Fourier-Stieltjes algebras of locally compact groupoids

This paper gives a first step toward extending the theory of Fourier-Stieltjes algebras from groups to groupoids. If G is a locally compact (second countable) groupoid, we show that B(G), the linear span of the Borel positive definite functions on G, is a Banach algebra when represented as an algebra of completely bounded maps on a C^*-algebra associated with G. This necessarily involves identifying equivalent elements of B(G). An example shows that the linear span of the continuous positive definite functions need not be complete. For groups, B(G) is isometric to the Banach space dual of C^*(G). For groupoids, the best analog of that fact is to be found in a representation of B(G) as a Banach space of completely bounded maps from a C^*-algebra associated with G to a C^*-algebra associated with the equivalence relation induced by G. This paper adds weight to the clues in the earlier study of Fourier-Stieltjes algebras that there is a much more general kind of duality for Banach algebras waiting to be explored.Comment: 34 page

Claude E. Ramsay to Dr. Silver, 28 June 1961

Professional correspondenc

Investigating the Rotational Phase of Stellar Flares on M dwarfs Using K2 Short Cadence Data

We present an analysis of K2 short cadence data of 34 M dwarfs which have spectral types in the range M0 - L1. Of these stars, 31 showed flares with a duration between $\sim$10-90 min. Using distances obtained from Gaia DR2 parallaxes, we determined the energy of the flares to be in the range $\sim1.2\times10^{29}-6\times10^{34}$ erg. In agreement with previous studies we find rapidly rotating stars tend to show more flares, with evidence for a decline in activity in stars with rotation periods longer than $\sim$10 days. The rotational modulation seen in M dwarf stars is widely considered to result from a starspot which rotates in and out of view. Flux minimum is therefore the rotation phase where we view the main starspot close to the stellar disk center. Surprisingly, having determined the rotational phase of each flare in our study we find none show any preference for rotational phase. We outline three scenarios which could account for this unexpected finding. The relationship between rotation phase and flare rate will be explored further using data from wide surveys such as NGTS and TESS.Comment: Accepted main Journal MNRA

Claude Ramsay to Dr. Silver, 12 February 1962

Professional correspondenc

Swift observations of the 2015 outburst of AG Peg -- from slow nova to classical symbiotic outburst

Symbiotic stars often contain white dwarfs with quasi-steady shell burning on their surfaces. However, in most symbiotics, the origin of this burning is unclear. In symbiotic slow novae, however, it is linked to a past thermonuclear runaway. In June 2015, the symbiotic slow nova AG Peg was seen in only its second optical outburst since 1850. This recent outburst was of much shorter duration and lower amplitude than the earlier eruption, and it contained multiple peaks -- like outbursts in classical symbiotic stars such as Z And. We report Swift X-ray and UV observations of AG Peg made between June 2015 and January 2016. The X-ray flux was markedly variable on a time scale of days, particularly during four days near optical maximum, when the X-rays became bright and soft. This strong X-ray variability continued for another month, after which the X-rays hardened as the optical flux declined. The UV flux was high throughout the outburst, consistent with quasi-steady shell burning on the white dwarf. Given that accretion disks around white dwarfs with shell burning do not generally produce detectable X-rays (due to Compton-cooling of the boundary layer), the X-rays probably originated via shocks in the ejecta. As the X-ray photo-electric absorption did not vary significantly, the X-ray variability may directly link to the properties of the shocked material. AG Peg's transition from a slow symbiotic nova (which drove the 1850 outburst) to a classical symbiotic star suggests that shell burning in at least some symbiotic stars is residual burning from prior novae.Comment: Accepted by MNRAS 23 June 2016. Manuscript submitted in original form 5 April 201

The Turn-On of Mass Transfer in AM CVn Binaries: Implications for RX J0806+1527 and RX J1914+2456

We report on evolutionary calculations of the onset of mass transfer in AM CVn binaries, treating the donor's evolution in detail. We show that during the early contact phase, while the mass transfer rate, \Mdot, is increasing, gravity wave (GW) emission continues to drive the binary to shorter orbital period, \Porb. We argue that the phase where \Mdot > 0 and \nudot > 0 (\nu = 1/\Porb) can last between $10^3$ and $10^6$ yrs, significantly longer than previously estimated. These results are applied to RX J0806+1527 (\Porb = 321 s) and RX J914+2456 (\Porb=569 s), both of which have measured \nudot > 0. \emph{Thus, a \nudot > 0 does not select between the unipolar inductor and accretion driven models proposed as the source of X-rays in these systems}. For the accretion model, we predict for RX J0806 that \ddot{\nu} \approx \ee{1.0-1.5}{-28} Hz s$^{-2}$ and argue that timing observations can probe $\ddot{\nu}$ at this level with a total $\approx 20$ yr baseline. We also place constraints on each system's initial parameters given current observational data.Comment: 5 pages, 3 figures, accepted to ApJ

