A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Accountability for good faith in commercial dealing: The Carter v Boehm legacy 250 years on

In common law jurisdictions such as England, Australia, Canada and New Zealand good faith in contracting has long been recognised in specific areas of the law such as insurance law and franchising, and more recently the implied duties of good faith and mutual trust and convenience in employment contracts have generated a considerable volume of case law. Outside of these areas of law that may be characterised as being strongly‘relational’ in character,the courts in common law jurisdictions have been reluctant to embrace a more universal application of good faith in contracting and performance. However increasingly there are cases which support the proposition that there is a common law duty of good faith of general application to all commercial contracts. Most important in this context is the recent decision of the Supreme Court of Canada in Bhasin v Hrynew.1 However, this matter is by no means resolved in all common law jurisdictions. This article looks at the recent case law and literature and at various legislative incursions including statutes, codes of conduct and regulations impacting good faith in commercial dealings.

Does gender moderate the relationship between polydrug use and sexual risk-taking among Australian secondary school students under 16 years of age?

Introduction and Aims This study examines the association of alcohol and polydrug use with risky sexual behaviour in adolescents under 16 years of age and if this association differs by gender. Design and Methods The sample consisted of 5412 secondary school students under 16 years of age from Victoria, Australia. Participants completed an anonymous and confidential survey during class time. The key measures were having had sex before legal age of consent (16 years), unprotected sex before 16 (no condom) and latent-class derived alcohol and polydrug use variables based on alcohol, tobacco, cannabis, inhalants and other illegal drug use in the past month. Results There were 7.52% and 2.55% of adolescents who reported having sex and having unprotected sex before 16 years of age, respectively. After adjusting for antisocial behaviours, peers' drug use and family and school risk factors, girls were less likely to have unprotected sex (odds ratio = 0.31, P = 0.003). However, the interaction of being female and polydrug use (odds ratio = 4.52, P = 0.004) was significant, indicating that girls who engaged in polydrug use were at higher risk of having unprotected sex. For boys, the effect of polydrug use was non-significant (odds ratio = 1.44, P = 0.310). Discussion and Conclusions For girls, polydrug use was significantly associated with unprotected sex after adjusting for a range of risk factors, and this relationship was non-significant for boys. Future prevention programs for adolescent risky sexual behaviour and polydrug use might benefit from a tailored approach to gender differences.