A family of entire functions with Baker domains

In his paper [The iteration of polynomials and transcendental entire functions. J. Aust. Math. Soc. (Series A) 30 (1981), 483–495], Baker proved that the function f defined by f(z) = z+(sin?z/?z)+c has a Baker domain for c sufficiently large. In this paper we use a novel method to prove that f has a Baker domain for all c>0. We also prove that there exists an open unbounded set contained in the Baker domain on which the orbits of points under f are asymptotically horizontal

Fast computational aeroelastic analysis of helicopter rotor blades

The use of a new aeroelastic computer framework called Flexit is described and the frame-work is used to analyse the dynamic aeroelastic behaviour of a four-bladed helicopter main rotor. Flexit implements a loose coupling between unsteady vortex lattice method (UVLM) and numerical solution of the inhomogeneous Euler-Bernoulli partial differential equation (PDE).The framework is fast because most of the intensive computational functionality is performed on GPU using NVIDIA CUDA technology, and this makes it suitable for use in the early de-sign stages. The UVLM algorithm uses a free wake model, and solution of the Euler-Bernoulli PDE is approximated using a finite difference algorithm that includes a term to take account of centrifugal forces. The results of simulations are compared with analysis performed with CFD and FSI tools

On a novel approximate solution to the inhomogeneous Euler–Bernoulli equation with an application to aeroelastics

This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper

Understanding the biases to sepsis surveillance and quality assurance caused by inaccurate coding in administrative health data

Purpose Timely and accurate data on the epidemiology of sepsis are essential to inform policy decisions and research priorities. We aimed to investigate the validity of inpatient administrative health data (IAHD) for surveillance and quality assurance of sepsis care. Methods We conducted a retrospective validation study in a disproportional stratified random sample of 10,334 inpatient cases of age ≥ 15 years treated in 2015–2017 in ten German hospitals. The accuracy of coding of sepsis and risk factors for mortality in IAHD was assessed compared to reference standard diagnoses obtained by a chart review. Hospital-level risk-adjusted mortality of sepsis as calculated from IAHD information was compared to mortality calculated from chart review information. Results ICD-coding of sepsis in IAHD showed high positive predictive value (76.9–85.7% depending on sepsis definition), but low sensitivity (26.8–38%), which led to an underestimation of sepsis incidence (1.4% vs. 3.3% for severe sepsis-1). Not naming sepsis in the chart was strongly associated with under-coding of sepsis. The frequency of correctly naming sepsis and ICD-coding of sepsis varied strongly between hospitals (range of sensitivity of naming: 29–71.7%, of ICD-diagnosis: 10.7–58.5%). Risk-adjusted mortality of sepsis per hospital calculated from coding in IAHD showed no substantial correlation to reference standard risk-adjusted mortality (r = 0.09). Conclusion Due to the under-coding of sepsis in IAHD, previous epidemiological studies underestimated the burden of sepsis in Germany. There is a large variability between hospitals in accuracy of diagnosing and coding of sepsis. Therefore, IAHD alone is not suited to assess quality of sepsis care

BHPR research: qualitative1. Complex reasoning determines patients' perception of outcome following foot surgery in rheumatoid arhtritis

Background: Foot surgery is common in patients with RA but research into surgical outcomes is limited and conceptually flawed as current outcome measures lack face validity: to date no one has asked patients what is important to them. This study aimed to determine which factors are important to patients when evaluating the success of foot surgery in RA Methods: Semi structured interviews of RA patients who had undergone foot surgery were conducted and transcribed verbatim. Thematic analysis of interviews was conducted to explore issues that were important to patients. Results: 11 RA patients (9 ♂, mean age 59, dis dur = 22yrs, mean of 3 yrs post op) with mixed experiences of foot surgery were interviewed. Patients interpreted outcome in respect to a multitude of factors, frequently positive change in one aspect contrasted with negative opinions about another. Overall, four major themes emerged. Function: Functional ability & participation in valued activities were very important to patients. Walking ability was a key concern but patients interpreted levels of activity in light of other aspects of their disease, reflecting on change in functional ability more than overall level. Positive feelings of improved mobility were often moderated by negative self perception ("I mean, I still walk like a waddling duck”). Appearance: Appearance was important to almost all patients but perhaps the most complex theme of all. Physical appearance, foot shape, and footwear were closely interlinked, yet patients saw these as distinct separate concepts. Patients need to legitimize these feelings was clear and they frequently entered into a defensive repertoire ("it's not cosmetic surgery; it's something that's more important than that, you know?”). Clinician opinion: Surgeons' post operative evaluation of the procedure was very influential. The impact of this appraisal continued to affect patients' lasting impression irrespective of how the outcome compared to their initial goals ("when he'd done it ... he said that hasn't worked as good as he'd wanted to ... but the pain has gone”). Pain: Whilst pain was important to almost all patients, it appeared to be less important than the other themes. Pain was predominately raised when it influenced other themes, such as function; many still felt the need to legitimize their foot pain in order for health professionals to take it seriously ("in the end I went to my GP because it had happened a few times and I went to an orthopaedic surgeon who was quite dismissive of it, it was like what are you complaining about”). Conclusions: Patients interpret the outcome of foot surgery using a multitude of interrelated factors, particularly functional ability, appearance and surgeons' appraisal of the procedure. While pain was often noted, this appeared less important than other factors in the overall outcome of the surgery. Future research into foot surgery should incorporate the complexity of how patients determine their outcome Disclosure statement: All authors have declared no conflicts of interes

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements