Oscillation properties for parabolic equations of neutral type

summary:The oscillation of the solutions of linear parabolic differential equations with deviating arguments are studied and sufficient conditions that all solutions of boundary value problems are oscillatory in a cylindrical domain are given

Polarization in early optical afterglows of gamma-ray bursts driven by precessing jets

Jet precessions are widely involved in astrophysical phenomena from galaxies to X-ray binaries and gamma-ray bursts (GRBs). Polarization presents a unique probe of the magnetic fields in GRB jets. The precession of GRBs relativistic jets will change the geometry within the observable emitting region of the jet, which can potentially affect the polarization of the afterglow. In this paper, we take into account jet precession to study the polarization evolution and corresponding light curves in GRB early optical afterglows with ordered and random magnetic field geometries. We find that the jet precession in long-lived engines can significantly reduce the polarization degree (PD) regardless of the magnetic field structure. The strongest PD attenuation is found when the line of sight is aligned with the precession axis. Our results show that jet precession can provide new insight into the low PD measured in the early optical afterglows of GRBs.Comment: 10 pages, 3 figures, 1 table, accepted for publication in Ap

Inhibition of Return in the visual field

Inhibition of return (IOR) as an indicator of attentional control is characterized by an eccentricity effect, that is, the more peripheral visual field shows a stronger IOR magnitude relative to the perifoveal visual field. However, it could be argued that this eccentricity effect may not be an attention effect, but due to cortical magnification. To test this possibility, we examined this eccentricity effect in two conditions: the same-size condition in which identical stimuli were used at different eccentricities, and the size-scaling condition in which stimuli were scaled according to the cortical magnification factor (M-scaling), thus stimuli being larger at the more peripheral locations. The results showed that the magnitude of IOR was significantly stronger in the peripheral relative to the perifoveal visual field, and this eccentricity effect was independent of the manipulation of stimulus size (same-size or size-scaling). These results suggest a robust eccentricity effect of IOR which cannot be eliminated by M-scaling. Underlying neural mechanisms of the eccentricity effect of IOR are discussed with respect to both cortical and subcortical structures mediating attentional control in the perifoveal and peripheral visual field