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DEPARTMENT OF MATHEMATICS RESEARCH SCHOOL OF PHYSICAL SCIENCES

THE AUSTRALIAN NATIONAL UNIVERSITY

TELEGRAMS : NATUNIV

PROFESSOR B . H . NEUMANN , F . R .S .

PROFESSOR KURT MAHLER, F . R .S .

BOX 4, G.P.O.

PROFESSOR JOHN W. MILES (APPLIED MATHEMATICS)

CANBERRA A.C.T,

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4th December , 1963 .

The Rep;istrar, AUSTRALIAN NATIOrAL UNIVERsrrry .

Dear Ross ,

I have just had the memorandum I to all Heads of Departments in the 7 ..lo University, dated 2nd December, 1963, __...-­asking for Departmental Annual Repor~s . I feel I must protest against beine asked to pr pare a second list of academic publications in the same year . You will recall that such a list, covering the pel"iod 1st October, 1962, to 30th September, 1963, was asked for, to be included in th0 University Calendar . Now we are bein~ asked for a list that covers the Calendar Year 1963 May I SUfgest that collectinp such lists is a not very important part of th academic work o this UPiversity, and that, therefore, a sinr,le list, namely the one compiled for the Universi t~r Calendar, should al o suffice for the Annual RP.nort.

You vvill understand that I am not quarrelling with the neeo to compile an annual report: my quarrel is solely with the need to compile two different lists of academic publications, coverinp periods that differ by three months at each end only . This involves unnecessary time and ef.fort of every member of the Department, not only of myself . 17

Yours sincerely,

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60/1964 THE AUSTRALIAN NATIONAL UN IVERS fil

RESEARCH SCHOOL OF PHYSlCAL SCJENCES

Annual Report to Council for 1963

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Department of Mathematics

Professor and Head of Department

Professor

Professor (Applied Mathematics)

Professorial Fellows

Fellows

Senior Research Fellow

Research Fellows

Visiting Fellow

Honorary Research Assistant

Research Students

Staff

B.H. Neumann, Dr phil., Ph.D., D.Sc., F.R.S.

Kurt Mahler, Dr phil., D.Sc., F.~S. (arrived September).

J.W. Miles, M.S., A.E., Ph.D.

R.E. Edwards, B.Sc., Ph.D. Mrs Hanna Neumann, D.Phil., D.Sc. (arrived August).

W.A. Coppel, B.A. L.G. Kovacs, M.Sc., Ph.D. (arrived November).

B. Brainerd, S.B., Ph.D. (left August).

I.D. Macdonald, M.A., Ph.D. Z. Janko, Ph.D. Tekla Taylor, B.A., Ph.D. (left November).

Professor Sydney Goldstein, Ph.D., F.R.S. (arrived November).

Mrs Rosa R. Goldstein, Ph.D. (arrived November).

M.J. Dunwoody, B.Sc. Teresa Scruton, B.Sc. G.I. Gaudry, B.Sc. (arrived February). R.G. Burns, B.Sc. (arrived February).

General Remarks

M.A. Ward, B.Sc., B.A. (arrived March). E.F. nradley, B.Sc. (transferred to Mathematics in March). N.D. Gupta, M.Sc. (arrived April).

The department continued to grow and to develop in this second full year of its existence.

In January and February the third Summer Research

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Institute was held under the joint auspices of the Australian Mathematical Society and the Australian National University. More than 35 Australasian mathematicians met in the University, to work on various topics . The Institute was directed by Professor Neumann. Among the distinguished visitors to the Institute were Professor R.H. Bruck (University of Wisconsin), Professor Hermann Bondi, F.R.S. (King's College, London), and Dr R.A. Lyttleton, F.R.S. (University of Cambridge).

Visitors

Professor Edwin Hewitt, of the University of Washington, visited the Department from June to September; his visit was sponsored by the Fulbright Foundation, and he was given the status of an Honorary Fellow in the University. Other visitors on the Fulbright Foundation were Professor D.V. Widder (Harvard University), Professor A.H. Steinbrenner (University of Arizona), and Professor Carl B. Allendoer.fer (University of Washington). Brief visits, to address the Mathemati~al Colloquium of the departments in the School and in the Institute, or the Pure Mathematics Seminar of this Department, or both, were aloo paid by Dr G.R. Morris (University of Queensland), Professor T.M. Cherry, P.A.A., F.R.S. (University of Melbourne), Professor E.R. Love (University of Melbourne), Professor J.J. Mahony (University of Queensland),

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Dr A.P. Robertson (University of Glasgow), Dr Adrian Gill (University of Cambridge and Massachusetts Institute of Technology), Dr A.F. Horadam (University of New England), Mrs E.M. Horadam (University of New England), Professor C.S. Davis (University of Queensland), Professor George Szekeres, F.A.A., (University of New South Wales), Dr M.C.R. Butler (University of Liverpool and University of Melbourne).

Other visitors to the Department included Professor E.S. Barnes, F.A.A. (University of Adelaide), Dr C.J.F. Upton (University of Melbourne), and Professor A.L. Blakers (University of Western Australia).

Research programme

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Research in pure mathematics has been carried out in group theory and semigroup theory, in functional analysis, in non-linear differential equations, abstract harmonic analysis, and in analytic lattice algebra.

Research in applied mathematics has been primarily in fluid mechanics with emphasis on hydro-dynamic stability and surface-wave generation.

Other activities

Members of the Department joined with members of the sister department in the School and with mathematics staffs at the Royal Military College Duntroon and at local secondary schools in launching the Canberra Mathematical Association; Professor Neumann is its first President.

