature with a hybrid bibliometric method that combines co-citation and bibliographic coupling analysis for the first time in entrepreneurial intention studies to show the field's knowledge base and research fronts and to examine how divergent perspectives have challenged the core knowledge of the field. We highlight three recurring dimensions of entrepreneurial intention studies: (1) personal factors, (2) social factors and (3) investigational settings. In addition to introducing new constructs, divergent perspectives have emphasised the interplay between these components and challenged the mechanisms connecting them. Based on these findings, we extend previous classifications in the literature by providing a framework that integrates divergent perspectives with the field's knowledge base, helping establish future research avenues and improving the theorising process of entrepreneurial intention

Determination of the photodisintegration reaction rates involving charged particles: systematical calculations and proposed measurements based on Extreme Light Infrastructure - Nuclear Physics (ELI-NP)

Photodisintegration reaction rates involving charged particles are of relevance to the p-process nucleosynthesis that aims at explaining the production of the stable neutron-deficient nuclides heavier than iron. In this study, the cross sections and astrophysical rates of (g,p) and (g,a) reactions for about 3000 target nuclei with 10<Z<100 ranging from stable to proton dripline nuclei are computed. To study the sensitivity of the calculations to the optical model potentials (OMPs), both the phenomenological Woods-Saxon and the microscopic folding OMPs are taken into account. The systematic comparisons show that the reaction rates, especially for the (g,a) reaction, are dramatically influenced by the OMPs. Thus the better determination of the OMP is crucial to reduce the uncertainties of the photodisintegration reaction rates involving charged particles. Meanwhile, a gamma-beam facility at ELI-NP is being developed, which will open new opportunities to experimentally study the photodisintegration reactions of astrophysics interest. Considering both the important reactions identified by the nucleosynthesis studies and the purpose of complementing the experimental results for the reactions involving p-nuclei, the measurements of six (g,p) and eight (g,a) reactions based on the gamma-beam facility at ELI-NP and the ELISSA detector for the charged particles detection are proposed, and the GEANT4 simulations are correspondingly performed. The minimum required energies of the gamma-beam to measure these reactions are estimated. It is shown that the direct measurements of these photonuclear reactions within the Gamow windows at T_9=2.5 for p-process are fairly feasible and promising at ELI-NP. The expected experimental results will be used to constrain the OMPs of the charged particles, which can eventually reduce the uncertainties of the reaction rates for the p-process nucleosynthesis.Comment: 14 pages, 8 figures, Phys. Rev. C accepte