This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function theory and potential theory. MSC: 30C10, 30C15, 41A10

CSG Action Plan: Availability of survey data: Moderate Need for wild population recovery: Low Potential for sustainable management: Moderate 2009 IUCN Red List: LR/cd (Least Risk, conservationdependent; reported to have undergone substantial recovery in several parts of its range. Recent surveys suggest that species remains widespread, locally abundant and extinction is unlikely; IUCN 2009) (la...

The Queensland Government’s Health Report, ‘Coal seam gas in the Tara region: Summary risk assessment of health complaints and environmental monitoring data, March 2013’, [Health Report] and the reports on which it is based, do not provide a comprehensive investigation of the potential impacts of coal seam gas (CSG) activities on the residents of Tara. The Health Report should not be used by go...

In the context of Kolmogorov’s algorithmic approach to the foundations of probability, Martin-Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibility. We prove a direct conversion of a constructive martingale into a measure of impossibility and vice versa, s...