Solid immersion lens applications for nanophotonic devices

Solid immersion lens (SIL) microscopy combines the advantages of conventional microscopy with those of near-field techniques, and is being increasingly adopted across a diverse range of technologies and applications. A comprehensive overview of the state-of-the-art in this rapidly expanding subject is therefore increasingly relevant. Important benefits are enabled by SIL-focusing, including an improved lateral and axial spatial profiling resolution when a SIL is used in laser-scanning microscopy or excitation, and an improved collection efficiency when a SIL is used in a light-collection mode, for example in fluorescence micro-spectroscopy. These advantages arise from the increase in numerical aperture (NA) that is provided by a SIL. Other SIL-enhanced improvements, for example spherical-aberration-free sub-surface imaging, are a fundamental consequence of the aplanatic imaging condition that results from the spherical geometry of the SIL. Beginning with an introduction to the theory of SIL imaging, the unique properties of SILs are exposed to provide advantages in applications involving the interrogation of photonic and electronic nanostructures. Such applications range from the sub-surface examination of the complex three-dimensional microstructures fabricated in silicon integrated circuits, to quantum photoluminescence and transmission measurements in semiconductor quantum dot nanostructures

The use of segmented regression in analysing interrupted time series studies : an example in pre-hospital ambulance care

Peer reviewedPublisher PD

Systematic review of antimicrobial drug prescribing in hospitals.

Prudent antibiotic prescribing to hospital inpatients has the potential to reduce the incidences of antimicrobial resistance and healthcare-associated infection. We reviewed the literature from January 1980 to November 2003 to identify rigorous evaluations of interventions to improve hospital antibiotic prescribing. We identified 66 studies with interpretable data of which 16 reported 20 microbiological outcomes: Gram negative resistant bacteria (GNRB), 10 studies; Clostridium difficile associated diarrhoea (CDAD), 5 studies; vancomycin resistant enterococci (VRE), 3 studies and methicillin resistant Staphylococcus aureus (MRSA), 2 studies. Four studies provide good evidence that the intervention changed microbial outcomes with low risk of alternative explanations, eight studies provide less convincing evidence and four studies were negative. The strongest and most consistent evidence was for CDAD but we were able to analyse only the immediate impact of interventions because of nonstandardised durations of follow up. The ability to compare results of studies could be substantially improved by standardising methodology and reporting

Acute and chronic effects of multivitamin/mineral supplementation on objective and subjective energy measures

Background: Vitamins and minerals play an essential role within many cellular processes including energy production and metabolism. Previously, supplementation with a multivitamin/mineral (MVM) for ≥28 days resulted in improvements to cognition and subjective state. We have also demonstrated shifts in metabolism during cognitively demanding tasks following MVM in females, both acutely and following 8-week supplementation. The current study aimed to assess these effects further in males and females using metabolically challenging exercise and cognitive tasks. Methods: The current randomised, placebo-controlled, parallel groups study investigated the effects of a MVM complex in 82 healthy young (18-35y) exercisers. Subjective ratings and substrate metabolism were assessed during 30 min each of increasingly effortful incremental exercise and demanding cognitive tasks. Assessments took place on acute study days following a single dose (Day 1) of MVM, containing 3 times recommended daily allowance of water-soluble vitamins plus CoQ10, and following 4-week supplementation (Day 28). Results: Energy expenditure (EE) was increased during cognitive tasks following MVM across Day 1 and Day 28, with greater effects in males. In males, MVM also increased carbohydrate oxidation and energy expenditure during exercise across Day 1 and Day 28. In females, mental tiredness was lower during exercise; increases in physical tiredness following 30 min of exercise were attenuated; and stress ratings following cognitive tasks were reduced following MVM. In males, MVM only lowered mental tiredness following 10 min of exercise. These effects were apparent irrespective of day, but effects on mental tiredness were greater on Day 28. Ferritin levels were also higher on Day 28 in those receiving MVM. Conclusion: These findings extend on existing knowledge, demonstrating increased carbohydrate oxidation and increased energy expenditure in males following MVM supplementation for the first time. Importantly, they show modulation of energy expenditure and subjective tiredness following a single dose, providing further evidence for acute effects of MVM. Differential effects in men and women suggest that sex may play an important role in the effects of MVM on energy metabolism and should be considered in future research. Trial registration: ClinicalTrials.gov, NCT03003442. Registered 22nd November 2016 – retrospectively registere