A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

Functions f(z)= z+E°2 anzn that are analytic in the unit disk and satisfy the differential equation f'(z) + azf"(z)+yz2f"(z) = g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z) = (10(10G(ztμsν�t−μs−νds dt with G" subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h

Numerical study of a non-equilibrium interface model

We have carried out extensive computer simulations of one-dimensional models related to the low noise (solid-on-solid) non-equilibrium interface of a two dimensional anchored Toom model with unbiased and biased noise. For the unbiased case the computed fluctuations of the interface in this limit provide new numerical evidence for the logarithmic correction to the subnormal L^(1/2) variance which was predicted by the dynamic renormalization group calculations on the modified Edwards-Wilkinson equation. In the biased case the simulations are in close quantitative agreement with the predictions of the Collective Variable Approximation (CVA), which gives the same L^(2/3) behavior of the variance as the KPZ equation.Comment: 15 pages revtex, 4 Postscript Figure

On Planar Harmonic Mappings And Minimal Surfaces

The project seeks to study the geometric properties of planar harmonic mappings (and related mappings), and aims to apply the findings in the investigation of minimal surfaces

A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

Functions f(z)=z+∑2∞‍anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z)=∫01∫01‍G(ztμsν)t-μs-νds dt with G' subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h

Improving recruitment to a study of telehealth management for long-term conditions in primary care: two embedded, randomised controlled trials of optimised patient information materials

Background: Patient understanding of study information is fundamental to gaining informed consent to take part in a randomised controlled trial. In order to meet the requirements of research ethics committees, patient information materials can be long and need to communicate complex messages. There is concern that standard approaches to providing patient information may deter potential participants from taking part in trials. The Systematic Techniques for Assisting Recruitment to Trials (MRC-START) research programme aims to test interventions to improve trial recruitment. The aim of this study was to investigate the effect on recruitment of optimised patient information materials (with improved readability and ease of comprehension) compared with standard materials. The study was embedded within two primary care trials involving patients with long-term conditions. Methods: The Healthlines Study involves two linked trials evaluating a telehealth intervention in patients with depression (Healthlines Depression) or raised cardiovascular disease risk (Healthlines CVD). We conducted two trials of a recruitment intervention, embedded within the Healthlines host trials. Patients identified as potentially eligible in each of the Healthlines trials were randomised to receive either the original patient information materials or optimised versions of these materials. Primary outcomes were the proportion of participants randomised (Healthlines Depression) and the proportion expressing interest in taking part (Healthlines CVD). Results: In Healthlines Depression (n = 1364), 6.3 % of patients receiving the optimised patient information materials were randomised into the study compared to 4.0 % in those receiving standard materials (OR = 1.63, 95 % CI = 1.00 to 2.67). In Healthlines CVD (n = 671) 24.0 % of those receiving optimised patient information materials responded positively to the invitation to participate, compared to 21.9 % in those receiving standard materials (OR = 1.12, 95 % CI = 0.78 to 1.61). Conclusions: Evidence from these two embedded trials suggests limited benefits of optimised patient information materials on recruitment rates, which may only be apparent in some patient populations, with no effects on other outcomes. Further embedded trials are needed to provide a more precise estimate of effect, and to explore further how effects vary by trial context, intervention, and patient population