Professor Neumann delivered the opening address, "Ferment in School Mathematics", of the Summer School for Mathematics Teachers in the University of New South Wales; he also gave an invited lecture at the Annual Meeting of the Australian Mathematical Society at Monash University, and was elected a Vice-President of the Society. He also paid visits to the Universities of Adelaide, Melbourne, Sydney, and Queensland, and to Townsville University College, and gave seminar lectures at the three last-named institutions.

Professor Mahler, who was appointed to the third Chair of Mathematics and arrived in September to take up the appointment, visited the Universities of Sydney and New South Wales on his way from the U.S.A. to Canberra, and delivered seminar lectures at both.

Professor Miles spent the months of July and August at the Institute of Geophysics on the Los Angeles and La Jolla campuses of the University of California and gave an invited address to the International Union of Geodesy and Geophysics on the Berkeley campus. This visit was supported by the National Science Foundation (USA).

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' He also paid another short visit, in November, to the University of California at Los Angeles for consultation on their new progrannne in applied mathematics, spent some time as a consultant to the Aerospace Corporation, and gave seminars at the Universities of Melbourne and Sydney and a paper at the Australian Mathematical Society meeting at Monash.

Professor Sydney Goldstein, F.R.S., of Harvard

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University, arrived in Australia in September, on a visit sponsored principally by this University. He visited CSIRO at Sydney and the Universities of Sydney, Queensland, Western Australia, Melbourne, and Monash University before finally coming to Canberra; and delivered a number of lectures.

Dr Hanna Neumann visited the Universities of Western Australia and Adelaide en route from Manchester to Canberra, and later gave seminar lectures at Townsville University College and the University of Sydney; and also visited the Universities of Queensland and New South Wales.

Dr Macdonald conducted a course of lectures entitled "Content and background of the new secondary course in Mathematics in New South Wales" for members of the teaching profession. Dr Janko was seconded to the University of Western Australia for the first term, March to May.

The collaboration with the sister Department of Mathematics in the School of General Studies was not confined to the joint Mathematical Colloquium; both departments exchanged research supervision and other advanced teaching.

Buildings

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The new Mathematical Sciences Building was, after several months delay, taken into use in August. As reported last year, an error in the execution of the architects' plans gave rise to anxiety, and the remedial action taken gave rise to further anxiety: this anxiety continues unabated; and the quality of the finish of the building does nothing to allay the users' anxieties. The building is, however, well designed for its purpose, and when its last two bays are built, it will provide adequate acconnnodation, with a beautiful view of Lake Burley Griffin, for the departments and library it houses. The move to the new building has put a mile between the two sister departments of mathematics; but the cordial bonds between them have remained unimpaired, and new bonds have been formed with the Department of Statistics of the Institute and with the Department of Theoretical Physics, with which this Department shares the building;

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and also with the rest of the Research School of Physical Sciences, whose library occupies the ground floor of the building.

Publications

BRAINERD, Barron "On the normalizer of an f-ring." Proc. Japan Acad., .2§_, 438-43, 1962

"On the structure of averaging operators." J. Math. Analysis and Appl., 2• 347-77, 1962.

DUNWOODY, M. J. "On relation groups." Math. Zeitschr., 81, 18o-6, 1963.

"On T-systems of groups." J. Austral. Math. Soc., 2• 172-9, 1963.

EDWARDS, R.E. 1 "On certain direct sum decompositions of L spaces."

JANKO,

J. Austral. Math. Soc., 1• 151-8, 1963.

"Weak convergence of vector-valued series and integrals. 11

J. Austral. Math. Soc., 2• 159-66, 1963.

Zvonimir "Eine Bemerkung uber die ~-Untcrgruppe endlicher Gruppen." Acta Sci. Math.,~. 247-8, 1962.

"Finite groups with invariant fourth maximal subgroups." Math. Zeitschr., 82, 82-9, 1963.

MACDONALD, l.D. "On a class of finitely presented groups." Canad. J. Math., 14, 602-13, 1962.

"On central series." Proc. Edinburgh Math. Soc., (2) 12• 175-8, 1962.

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MAHLER, Kurt "On some inequalities for polynomials in several variables." J. London Math. Soc.,~. 341-6, 1962.

MILES, John W.

"On the stability of heterogeneous shear flows. Part 2." J. Fluid Mechanics, 16, 209-27, 1963.

"Principles of classical mechanics and field theory." J. Fluid Mechanics, 16, 313-20, 1963.

"On the annular damper for a freely precessing gyroscope II." J. Appl. Mechanics, ~. 189-92, 1963.

MILES, J.W., FEJER, J.A.* tton the stability of a plane vortex sheet with respect to three-dimensional disturbances." J. Fluid Mechanics, ~. 335-6, 1963.

NEUMANN, B.H. "Twisted wreath products of groups." Arch. Math., 14, 1-6, 1963.

"A further note on means in groups." J. London Math. Soc., 2§., 226-7, 1963.

NEUMANN, B.H., NEUMANN, Hanna, NEUMANN, Peter M.* '1Wreath products and varieties of groups." Math. Zeitschr., So, 44-62, 1962.

NEUMANN, B.H., TAYLOR, Tekla "Subsemigroups of nilpotent groups." Proc. Roy. Soc. London, A, 274, 1-4, 1963.

NEUMANN, Hanna

*

"On a theorem by Gaschiitz." J. reine angew. Math., 212, 109-12, 1963.

"Varieties of groups." Notes by I.M.S. Dey* and C.H. Houghton*, Department of Mathematics, Manchester College of Science and Technology, 1963.

Not a member of this University.

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