Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Official warnings on thromboembolism risk with oral contraceptives fail to inform users adequately

Following the 1995 “pill scare” relating to the risk of venous thrombosis from taking second- or third-generation oral contraceptives, the Committee on Safety of Medicines (CSM) withdrew their earlier recommended restrictions on the use of third-generation pills and published recommended wording to be used in patient information leaflets. However, the effectiveness of this wording has not been tested. An empirical study (with 186 pill users, past users, and non-users) was conducted to assess understanding, based on this wording, of the absolute and relative risk of thrombosis in pill users and in pregnancy. The results showed that less than 12% of women in the (higher education) group fully understood the absolute levels of risk from taking the pill and from being pregnant. Relative risk was also poorly understood, with less than 40% of participants showing full understanding, and 20% showing no understanding. We recommend that the CSM revisit the wording currently provided to millions of women in the UK.

Excess open solar magnetic flux from satellite data: 1. Analysis of the third perihelion Ulysses pass

We use the third perihelion pass by the Ulysses spacecraft to illustrate and investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the potential effects of small-scale structure in the heliospheric field (giving fluctuations in the radial component on timescales smaller than 1 h) and kinematic time-of-flight effects of longitudinal structure in the solar wind flow. We show that the flux excess is explained by neither very small-scale structure (timescales < 1 h) nor by the kinematic “bunching effect” on spacecraft sampling. The observed flux excesses is, however, well explained by the kinematic effect of larger-scale (>1 day) solar wind speed variations on the frozen-in heliospheric field. We show that averaging over an interval T (that is long enough to eliminate structure originating in the heliosphere yet small enough to avoid cancelling opposite polarity radial field that originates from genuine sector structure in the coronal source field) is only an approximately valid way of allowing for these effects and does not adequately explain or account for differences between the streamer belt and the polar coronal holes.