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

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

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

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

Aging functions and multivariate notions of NBU and IFR

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals

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