Abstract:
We study the Horn problem in the context of algebraic codes on a smooth projective curve defined over a finite field, reducing the problem to the representation theory of the special linear group $SL(2,F_q)$. We characterize the coefficients that appear in the Kronecker product of symmetric functions in terms of Gromov-Witten invariants of the Hilbert scheme of points in the plane. In addition we classify all the algebraic codes defined over the rational normal curve.

Abstract:
Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.

Abstract:
We study plane algebraic curves defined over a field k of arbitrary characteristic as coverings of the the projective line and the problem of enumerating branched coverings of $\mathbb{P}^{1}$ by using combinatorial methods.

Abstract:
We study cyclic finite Galois extensions of the rational function field of the projective line P^{1}(F_q) over a finite field F_q with q elements defined by considering quotient curves by finite subgroups of the projective linear group PGL(2,q), and we enumerate them expressing the count in terms of Stirling numbers.

Abstract:
A long standing conjecture, known to us as the Eisenbud Goto conjecture, states that an n-dimensional variety embedded with degree $d$ in the $N$- dimensional projective space is $(d-(N-n)+1)$-regular in the sense of Castelnuovo-Mumford. In this work the conjecture is proved for all smooth varieties $X$ embedded by the complete linear system associated with a very ample line bundle $L$ such that $\Delta (X,L) \le 5$ where $\Delta (X,L) = \dim{X} + \deg{X} -h^0(L).$ As a by-product of the proof of the above result the projective normality of a class of surfaces of degree nine in $\Pin{5}$ which was left as an open question in a previous work of the second author and S. Di Rocco alg-geom/9710009 is established. The projective normality of scrolls $X =\Proj{E}$ over a curve of genus 2 embedded by the complete linear system associated with the tautological line bundle assumed to be very ample is investigated. Building on the work of Homma and Purnaprajna and Gallego alg-geom/9511013, criteria for the projective normality of three-dimensional quadric bundles over elliptic curves are given, improving some results due to D. Butler.

Abstract:
We model and compute the probability distribution of the letters in random generated words in a language by using the theory of set partitions, Young tableaux and graph theoretical representation methods. This has been of interest for several application areas such as network systems, bioinformatics, internet search, data mining and computacional linguistics.

Abstract:
In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle which is ample and normally generated is automatically very ample. Therefore the condition found in Butler's work, together with Miyaoka's well known ampleness criterion, give a sufficient condition for the very ampleness of D on X. This work is devoted to the study of numerical criteria for very ampleness of divisors D which do not satisfy the above criterion, in the case of C elliptic. Numerical conditions for the very ampleness of D are proved,improving existing results. In some cases a complete numerical characterization is found.

Abstract:
The global economic crisis is affecting performances of not-for-profits. At the same time donors are targeted by a pressing good-cause related marketing, so that the competition for philanthropy is particularly keen. U.S. universities can be public, not-for-profit and for-profit. U.S. not-for-profit universities are confronted with different marketing, fundraising and revenue diversification. Above all, marketing concerns customers and their segmentation and their purchasing-power exploitation; fundraising aims to gain the trustworthiness of donors, instead. The aim of this paper is the analysis of the revenue diversification of a sample of 100 U.S. not-for-profit universities according to IRS (Internal Revenue Service) Forms. These 100 U.S. universities had the highest 2012’s revenues for the Guidestar ranking (www.guidestar.org). The cluster analysis gives evidence that the highest gain and the highest solvency are both connected with the implementation of revenue diversification for one profile. The most crowded cluster is the Marketing Expert with the second highest gain.

Abstract:
The contemporary crisis is giving evidence of failing macroeconomic theories and policies, after decades of focusing on the aggregate domestic demand and the role of the public expenditure. The contemporary crisis has shown the weakness of fiscal policy. With very low interest rates, the monetary policy does not seem to provide an alternative exit strategy out of the crisis, too. In this paper we discuss the hypothesis that GDP can still be a reliable estimate of growth. Nevertheless, at crisis times, only if the focus is on the foreign demand like International Tourism Receipts and Exports, and Exports can be an exit strategy. One component of Exports and International Tourism Receipts are worthy of attention. Thanks to a cluster analysis of per year variations of International Tourism Receipts (ITRs), GDP and Exports (World Bank Database) from 2007 to 2011, average positive variations of GDPs are matching with positive ITRs and Exports for “clusters” of countries. Performances of Europe and USA are worse than China, Brazil, India and South Africa and these continents and countries are separated in two different clusters. This result can be related to an increase of trade in emerging economies more than in mature ones, whose exit out of the crisis is much more demanding. The research confirms that Tourism and Exports are having an impact on the growth at different intensities (Europe and America vs. Asia) at crisis times.

Abstract:
The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such threefolds of degree from 7 to 11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed. A relationship with the locus of good determinantal subschemes is investigated