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.

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.

Effect of hyaluronidase on ocular motility and eyelid function in sub-Tenon's anaesthesia: randomised controlled trial

Purpose: To assess the effect of hyaluronidase on eye and eyelid movements when used as an adjunct in sub-Tenon's anaesthesia. Methods: A total of 60 patients who had sub-Tenon's anaesthesia prior to phacoemulsification surgery were divided into two equal groups in a double-masked randomised controlled fashion. Of these, Group A had 4 ml lignocaine 2%, while Group B had 4ml lignocaine 2% with the addition of sodium hyaluronidase 75 IU/ml. Ocular motility, levator, and orbicularis oculi function were measured in all patients at 5 and 8 min. Levator function was scored from 0 (no function) to 3 (complete function) while orbicularis function was scored from 0 to 2. The score for ocular motility was the sum in four positions of gaze, each position scoring from 0 to 2. Results were compared using a nonparametric test. Results Group B achieved significantly better ocular and lid akinesia than Group A both at 5 and 8 min with P < 0.01. The median scores for levator function at 5 and 8 min were 2 for Group A and 0 for Group B. For orbicularis function, the median scores at both time intervals were 2 for Group A and 1 for Group B. For ocular motility, the median score for Group A at 5 min was 3 and at 8 min was 2.5; for Group B at 5 min was 0.5 and at 8 min was 0. Conclusions: The addition of hyaluronidase in sub-Tenon's anaesthesia has a significant effect in improving ocular and lid (levator and orbicularis) akinesia.