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This prize, for outstanding contributions to the Society’s research publications, is fittingly named after the founding editors of those journals. The people it honours represent the three major aspects in the development of Australian mathematics.
Thomas Gerald Room (1902—1986), a geometer, was professor of pure mathematics at the University of Sydney from 1935 to 1968. Born in London and educated at Cambridge, he, like all the earliest professors in Australia’s first universities, was selected for the post by British mathematicians or on the advice of British mathematicians from mostly British applicants. He worked enthusiastically for the formation of the Society in 1956, and was appointed its Publications Secretary. The Journal first appeared in August 1959 and Room was its editor until 1965.
Bernhard Hermann Neumann (1909—2002) was born in Berlin and represents the wave of refugee mathematicians that came to Australia in the 1930s and '40s, many of whom were appointed to chairs around the country. Neumann was the foundation professor of mathematics at the Australian National University. He was appointed in 1962, having left Germany in 1933 with a doctorate from the University of Berlin, and was at the University of Manchester, where his eminence in group theory was established, before coming permanently to Australia. Neumann was a tireless worker for all facets of Australian mathematics. In 1969 he was appointed editor of the Society’s Bulletin, a journal which would insist on submissions in near-final form for which rapid publication (of those which were accepted) would be ensured. He had argued himself for this concept, and remained its editor for ten years.
John Joseph Mahony (1929—1992) was born in Melbourne and gained his PhD at the University of Melbourne. He exemplifies the Australian-born mathematicians who now dominate the profession in their home country. Mahony was for a few years professor of applied mathematics at the University of Queensland before taking a similar position at the University of Western Australia, which he held from 1965 until his death. The Society’s Journal (Series B), later called the ANZIAM Journal, specialising in applied mathematics, first appeared in 1975 and Mahony was its editor until 1978.
José Madrid for the paper 'Sharp inequalities for the variation of the discrete maximal function', Bulletin of the Australian Mathematical Society, 95(1) (2017), 94–107.
Notes on the prize paper from the Editor: This is a paper about the regularity properties of the discrete analogues of the classical Hardy–Littlewood maximal function. The question of how maximal functions act on Sobolev spaces is natural and well studied. The author considers a version of this question in the discrete setting and proves a quantitative result with best constant. The examples showing optimality are simple and natural and the proofs are clever but not overly technical.
Abstract: In this paper we establish new optimal bounds for the derivative of some discrete maximal functions, in both the centred and uncentred versions. In particular, we solve a question originally posed by Bober et al. [‘On a discrete version of Tanaka’s theorem for maximal functions’, Proc. Amer. Math. Soc.140 (2012), 1669–1680].
Satish K. Pandey and Vern I. Paulsen for their paper ‘A spectral characterization of AN operators’, Journal of the Australian Mathematical Society.
Serena Dipierro, Luca Lombardini, Pietro Miraglio and Enrico Valdinoci for the paper 'The Phillip Island Penguin Parade (A Mathematical Treatment)', ANZIAM Journal.
Citation: An enjoyable paper to read, considering an interesting and new study of the movement of the penguins as they return to their nests in the evening on Phillip Island. It is very nice example of applied mathematics. The real situation is observed, equations are derived and investigated. Outcomes are compared with monitored penguin behaviour. Existence results are proven. The simplicity is compelling and it provides a nice understanding of a real process, with a rigorous underpinning.
Janusz Brzdek for the paper "A Hyperstability Result for the Cauchy Equation", Bulletin of the Australian Mathematical Society
Citation: The paper proves a hyperstability result for the Cauchy functional equation f(x + y) = f(x) + f(y), which complements earlier stability outcomes of J. M. Rassias. It exploits the fixed point method introduced in J. Brzdęk, J. Chudziak and Zs. Páles, ‘A fixed point approach to stability of functional equations’, Nonlinear Anal. 74 (2011), 6728–6732. The notion of hyperstability for this functional equation (also introduced by J. Brzdęk) is that if a mapping is in some sense ‘close’ to being additive, is it necessarily ‘close’ to an additive mapping.
The methods introduced in the paper are presented in a form that has been shown to be widely applicable and has influenced others working in this field with applications to many other functional equations and in more general settings. The fixed point method from Brzdęk, Chudziak and Páles has also been developed in many papers to a number of functional equations and to a number of settings beyond the original setting in Banach space and the application to the Cauchy equation.
This paper continues to be strongly cited as one of a growing number of examples of hyperstability, acknowledging the significance of the early application of the method to the Cauchy equation.
Valentino Magnani for the paper 'Towards differential calculus in stratified groups', Journal of the Australian Mathematical Society
Lawrence K. Forbes for his paper 'On turbulence modelling and the transition from laminar to turbulent flow', ANZIAM Journal
F. Aragón Artacho, J. Borwein, M. Tam for their paper 'Douglas–Rachford feasibility methods for matrix completion problems', ANZIAM Journal
Jason P. Bell, Michael Coons and Kevin G. Hare for their paper ‘The minimal growth of a k-regular sequence’, Bulletin of the Australian Mathematical Society
Citation: The paper gives a lower bound for the growth of an unbounded integer-valued k-regular sequence. The ideas are applied to answer a question of Borwein, Choi and Coons on the sums of completely multiplicative automatic functions. There is a connection with a famous problem of Erdös in this area. The paper attacks a concrete and nontrivial problem and gives a very comprehensive solution, including both an asymptotic lower bound and examples to demonstrate that this estimate is best possible. The paper sheds light on important conjectures about automatic sequences. The exposition is excellent. The paper is well-cited and continues to be cited.
