Walter Bloom

Appeal medals were produced in Western Australia over the first four years of World War I in support of various worthy causes, including the Red Cross, Children’s Hospital and returned injured soldiers and widows of those who fought for Australia, the latter through the Ugly Men’s Voluntary Workers’ Association of Western Australia (Incorporated). There has been very little known about these medals, not even their manufacturer, but an analysis of the die characteristics together with an examination of newspapers of the day and other contemporary records leads us to their common manufacturer, Cumpston’s City Electric Engraving Works, then located in Hay Street, Perth.

The following theorem on the circle group T is due to Norbert Wiener: If f∈L1(T) has non-negative Fourier coefficients and is square integrable on a neighbourhood of the identity, then f∈L2(T). This result has been extended to even exponents including p=∞, but shown to fail for all other p∈(1,∞]. All of this was extended further (appropriately formulated) well beyond locally compact abelian groups. In this paper we prove Wiener's theorem for even exponents for a large class of commutative hypergroups. In addition, we present examples of commutative hypergroups for which, in sharp contrast to the group case, Wiener's theorem holds for all exponents p∈[1,∞]. For these hypergroups and the Bessel-Kingman hypergroup with parameter 12 we characterise those locally integrable functions that are of positive type and square-integrable near the identity in terms of amalgam spaces.

Within the last five years two New South Wales coin hoards fortuitously came intact on to the market. It was immediately recognized that these modern coins dating from the Victorian period through to just after World War I were not simply accumulations or coin collections, but must have come from hoards. This supposition was confirmed with the owners. Realizing the hoards’ importance, the authors recorded the coins by country (British and Australian), date, mint, and most importantly, their individual weights. This article is a report on these findings together with a statistical analysis of the weight loss of the coins during circulation. We show that for the Australian silver coins in the combined hoards, the mean percentage weight loss per year per coin by denomination follows a linear relationship, and that the smaller the coin, the larger the percentage weight loss.

Due to the changing nature of learning and teaching in universities, there is a growing need for professional development for lecturers and tutors teaching in disciplines in the mathematical sciences. Mathematics teaching staff receive some training in learning and teaching but many of the courses running at university level are not tailored to the mathematical sciences. This article reports on a collaborative research project aimed at investigating the type of professional development that Australian tertiary mathematics teachers need and their preference for delivery modes. Effective teaching promotes effective learning in our students and discipline-specific professional development will enhance outcomes for teachers, students, and mathematics.