Landau gave a lower estimate for the radius of a schlicht disk centered at the origin and contained in the image of the unit disk under a bounded holomorphic function f normalized by f(0) = f ′(0)− 1 = 1. Chen, Gauthier, and Hengartner established analogous versions for bounded harmonic functions. We improve upon their estimates.

Deckelnick and Dziuk (2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of Willmore flow/elastic flow of closed curves in R, d ≥ 2. We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett, Garcke, and Nürnberg (2007b, 2008b, 2010b)...

Title: Modelling Aggregate Interlock Load Transfer at Concrete Pavement Joints Author: Anna-Carin Brink Supervisor: Prof Emile Horak Co-Supervisor: Prof Alex Visser Department: Civil Engineering University: University of Pretoria Degree: Philosophiae Doctor (Engineering)