Maximizers for the Strichartz inequality

We compute explicitely the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrodinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer.Comment: 32 pages (uses Tikz/PGF code for pictures). Simplified the computation of some integrals using invariance properties. Corrected a wrong proof of a lemma (thanks to the referee

Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality

We show that constant functions are global maximizers for the adjoint Fourier restriction inequality for the sphere.Comment: corrected few typos and the value of the best constant of the estimate which was not computed correctly in the first draw of the pape

Interval bounds for the optimal burn-in times for concave or convex reward functions

An interesting problem in reliability is to determine the optimal burn-in time. In a previous work, the authors studied the solution of such a problem under a particular cost structure. It has been shown there that a key role in the problem is played by a function $\rho$, representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when $\rho$ is linear. In this paper, we explore further the linear case and use its solutions as a benchmark for determining the locally optimal times when the function $\rho$ is not linear or under a different cost structure

Interactions between ageing and risk properties in the analysis of burn-in problems

Several relevant problems in reliability can be looked at as problems of risk management and of decisions in the face of uncertainty. However, in this frame, the so-called burn-in problem can be seen as a problem of risk taking par excellence. In this paper, we in particular point out some aspects concerning interactions between the probabilistic model for lifetimes and considerations of an economic kind. As one of the features of our work, we hinge on some unexplored connections between ageing properties of a one-dimensional survival function Formula and risk-aversion-type properties of the function u(t) = bG(t), b > 0, when the latter is seen as a utility function

Flipping the roles: Analysis of a university course where students become co-creators of curricula

In this paper I present the transformation of a university course inspired by the theoretical background of the student voice approach (Fielding, 2004a and 2004b; Cook-Sather, 2006) and, in particular, the ways students are encouraged to be \u201cco-creators of curricula\u201d through partnership with faculty (Bovill, Cook\u2010Sather & Felten, 2011). I introduce active learning practices centered on \u201cstudent generated content\u201d (Sener, 2007; Bates et al., 2012), allowing a new rendering of the traditional lesson cycle: frontal lesson, individual study, and final exam. The change in students\u2019 attitude towards study and final exam support the effectiveness of this methodology

Calibration of the Hobson&Rogers model: empirical tests

The path-dependent volatility model by Hobson and Rogers is considered. It is known that this model can potentially reproduce the observed smile and skew patterns of different directions, while preserving the completeness of the market. In order to quantitatively investigate the pricing performance of the model a calibration procedure is here derived. Numerical results based on S&P500 option prices give evidence of the effectiveness of the model.

Missing Links in Multiple Trade Networks

In this paper we develop a network model of international trade which is able to replicate the concentrated and sparse nature of trade data. Our model extends the preferential attachment (PA) growth model to the case of multiple networks. Countries trade a variety of goods of different complexity. Every country progressively evolves from trading less sophisticated to high-tech goods. The probability to capture more trade opportunities at a given level of complexity and to start trading more complex goods are both proportional to the number of existing trade links. We provide a set of theoretical predictions and simulative results. A calibration exercise shows that our model replicates the same concentration level of world trade as well as the sparsity pattern of the trade matrix. Moreover, we find a lower bound for the share of genuine missing trade links. We also discuss a set of numerical solutions to deal with large multiple networks