Star configuration points and plane curves

2siLet ℓ1,...,ℓ1 be l lines in ℙ2 such that no three lines meet in a point. Let X(l) be the set of points {ℓi ∩ ℓj {divides} 1 ≤ i < j ≤ l} ⊆ ℙ2. We call X(l) a star configuration. We describe all pairs (d, l) such that the generic degree d curve in ℙ2 contains an X(l). Our proof strategy uses both a theoretical and an explicit algorithmic approach. We also describe how one may extend our algorithmic approach to similar problems. © 2011 American Mathematical Society.openopenCarlini E.; van Tuyl A.Carlini, E.; van Tuyl, A

Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms

Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic discussion. Introducing in the half-line a Fourier-like Transform, the procedure is extended to R^+ and can be easily generalized to R^n and to spherical reference systems.Comment: 12 pages, Contribution to the 30th International Colloquium on Group Theoretical Methods in Physics, July 14-18, 2014, Gent (Belgium

Relative Prym varieties associated to the double cover of an Enriques surface

Given an Enriques surface T , its universal K3 cover f : S → T , and a genus g linear system |C| on T, we construct the relative Prym variety PH = Prymv,H(D/C), where C → |C| and D → |f∗C| are the universal families, v is the Mukai vector (0, [D], 2−2g) and H is a polarization on S. The relative Prym variety is a (2g−2)-dimensional possibly singular variety, whose smooth locus is endowed with a hyperk ̈ahler structure. This variety is constructed as the closure of the fixed locus of a symplectic birational involution defined on the moduli space Mv,H (S). There is a natural Lagrangian fibration η : PH → |C|, that makes the regular locus of PH into an integrable system whose general fiber is a (g − 1)-dimensional (principally polarized) Prym variety, which in most cases is not the Jacobian of a curve. We prove that if |C| is a hyperelliptic linear system, then PH admits a symplectic resolution which is birational to a hyperk ̈ahler manifold of K3[g−1]-type, while if |C| is not hyperelliptic, then PH admits no symplectic resolution. We also prove that any resolution of PH is simply connected and, when g is odd, any resolution of PH has h2,0-Hodge number equal to one

Beyond Gender Differences in U.S. Life Cycle Happiness

An integration of methods and theories from economics, psychology, sociology and gerontology offers a more useful means for understanding gender differences in life-cycle happiness.

Hub Premium, Airport Dominance and Market Power in the European Airline Industry.

Using evidence from an original dataset of more than 12 million fares, this study sheds light on two issues relating to the pricing behaviour of the main European airlines: 1) the extent to which an airline’s dominant position at the origin airport, at the route and the city-pair level affects the airlines’ market power; 2) whether fares follow a monotonic time path consistent with the pursuing of an inter-temporal price discrimination strategy. Our estimates reveal that enjoying a dominant position within a route is conducive to higher fares, possibly because of the limited size of many “natural monopoly” routes that facilitate the incumbent’s engagement in a limit pricing strategy. On the contrary, a larger share within a city-pair does not seem to facilitate the exercise of market power, thereby suggesting the existence of a large degree of substitutability between the routes in a city-pair.on-line pricing; price discrimination; dispersion; yield management.

How are topics born? Understanding the research dynamics preceding the emergence of new areas

The ability to promptly recognise new research trends is strategic for many stake- holders, including universities, institutional funding bodies, academic publishers and companies. While the literature describes several approaches which aim to identify the emergence of new research topics early in their lifecycle, these rely on the assumption that the topic in question is already associated with a number of publications and consistently referred to by a community of researchers. Hence, detecting the emergence of a new research area at an embryonic stage, i.e., before the topic has been consistently labelled by a community of researchers and associated with a number of publications, is still an open challenge. In this paper, we begin to address this challenge by performing a study of the dynamics preceding the creation of new topics. This study indicates that the emergence of a new topic is anticipated by a significant increase in the pace of collaboration between relevant research areas, which can be seen as the ‘parents’ of the new topic. These initial findings (i) confirm our hypothesis that it is possible in principle to detect the emergence of a new topic at the embryonic stage, (ii) provide new empirical evidence supporting relevant theories in Philosophy of Science, and also (iii) suggest that new topics tend to emerge in an environment in which weakly interconnected research areas begin to cross-fertilise

Pricing strategies by European traditional and low cost airlines. Or, when is it the best time to book on line?

It is often assumed that the airlines’ fares increase monotonically over time, peaking a few days before the departure. Using fares for about 650 thousand flights operated by both Low-Cost and Full Service Carriers, we show several instances in which the monotonic property does not hold. We also show that the volatility of fares increase in the last four weeks before departure, which is the period when the airlines can formulate a better prediction for a flight’s load factor. Finally, especially within the last two weeks, Full Service Carriers may offer lower fares than those posted by Low Cost Carriers.on-line pricing; price discrimination; dispersion; yield management.

Pricing strategies by European Low Cost Carriers.

We introduce an on-line pricing tactic where airlines post, at the same time and for the same flight, fares in different currencies that violate the law of One Price. Unexpectedly for an on-line market, we find that price discrimination may be accompanied by arbitrage opportunities and that both tend to persist before a flight’s departure. We find discrimination to be of a competitive type, although arbitrage opportunities are more likely in concentrated routes. Finally, the evidence suggests that discrimination may be used to manage stochastic demand.on-line pricing; price discrimination; Law of One Price; sample selection; dispersion; airlines, exchange rate.