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.

G protein ss gamma subunits mediate presynaptic inhibition of transmitter release from rat superior cervical ganglion neurones in culture

The activation of presynaptic G protein-coupled receptors (GPCRs) is widely reported to inhibit transmitter release; however, the lack of accessibility of many presynaptic terminals has limited direct analysis of signalling mediators. We studied GPCR-mediated inhibition of fast cholinergic transmission between superior cervical ganglion neurones (SCGNs) in culture. The adrenoceptor agonist noradrenaline (NA) caused a dose-related reduction in evoked excitatory postsynaptic potentials (EPSPs). NA-induced EPSP decrease was accompanied by effects on the presynaptic action potential (AP), reducing AP duration and amplitude of the after-hyperpolarization (AHP), without affecting the pre- and postsynaptic membrane potential. All effects of NA were blocked by yohimbine and synaptic transmission was reduced by clonidine, consistent with an action at presynaptic alpha 2-adrenoceptors. NA-induced inhibition of transmission was sensitive to pre-incubation of SCGNs with pertussis toxin (PTX), implicating the involvement of G alpha(i)/(o)beta y subunits. Expression of G alpha transducin, an agent which sequesters G protein beta gamma (G beta y) subunits, in the presynaptic neurone caused a time-dependent attenuation of NA-induced inhibition. Injection of purified G beta gamma subunits into the presynaptic neurone inhibited transmission, and also reduced the AHP amplitude. Furthermore, NA-induced inhibition was occluded by pre-injection of G beta gamma subunits. The Ca2+ channel blocker Cd2+ mimicked NA effects on transmitter release. Cd2+, NA and G beta gamma subunits also inhibited somatic Ca2+ current. In contrast to effects on AP-evoked transmitter release, NA had no clear action on AP-independent EPSPs induced by hypertonic solutions. These results demonstrate that G beta gamma subunits functionally mediate inhibition of transmitter release by alpha 2-adrenoceptors and represent important regulators of synaptic transmission at mammalian presynaptic terminals.