The Fourier dimension is not finitely stable

The Fourier dimension is not in general stable under finite unions of sets. Moreover, the stability of the Fourier dimension on particular pairs of sets is independent from the stability of the compact Fourier dimension.Comment: Improves one of the results of arXiv:1406.148

Fourier dimension of random images

Given a compact set of real numbers, a random $C^{m + \alpha}$-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number $s$, almost surely has Fourier dimension greater than or equal to $s / (m + \alpha)$. This is used to show that every Borel subset of the real numbers of Hausdorff dimension $s$ is $C^{m + \alpha}$-equivalent to a set of Fourier dimension greater than or equal to $s / (m + \alpha)$. In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under $C^m$-diffeomorphisms for any $m$.Comment: Minor improvements of expositio

Equatorial mass loss from Be stars

Be stars are thought to be fast rotating stars surrounded by an equatorial disc. The formation, structure and evolution of the disc are still not well understood. In the frame of single star models, it is expected that the surface of an initially fast rotating star can reach its keplerian velocity (critical velocity). The Geneva stellar evolution code has been recently improved, in order to obtain some estimates of the total mass loss and of the mechanical mass loss rates in the equatorial disc during the whole critical rotation phase. We present here the first results of the computation of a grid of fast rotating B stars evolving towards the Be phase, and discuss the first estimates we obtained.Comment: 2 pages, 2 figures To appear in the proceedings of the IAUS 272 on "Active OB stars: structure, evolution, mass loss and critical limits

Boundary conditions for the single-factor term structure equation

We study the term structure equation for single-factor models that predict nonnegative short rates. In particular, we show that the price of a bond or a bond option is the unique classical solution to a parabolic differential equation with a certain boundary behavior for vanishing values of the short rate. If the boundary is attainable then this boundary behavior serves as a boundary condition and guarantees uniqueness of solutions. On the other hand, if the boundary is nonattainable then the boundary behavior is not needed to guarantee uniqueness but it is nevertheless very useful, for instance, from a numerical perspective.Comment: Published in at http://dx.doi.org/10.1214/10-AAP698 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian sequential testing of the drift of a Brownian motion

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing in time, which enables us to prove monotonicity and continuity of the optimal stopping boundaries as well as to characterize them completely in the finite-horizon case as the unique continuous solution to a pair of integral equations. In the infinite-horizon case, the boundaries are shown to solve another pair of integral equations and a convergent approximation scheme for the boundaries is provided. Also, we describe the dependence between the prior distribution and the long-term asymptotic behaviour of the boundaries.Comment: 28 page

Hausdorff dimension of random limsup sets

We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in $\mathbf{R}^d$ whose centres are independent, identically distributed random variables. The formulas obtained involve the rate of decrease of the radii of the balls and multifractal properties of the measure according to which the balls are distributed, and generalise formulas that are known to hold for particular classes of measures.Comment: 26 pages, 2 figures; v2: Minor correction

Mass loss of red supergiants: a key ingredient for the final evolution of massive stars

Mass-loss rates during the red supergiant phase are very poorly constrained from an observational or theoretical point of view. However, they can be very high, and make a massive star lose a lot of mass during this phase, influencing considerably the final evolution of the star: will it end as a red supergiant? Will it evolve bluewards by removing its hydrogen-rich envelope? In this paper, we briefly summarise the effects of this mass loss and of the related uncertainties, particularly on the population of blue supergiant stars.Comment: 6 pages, 2 figures, to appear in the proceedings of the conference "The physics of evolved stars" dedicated to the memory of O. Chesneau (Nice, 2015). Will be published in EAS publications serie

Resolving Malpractice Disputes: Imaging the Jury’s Shadow

The ability of juries to resolve malpractice suits was studied. Results showed that most of the time, jury outcomes represent a fair resolution of the claim, but the risk that the result will not be fair is real and troubling