The Extremal Structure Of Locally Compact Convex Sets

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved

Radio Emission Signatures in the Crab Pulsar

Our high time resolution observations of individual pulses from the Crab pulsar show that both the time and frequency signatures of the interpulse are distinctly different from those of the main pulse. Main pulses can occasionally be resolved into short-lived, relatively narrow-band nanoshots. We believe these nanoshots are produced by soliton collapse in strong plasma turbulence. Interpulses at centimeter wavelengths are very different. Their dynamic spectrum contains regular, microsecond-long emission bands. We have detected these bands, proportionately spaced in frequency, from 4.5 to 10.5 GHz. The bands cannot easily be explained by any current theory of pulsar radio emission; we speculate on possible new models.Comment: 26 pages, 10 figures, to appear in Ap

An Infrared Study of the Circumstellar Material Associated with the Carbon Star R Sculptoris

The asymptotic giant branch (AGB) star R Sculptoris (R Scl) is one of the most extensively studied stars on the AGB. R Scl is a carbon star with a massive circumstellar shell ($M_{shell}\sim 7.3\times10^{-3}~M_{\odot}$) which is thought to have been produced during a thermal pulse event $\sim2200$ years ago. To study the thermal dust emission associated with its circumstellar material, observations were taken with the Faint Object InfraRed CAMera for the SOFIA Telescope (FORCAST) at 19.7, 25.2, 31.5, 34.8, and 37.1 $\mu$m. Maps of the infrared emission at these wavelengths were used to study the morphology and temperature structure of the spatially extended dust emission. Using the radiative transfer code DUSTY and fitting the spatial profile of the emission, we find that a geometrically thin dust shell cannot reproduce the observed spatially resolved emission. Instead, a second dust component in addition to the shell is needed to reproduce the observed emission. This component, which lies interior to the dust shell, traces the circumstellar envelope of R Scl. It is best fit by a density profile with $n \propto r^{\alpha}$ where $\alpha=0.75^{+0.45}_{-0.25}$ and dust mass of $M_d=9.0^{+2.3}_{-4.1}\times10^{-6}~M_{\odot}$. The strong departure from an $r^{-2}$ law indicates that the mass-loss rate of R Scl has not been constant. This result is consistent with a slow decline in the post-pulse mass-loss which has been inferred from observations of the molecular gas.Comment: 10 pages, 10 figures, accepted to Ap

What makes the Crab pulsar shine?

Our high time resolution observations of individual pulses from the Crab pulsar show that the main pulse and interpulse differ in temporal behavior, spectral behavior, polarization and dispersion. The main pulse properties are consistent with one current model of pulsar radio emission, namely, soliton collapse in strong plasma turbulence. The high-frequency interpulse is quite another story. Its dynamic spectrum cannot easily be explained by any current emission model; its excess dispersion must come from propagation through the star's magnetosphere. We suspect the high-frequency interpulse does not follow the ``standard model'', but rather comes from some unexpected region within the star's magnetosphere. Similar observations of other pulsars will reveal whether the radio emission mechanisms operating in the Crab pulsar are unique to that star, or can be identified in the general population.Comment: 5 pages, 2 figures, to appear in proceedings of meeting "Forty Years of Pulsars: Millisecond Pulsars, Magnetars and More", Montreal, August 200

Parents' expressed emotion and mood, rather than their physical disability are associated with adolescent adjustment. A longitudinal study of families with a parent with multiple sclerosis

Objective. This study investigated the impact of the severity of parental multiple sclerosis, parents’ expressed emotion and psychological well-being on offspring’s psychological difficulties. Design: A longitudinal study including baseline and 6-month follow-up data collected from parents and children. Subjects: Adolescents (n=75), their parents with multiple sclerosis (n=56) and the partner without multiple sclerosis (n=40) Main measures: Parents completed the Hospital Anxiety and Depression Scale and the Five Minutes Speech Sample, a standardised interview of expressed emotion towards their child. Parents with multiple sclerosis also completed the Expanded Disability Status Scale, a measure of illness severity. Adolescents completed the Strength and Difficulties Questionnaire, a self-report measure of psychological difficulties. Results: Higher depression scores of the parents with multiple sclerosis at baseline correlated with increased adolescents’ internalising symptoms at 6-month follow-up (γdep=0.31, p=.004). Higher expressed emotion scores of parents with multiple sclerosis at baseline were associated with increased adolescent externalising symptoms at 6-month follow-up (γEE=4.35, p=.052). There was no direct effect of severity, duration or type of multiple sclerosis on adolescents’ adjustment at baseline or follow-up. Conclusions: Emotional distress and expressed emotion in parents with multiple sclerosis, rather than the severity and type of multiple sclerosis had an impact on adolescents’ psychological difficulties

Scattering and Diffraction in Magnetospheres of Fast Pulsars

We apply a theory of wave propagation through a turbulent medium to the scattering of radio waves in pulsar magnetospheres. We find that under conditions of strong density modulation the effects of magnetospheric scintillations in diffractive and refractive regimes may be observable. The most distinctive feature of the magnetospheric scintillations is their independence on frequency. Results based on diffractive scattering due to small scale inhomogeneities give a scattering angle that may be as large as 0.1 radians, and a typical decorrelation time of $10^{-8}$ seconds. Refractive scattering due to large scale inhomogeneities is also possible, with a typical angle of $10^{-3}$ radians and a correlation time of the order of $10^{-4}$ seconds. Temporal variation in the plasma density may also result in a delay time of the order of $10^{-4}$ seconds. The different scaling of the above quantities with frequency may allow one to distinguish the effects of propagation through a pulsar magnetosphere from the interstellar medium. In particular, we expect that the magnetospheric scintillations are relatively more important for nearby pulsars when observed at high frequencies.Comment: 19 pages, 1 Figur

A VLA Search for the Geminga Pulsar: A Bayesian Limit on a Scintillating Source

We derive an upper limit of 3 mJy (95% confidence) for the flux density at 317 MHz of the Geminga pulsar (J0633+1746). Our results are based on 7 hours of fast-sampled VLA data, which we averaged synchronously with the pulse period using a period model based on CGRO/EGRET gamma-ray data. Our limit accounts for the fact that this pulsar is most likely subject to interstellar scintillations on a timescale much shorter than our observing span. Our Bayesian method is quite general and can be applied to calculate the fluxes of other scintillated sources. We also present a Bayesian technique for calculating the flux in a pulsed signal of unknown width and phase. Comparing our upper limit of 3 mJy with the quoted flux density of Geminga at 102 MHz, we calculate a lower limit to its spectral index of 2.7. We discuss some possible reasons for Geminga's weakness at radio wavelengths, and the likelihood that many of the unidentified EGRET sources are also radio-quiet or radio-weak Geminga-like pulsars.Comment: 27 pages, including figures. Published in Ap