Asymptotic behaviour of zeros of bieberbach polynomials

AbstractLet Ω be a simply-connected domain in the complex plane and let πn denote the nth-degree Bieberbach polynomial approximation to the conformal map f of Ω onto a disc. In this paper we investigate the asymptotic behaviour (as n→σ) of the zeros of πn, πn′ and also of the zeroes of certain closely related rational approximants to f. Our result show that, in each case, the distribution of the zeros is governed by the location of the singularities of the mapping function f in C⧹ω, and we present numerical examples illustrating this

Are Eye Clinics Safe For The Road? An Observational Report

We report an observational study, based on the examination of 319 medical records, identifying the proportion of patients whose driving status was documented on the first and subsequent glaucoma clinic visits. We also established the proportion of patients with documented Driving and Vehicle Licencing Agency (DVLA)-related advice when they did not meet driving standards based on their visual acuity and/or visual fields (VF). On presentation, driving status was assessed in 61% (n=195) patients. Of the remaining 124, 44% (n=55) had their driving status documented at a subsequent visit, on an average 8 years later. Of all patients (78%, n=250) whose driving status was assessed at some stage, 42% (n=134) were drivers. Of the 203 patients who were either drivers or whose driving status was unknown, 37% (n=75) were assessed as having a visual acuity or bilateral VF defect that was below the legal limit for driving, 39 of whom were known drivers. Only 13 were advised to inform the DVLA, and only 5 patients were advised to update their spectacles or listed for surgery to improve their vision. We therefore potentially failed to perform our DVLA duty in 76% (n=57) of patients. We have made suggestions for improving the current performance in this respect based on the findings of this study

Boundary elements in potential and elasticity theory

A general theory that describes the B.I.E. linear approximation in potential and elasticity problems, is developed. A method to tread the Dirichlet condition in sharp vertex is presented. Though the study is developed for linear elements, its extension to higher order interpolation is straightforward. A new direct assembling procedure of the global of equations to be solved, is finally showed

Variations in Treatment Delivery for Patients with Neovascular AMD in the UK: Results from an Ophthalmology Trainee Clinical Research Network Study

INTRODUCTION: The aim of this study was to determine treatment delivery patterns for patients with neovascular age-related macular degeneration (nAMD) across the UK through an ophthalmology trainee research network delivered observational study. METHODS: Data were collected via an online tool by potential research collaborators identified by the Ophthalmology Trainee Clinical Trial Network (OCTN). Collaborators were asked to comment on periprocedural practices of treatment of nAMD in their eye unit including treatment location and injectors, clinical assessment and routine observation in patients undergoing intravitreal treatment. RESULTS: Data were available from 26 units around the United Kingdom. Survey methodology refinement was approximately 3 months, and the average response time was 4.9 ± 2.4 days. The majority of responders confirmed that treatment was undertaken as a "one-stop" service (n = 15, 58%), delivered in a clean room (n = 23, 88%). In the majority of units, doctors administered injections (n = 24, 92%), but significant treatment was also given by nurse injectors (n = 21, 81%). All collaborators reported that patients underwent visual acuity testing and optical coherence tomography imaging at all visits, but other imaging including fundus fluorescein angiography (FFA) did not take place in all cases (n = 17, 65%) and only at baseline visit. CONCLUSIONS: These results demonstrate the feasibility of conducting ophthalmology trainee led and delivered observational studies. Our results show that FFA is not routinely used in the diagnosis of nAMD in the units sampled; most injections are carried out in a clean room, and ophthalmic nurses delivering injections is a highly prevalent model of care in the UK

Metaverse and circular economy

The revolutionary concepts of the Metaverse and circular economy are poised to reshape the future of society, academia and all business sectors. The Metaverse as a digital realm promises to transform peoples' way of life, while circular economy offers a sustainable and regenerative approach to economic growth. Together, these concepts can be combined to unlock new opportunities, drive innovation and address pressing challenges facing humanity. Within this new era of technological and environmental transformation, understanding the capabilities and potential of the Metaverse intertwined with the circular economy is crucial for individuals and nations alike

Importance of the First Postoperative Year in the Prognosis of Elderly Colorectal Cancer Patients

Surgical oncolog