Quasi-uniformity of Minimal Weighted Energy Points on Compact Metric Spaces

For a closed subset $K$ of a compact metric space $A$ possessing an $\alpha$-regular measure $\mu$ with $\mu(K)>0$, we prove that whenever $s>\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations $\omega_N=\{x_{i,N}^{(s)}\}_{i=1}^N$ on $K$ (for `nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as $N$ grows large. Furthermore, if $K$ is an $\alpha$-rectifiable compact subset of Euclidean space ($\alpha$ an integer) with positive and finite $\alpha$-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as $N\to \infty$) a prescribed positive continuous limit distribution with respect to $\alpha$-dimensional Hausdorff measure. As a consequence of our energy related results for the unweighted case, we deduce that if $A$ is a compact $C^1$ manifold without boundary, then there exists a sequence of $N$-point best-packing configurations on $A$ whose mesh-separation ratios have limit superior (as $N\to \infty$) at most 2

Exact averages of central values of triple product L-functions

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla

Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce first cores with a slightly higher radius and central temperature. We also performed simulations of the collapse of a 10 and 0.1 solar mass cloud, which showed the properties of the first core to be independent of the initial cloud mass, with again no major differences between grey and multigroup models. For Larson's first collapse, where temperatures remain below 2000 K, the vast majority of the radiation energy lies in the IR regime and the system is optically thick. In this regime, the grey approximation does a good job reproducing the correct opacities, as long as there are no large opacity variations on scales much smaller than the width of the Planck function. The multigroup method is however expected to yield more important differences in the later stages of the collapse when high energy (UV and X-ray) radiation is present and matter and radiation are strongly decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&

Loudly sing cuckoo : More-than-human seasonalities in Britain

This research was funded by a grant from the Arts and Humanities Research Council, grant number AH/E009573/1.Peer reviewedPostprin

Are autistic traits in the general population stable across development?

There is accumulating evidence that autistic traits (AT) are on a continuum in the general population, with clinical autism representing the extreme end of a quantitative distribution. While the nature and severity of symptoms in clinical autism are known to persist over time, no study has examined the long-term stability of AT among typically developing toddlers. The current investigation measured AT in 360 males and 400 males from the general population close to two decades apart, using the Pervasive Developmental Disorder subscale of the Child Behavior Checklist in early childhood (M = 2.14 years; SD = 0.15), and the Autism-Spectrum Quotient in early adulthood (M = 19.50 years; SD = 0.70). Items from each scale were further divided into social (difficulties with social interaction and communication) and non-social (restricted and repetitive behaviours and interests) AT. The association between child and adult measurements of AT as well the influence of potentially confounding sociodemographic, antenatal and obstetric variables were assessed using Pearson's correlations and linear regression. For males, Total AT in early childhood were positively correlated with total AT (r = .16, p = .002) and social AT (r = .16, p = .002) in adulthood. There was also a positive correlation for males between social AT measured in early childhood and Total (r = .17, p = .001) and social AT (r = .16, p = .002) measured in adulthood. Correlations for non-social AT did not achieve significance in males. Furthermore, there was no significant longitudinal association in AT observed for males or females. Despite the constraints of using different measures and different raters at the two ages, this study found modest developmental stability of social AT from early childhood to adulthood in boys

The first legal mortgagor: a consumer without adequate protection?

This article contends that the UK government’s attempt to create a well-functioning consumer credit market will be undermined if it fails to reform the private law framework relating to the first legal mortgage. Such agreements are governed by two distinct regulatory regimes that are founded upon very different conceptions of the mortgagor. The first, the regulation of financial services overseen by the Financial Conduct Authority, derives from public law and is founded upon a conception of the mortgagor as “consumer”. The other is land law, private law regulation implemented by the judiciary and underpinned by a conception of the mortgagor as “landowner”. Evidence suggests that the operation of these two regimes prevents mortgagors from receiving fair and consistent treatment. The current reform of financial services regulation therefore will change only one part of this governance regime and will leave mortgagors heavily reliant upon a regulator that still has to prove itself. What this article argues is that reform of the rules of private law must also be undertaken with the aim of initiating a paradigm shift in the conception of the mortgagor from “landowner” to “consumer”. Cultural shifts of this kind take time but the hope is that this conceptual transformation will occur in time to deter the predicted rise in mortgage possessions

Outbreak of gastroenteritis caused by Yersinia pestis in Afghanistan.

Plague, which is most often caused by the bite of Yersinia pestis-infected fleas, is a rapidly progressing, serious disease that can be fatal without prompt antibiotic treatment. In late December 2007, an outbreak of acute gastroenteritis occurred in Nimroz Province of southern Afghanistan. Of the 83 probable cases of illness, 17 died (case fatality 20·5%). Being a case was associated with consumption or handling of camel meat (adjusted odds ratio 4·4, 95% confidence interval 2·2-8·8, P<0·001). Molecular testing of patient clinical samples and of tissue from the camel using PCR/electrospray ionization-mass spectrometry revealed DNA signatures consistent with Yersinia pestis. Confirmatory testing using real-time PCR and immunological seroconversion of one of the patients confirmed that the outbreak was caused by plague, with a rare gastrointestinal presentation. The study highlights the challenges of identifying infectious agents in low-resource settings; it is the first reported occurrence of plague in Afghanistan

Deep Eutectic Solvents Based on Natural Ascorbic Acid Analogues and Choline Chloride

Deep eutectic solvents (DES) are one of the most promising green technologies to emerge in recent years given their combination of environmentally friendly credentials and useful functionalities. Considering the continued search for new DES -- especially those that exemplify the aforementioned characteristics, we report the preparation of DES based on natural analogues of L-ascorbic acid for the first time. The onset of eutectic melting occurred at temperatures far below the melting point of the individual components and resulted in the generation of glass forming fluids with glass transition temperatures, viscosities and flow behavior that are comparable to similar systems. This work expands the current array of DES that can be produced using naturally occurring components, which given their potential to be bio-derived, interesting physicochemical properties (e.g. propensity to supercool and vitrify) and apparent antibacterial nature, may provide utility within a range of applications

Influence of blade aerodynamic model on the prediction of helicopter high-frequency airloads

Brown’s vorticity transport model has been used to investigate the influence of the blade aerodynamic model on the accuracy with which the high-frequency airloads associated with helicopter blade–vortex interactions can be predicted. The model yields an accurate representation of the wake structure yet allows significant flexibility in the way that the blade loading can be represented. A simple lifting-line model and a somewhat more sophisticated liftingchord model, based on unsteady thin aerofoil theory, are compared. A marked improvement in the accuracy of the predicted high-frequency airloads of the higher harmonic control aeroacoustic rotor is obtained when the liftingchord model is used instead of the lifting-line approach, and the quality of the prediction is affected less by the computational resolution of the wake. The lifting-line model overpredicts the amplitude of the lift response to blade–vortex interactions as the computational grid is refined, exposing the fundamental deficiencies in this approach when modeling the aerodynamic response of the blade to interactions with vortices that are much smaller than its chord. The airloads that are predicted using the lifting-chord model are relatively insensitive to the resolution of the computation, and there are fundamental reasons to believe that properly converged numerical solutions may be attainable using this approach