54 research outputs found
Real line bundles on spheres
No full textIn a recent paper the author proved a classification theorem for Atiyah-real vector bundles on spaces with free involutions. This result is now applied to the group of Atiyah-real line (i.e., one-dimensional) bundles on spheres, denoted
L
R
(
S
n
)
{L_R}({S^n})
. It is proved that such bundles are classified by maps into a complex quadric
Q
C
n
Q{C^n}
. Using this classification it is proved that
L
R
(
S
1
)
=
0
{L_R}({S^1}) = 0
and that for
n
≧
3
n \geqq 3
the groups are all isomorphic.</p
Motion detection technology as a tool for cardiopulmonary resuscitation (CPR) quality improvement
No full textThe most popular method of training in basic life support and AED remains instructor-led training courses. Recent reviews provide good evidence to support alternative methods of training including lay instructors, self-directed learning (web, video, poster) and CPR feedback/prompt devices
The Structure Of The Solutions To Semilinear Equations At A Critical Exponent
No full textThis article is concerned with the structure of the solutions to the semilinear elliptic equation (1.1) \Gamma\Deltau = f(jxj)
Correlated X-ray/ultraviolet/optical variability in the very low mass AGN NGC 4395
No full textWe report the results of a 1-yr Swift X-ray/ultraviolet (UV)/optical programme monitoring the dwarf Seyfert nucleus in NGC4395 in 2008-2009. The UV/optical flux from the nucleus was found to vary dramatically over the monitoring period, with a similar pattern of variation in each of the observed UV/optical bands (spanning 1900-5500 Å). In particular, the luminosity of NGC4395 in the 1900 Å band changed by more than a factor of 8 over the monitoring period. The fractional variability was smaller in the UV/optical bands than that seen in the X-rays, with the X-ray/optical ratio increasing with increasing flux. Pseudo-instantaneous flux measurements in the X-ray and each UV/optical band were well correlated, with cross-correlation coefficients of ≥0.7, significant at 99.9per cent confidence. Archival Swift observations from 2006 sample the intra-day X-ray/optical variability on NGC4395. These archival data show a very strong correlation between the X-ray and b bands, with a cross-correlation coefficient of 0.84 (significant at >99per cent confidence). The peak in the cross-correlation function is marginally resolved and asymmetric, suggesting that X-rays lead the b band, but by ≤1h. In response to recent (2011 August) very high X-ray flux levels from NGC4395 we triggered Swift target of opportunity observations, which sample the intra-hour X-ray/UV variability. These observations indicate, albeit with large uncertainties, a lag of the 1900 Å band behind the X-ray flux of ∼400s. The tight correlation between the X-ray and UV/optical lightcurves, together with the constraints we place on the lag time-scale, is consistent with the UV/optical variability of NGC4395 being primarily due to reprocessing of X-ray photons by the accretion disc
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The structure of the solutions to semilinear equations at a critical exponent
No full textThis paper is concerned with the structure of the solutions to subcritical elliptic
equations related to the Matukuma equation. In certain cases the complete structure of the
solution set is known, and is comparable to that of the original Matukuma equation. Here we
derive sufficient conditions for a more complicated solution set consisting of; (i)
crossing solutions for small initial conditions and large initial conditions; (ii) at least
one open interval of slowly decaying solutions; and (iii) at least two rapidly decaying
solutions. As a consequence we obtain multiplicity results for rapidly decaying, or minimal
solutions
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