Analysis of Vibration Eigenfrequencies of a Thin Plate by the Keller-Rubinow Wave Method .1. Clamped Boundary-Conditions with Rectangular or Circular Geometry

The wave method of Keller and Rubinow [Ann. Physics, 9 (1960), p. 24-75] is extended to the biharmonic eigenvalue problem with rectangular or circular geometry and clamped boundary conditions. First, it is noted from the clues of computer graphics that mode shapes of a clamped circular plate and those of a circular membrane look very similar to each other. This suggests that plate and membrane should have very similar vibration behavior and leads to the assumption that the covering space of a rectangular plate is still a torus. By adding several waves on the boundary, approximate eigenfrequency equations are derived. Their solutions are shown to agree remarkably with numerical solutions obtained by the Legendre-tau spectral method here and by the finite-element method elsewhere at all frequency ranges. The same idea is also applied to the circular plate and yields excellent agreement between the exact values of eigenfrequencies and the asymptotic solutions

The Vibration Spectrum of Two Euler–Bernoulli Beams Coupled Via a Dissipative Joint

The asymptotic estimation of the vibration spectrum for a system of two identical Euler–Bernoulli beams coupled via each of the four standard types of linear dissipative joint has been solved for the case when one beam is clamped and the other beam is free at the outer ends. Here, we generalize those results and solve the problem for all 40 combinations of energy-conserving end conditions. We provide both asymptotic and numerical results, and we compare the various systems with an eye toward determining which configurations lead to asymptotically equivalent vibration spectra

“What is a referendum?” How we might open up pre-vote TV debates to genuine public scrutiny

The 2015 TV election debates proved their civic value – as they had in 2010, write Stephen Coleman (left), Nick Anstead, Jay G Blumler, Giles Moss and Matt Homer. But in these edited extracts from a University of Leeds report, Democracy on Demand?, Dr Anstead questions whether Twitter is – as some media organisations seemed to imply – representative of public opinion. The authors also urge the media to experiment with the format of any TV debates during the EU referendum campaign to make them more responsive to the public’s questions and reactions

General practitioners' views of clinically led commissioning: cross-sectional survey in England.

OBJECTIVES: Involving general practitioners (GPs) in the commissioning/purchasing of services has been an important element in English health policy for many years. The Health and Social Care Act 2012 handed responsibility for commissioning of the majority of care for local populations to GP-led Clinical Commissioning Groups (CCGs). In this paper, we explore GP attitudes to involvement in commissioning and future intentions for engagement. DESIGN AND SETTING: Survey of a random sample of GPs across England in 2015. METHOD: The Eighth National GP Worklife Survey was distributed to GPs in spring 2015. Responses were received from 2611 respondents (response rate = 46%). We compared responses across different GP characteristics and conducted two sample tests of proportions to identify statistically significant differences in responses across groups. We also used multivariate logistic regression to identify the characteristics associated with wanting a formal CCG role in the future. RESULTS: While GPs generally agree that they can add value to aspects of commissioning, only a minority feel that this is an important part of their role. Many current leaders intend to quit in the next 5 years, and there is limited appetite among those not currently in a formal role to take up such a role in the future. CCGs were set up as 'membership organisations' but only a minority of respondents reported feeling that they had 'ownership' of their local CCG and these were often GPs with formal CCG roles. However, respondents generally agree that the CCG has a legitimate role in influencing the work that they do. CONCLUSION: CCGs need to engage in active succession planning to find the next generation of GP leaders. GPs believe that CCGs have a legitimate role in influencing their work, suggesting that there may be scope for CCGs to involve GPs more fully in roles short of formal leadership

Exercise Similarly Facilitates Men and Women’s Selective Attention Task Response Times but Differentially Affects Memory Task Performance

Previous research has found that acute, moderate-intensity physical exercise enhances selective attention and memory and that men and women show differential performance on tasks measuring these skills. Although exercise and participant sex have been examined separately, it remains unknown whether acute, moderate-intensity exercise differentially affects men and women’s selective attention and memory encoding and retrieval. Participants in the present study completed two 10-min sessions of either moderate-intensity exercise comprised of jumping rope alternating with walking in place or an active control protocol comprised of watching wellness videos alternating with walking in place. Each participant completed a selective attention task and a task assessing recognition and object location memory immediately after exercising. Exercise was related to overall faster performance during the selective attention task, with no differences in men and women’s performance. Women showed better recognition memory compared to men. Exercise specifically improved object location memory among men, but only among participants who completed the memory task second. These findings suggest that acute, moderate-intensity exercise differentially affects men and women’s memory, which may be related to complex interactions between exercise, sex hormones, and the neurotrophin BDNF

Problem drug use prevalence estimation revisited:heterogeneity in capture-recapture and the role of external evidence

BACKGROUND AND AIMS: Capture–recapture (CRC) analysis is recommended for estimating the prevalence of problem drug use or people who inject drugs (PWID). We aim to demonstrate how naive application of CRC can lead to highly misleading results, and to suggest how the problems might be overcome. METHODS: We present a case study of estimating the prevalence of PWID in Bristol, UK, applying CRC to lists in contact with three services. We assess: (i) sensitivity of results to different versions of the dominant (treatment) list: specifically, to inclusion of non‐incident cases and of those who were referred directly from one of the other services; (ii) the impact of accounting for a novel covariate, housing instability; and (iii) consistency of CRC estimates with drug‐related mortality data. We then incorporate formally the drug‐related mortality data and lower bounds for prevalence alongside the CRC into a single coherent model. RESULTS: Five of 11 models fitted the full data equally well but generated widely varying prevalence estimates, from 2740 [95% confidence interval (CI) = 2670, 2840] to 6890 (95% CI = 3740, 17680). Results were highly sensitive to inclusion of non‐incident cases, demonstrating the presence of considerable heterogeneity, and were sensitive to a lesser extent to inclusion of direct referrals. A reduced data set including only incident cases and excluding referrals could be fitted by simpler models, and led to much greater consistency in estimates. Accounting for housing stability improved model fit considerably more than did the standard covariates of age and gender. External data provided validation of results and aided model selection, generating a final estimate of the number of PWID in Bristol in 2011 of 2770 [95% credible interval (Cr‐I) = 2570, 3110] or 0.9% (95% Cr‐I = 0.9, 1.0%) of the population aged 15–64 years. CONCLUSIONS: Steps can be taken to reduce bias in capture–recapture analysis, including: careful consideration of data sources, reduction of lists to less heterogeneous subsamples, use of covariates and formal incorporation of external data

Dirty black holes: Entropy versus area

Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\ell_P^2)} + {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu + \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector, V^\mu the four velocity of a co--rotating observer.) If no hair is present the validity of the ``entropy = (1/4) area'' law reduces to the question of whether or not the Lorentzian energy density for the system under consideration is formally equal to the Euclideanized Lagrangian. ****** To appear in Physical Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision