# Research Publications for 1989

## Books

**A1.**
Hillman JA**:**
*2-knots and their Groups.*
Australian Mathematical Society Lecture Series,
**5**
Cambridge University Press,
1989.
MR90d:57025

**A2.**
Walters RFC and Wehrhahn KH**:**
*Calculus I.*
Second Edition, revised and extended,
Carslaw Publications,
1989.

## Chapters in Books

**B1.**
Salganik M, Groshev M, Mostinsky A, Zheligovsky VA, Stepanova N and Shteinberg V**:**
Modeling of accelerograms, expected for the maximal assumed earthquake: comparison of methods,
*Study of seismic oscillations, grounds and constructions.*
Seismological studies,
**11**,
Geophysical Committee of Presidium of the USSR Academy of Science, Moscow,
1989,
122–127.

**B1.**
Zheligovsky VA**:**
On magnetic field generation by a class of flows of conducting fluid in a sphere,
*Theory and algorithms of geophysical data interpretation.*
Computational Seismology,
**22**,
Nauka, Moscow,
1989,
92–108.

## Journal Articles

**C1.**
Barratt C, Fackerell ED and Rosenfeld D**:**
The application of spinors to solving the Bloch equations.
*Journal of Magnetic Resonance*,
85
(1989),
35–41.

**C1.**
Betti R and Walters RFC**:**
The calculus of ends over a base topos.
*Journal of Pure and Applied Algebra*,
56
(1989),
211–220.
MR90f:18008

**C1.**
Bird GJ, Kelly GM, Power AJ and Street RH**:**
Flexible limits for 2-categories.
*Journal of Pure and Applied Algebra*,
61
(1989),
1–27.
MR91a:18009

**C1.**
Blackwell R, Kelly GM and Power AJ**:**
Two-dimensional monad theory.
*Journal of Pure and Applied Algebra*,
59
(1989),
1–41.
MR91a:18010

**C1.**
Bunton JD, Large MI, Slee OB, Stewart RT and Thatcher JD**:**
Radio and optical observation of an intense flare on HD 32918.
*Proceedings of the Astronomical Society of Australia*,
8
(1989),
127–131.

**C1.**
Butler G and Cannon JJ**:**
Computing in permutation and matrix groups III : Sylow subgroups.
*Journal of Symbolic Computation*,
8
(1989),
241–252.
MR90i:20003

**C1.**
Cartwright DI**:**
On the asymptotic behaviour of convolution powers of probabilities on discrete groups.
*Monatshefte für Mathematik*,
107
(1989),
287–290.
MR91a:60024

**C1.**
Cartwright DI and Soardi PM**:**
Convergence to ends for random walks on the automorphism group of a tree.
*Proceedings of the American Mathematical Society*,
107
(1989),
817–823.
MR90f:60137

**C1.**
Chen KH and Robinson J**:**
Comparison of factor spaces of two related populations.
*Journal of Multivariate Analysis*,
28
(1989),
190–203.
MR90g:62128

**C1.**
Cheung AT, Buchen PW, Macaskill C and Robinson DE**:**
Backscatter spectrum of a randomly perturbed regular array of discrete scatterers.
*Journal of the Acoustical Society of America*,
86
(1989),
no.1,
407–413.

**C1.**
Dancer EN**:**
A counterexample to the Lazer-McKenna conjecture.
*Nonlinear Analysis. Theory, Methods and Applications*,
13
(1989),
19–21.
MR0973364

**C1.**
Dancer EN**:**
Degenerate critical points, Morse inequalities and homotopy indices III.
*Bulletin of the Australian Mathematical Society*,
40
(1989),
97–108.
MR91i:58025

**C1.**
Dancer EN**:**
On the influence of domain shape on the existence of large solutions of some superlinear problems.
*Mathematische Annalen*,
285
(1989),
647–669.
MR91h:35122

**C1.**
Dancer EN and Sweers G**:**
On the existence of a maximal weak solution for a semilinear elliptic equation.
*Differential and Integral Equations*,
2
(1989),
533–540.
MR90h:35049

**C1.**
Dudley ML and James RW**:**
Time-dependent kinematic dynamos with stationary flows.
*Royal Society of London. Proceedings*,
Series A. Mathematical and Physical Sciences,
425
(1989),
407–429.
MR90i:76151

**C1.**
Dudley ML and James RW**:**
Computer-aided derivation of spherical harmonic spectral equations in astrogeophysics.
*Physics Earth Planet International*,
8
(1989),
423–427.
MR1021614

**C1.**
Durrant CJ**:**
Linear force-free magnetic fields and coronal models.
*Australian Journal of Physics*,
42
(1989),
317–329.

**C1.**
Durrant CJ and Brown SF**:**
Coronal loops in solar active regions.
*Proceedings of the Astronomical Society of Australia*,
8
(1989),
137–141.

**C1.**
Easdown D**:**
The local semilattice of chains of idempotents.
*Semigroup Forum*,
(1989)

**C1.**
Field MJ**:**
Equivariant Bifurcation Theory and Symmetry Breaking.
*Journal of Dynamics and Differential Equations*,
1
(1989),
no.4,
369–421.
MR90j:58109

**C1.**
Field MJ and Richardson RW**:**
Symmetry breaking and the Maximal Isotropy Subgroup conjecture for reflection groups.
*Archive for Rational Mechanics and Analysis*,
105
(1989),
61–94.
MR89m:58153

**C1.**
Glasby SP**:**
The composition and derived lengths of a soluble group.
*Journal of Algebra*,
120
(1989),
406–413.
MR90j:20075

**C1.**
Glasser ML and Cosgrove CM**:**
Mallow's integral and some generalizations.
*Journal of Mathematical Analysis and Applications*,
139
(1989),
533–536.
MR90h:33002

**C1.**
Glasser ML and Cosgrove CM**:**
A Gaussian-geometric finite sum formula.
*Journal of Mathematical Analysis and Applications*,
142
(1989),
331–336.
MR90h:11074

**C1.**
Hillman JA**:**
The algebraic characterization of the exteriors of certain two-knots.
*Inventiones Mathematicae*,
97
(1989),
195–207.
MR90d:57026

**C1.**
Hillman JA**:**
A homotopy fibration theorem in dimension 4.
*Topology and its Applications*,
33
(1989),
151–161.
MR90k:57023

**C1.**
Hillman JA and Kearton C**:**
Stable isometry structures and the factorization of \(\mathbb{Q}\)-acyclic stable knots.
*Journal of the London Mathematical Society*,
39
(1989),
175–182.
MR90h:57026

**C1.**
Hillman JA and Wilson SMJ**:**
On the reflexivity of Cappell Shaneson 2-knots.
*The Bulletin of the London Mathematical Society*,
21
(1989),
591–593.
MR90k:57028

**C1.**
Ivers DJ**:**
On generalised toroidal-poloidal solutions of vector field equations.
*Journal of the Australian Mathematical Society*,
(Series B),
30
(1989),
436–449.
MR90e:86016

**C1.**
Karlov L**:**
Paul Kard and Lorentz-free special relativity.
*Phys. Educ.*,
24
(1989),
165–168.

**C1.**
Kelly GM**:**
Elementary observations on 2-categorical limits.
*Bulletin of the Australian Mathematical Society*,
39
(1989),
301–317.
MR90f:18004

**C1.**
Kelly GM and Lawvere FW**:**
On the complete lattice of essential localizations.
*Bulletin de la Société Mathématique de Belgique*,
Série A,
41
(1989),
289–319.
MR91c:18001

**C1.**
Kennedy JE and Quine MP**:**
The total variation distance between the binomial and Poisson distribution.
*The Annals of Probability*,
17
(1989),
396–400.
MR90i:60020

**C1.**
Kuo TC**:**
Generalized Newton-Puiseux Theory and Hensel's Lemma in \(\mathbb{C}[[x,y]]\).
*Canadian Journal of Mathematics*,
(1989),
1101–1116.
MR91d:14010

**C1.**
Kuo TC, Li PX and Trotman DJA**:**
Blowing up and Whitney (\(a\))-regularity conditions.
*Canadian Mathematical Bulletin*,
32
(1989),
482–485.
MR91b:58008

**C1.**
Luckock HC**:**
Quantum Geometry of Strings with Boundaries.
*Annals of Physics*,
194
(1989),
113–147.
MR90h:81173

**C1.**
Luckock HC and Moss IG**:**
The Quantum Geometry of Random Surfaces and Spinning Membranes.
*Classical and Quantum Gravity*,
6
(1989),
1993–2027.
MR91f:81154

**C1.**
Madan DB and Seneta E**:**
Chebyshev polynomial approximations for characteristic function estimation: some theoretical supplements.
*Journal of the Royal Statistical Society*,
Series B. Methodological,
51
(1989),
281–285.
MR91a:60048

**C1.**
Mills TM and Seneta E**:**
Goodness-of-fit for a branching process with immigration using sample partial autocorrelations.
*Stochastic Processes and their Applications*,
33
(1989),
151–161.
MR91j:62133

**C1.**
Myerscough MR and Swan MA**:**
A model for swimming unipolar spirilla.
*Journal of Theoretical Biology*,
139
(1989),
201–218.

**C1.**
Peiris MS and Singh N**:**
Optimal experimental design for linear time series models with stochastic coefficients.
*Journal of the Indian Society for Statistics and Operations Research*,
10
(1989),
1–4.
MR1201934

**C1.**
Robinson J**:**
Limit theorems for standardized partial sums of weakly exchangeable arrays.
*The Australian Journal of Statistics*,
31
(1989),
200–214.
MR91e:60081

**C1.**
Rylands LJ and Taylor DE**:**
Rubik's Clock.
*Australian Mathematical Society Gazette*,
16
(1989),
3–6.
MR0992513

**C1.**
Sun SH**:**
Another approach to extensions of continuous mappings.
*Bulletin of the Australian Mathematical Society*,
39
(1989),
1–9.
MR90a:54040

**C1.**
Sun SH**:**
On paracompact locales and metric locales.
*Commentationes Mathematicæ Universitatis Carolinæ*,
30
(1989),
101–107.
MR0995708

**C1.**
Thompson RS and Stevens RJ**:**
A mathematical model for interpretation of Doppler velocity waveform indices.
*Med. & Biol. Eng. & Comput.*,
27
(1989),
269–276.

**C1.**
Walters RFC**:**
Datatypes in distributive categories.
*Bulletin of the Australian Mathematical Society*,
40
(1989),
79–82.
MR90j:68030

**C1.**
Walters RFC**:**
A note on context-free languages.
*Journal of Pure and Applied Algebra*,
62
(1989),
199–203.
MR91e:68094

**C1.**
Walters RFC**:**
The free category with products on a multigraph.
*Journal of Pure and Applied Algebra*,
62
(1989),
205–210.
MR91a:18003

**C1.**
Weber NC**:**
Applying elementary probability to some statistical problems.
*Reflections*,
14
(1989),
79–82.

**C1.**
Wilson PR**:**
The solar dynamo and convective rolls.
*Solar Physics*,
117
(1989),
212.
MR0525022

**C1.**
Wilson PR**:**
The buoyancy of \(U\)-loops.
*Proceedings of the Astronomical Society of Australia*,
8
(1989),
32–37.

**C1.**
Winch DE**:**
Induction in a model ocean.
*Physics Earth Planet International*,
53
(1989),
328–336.

**C1.**
Winch DE**:**
Lunar geomagnetic variations.
*Pure and Applied Geophysics*,
131
(1989),
292–309.

**C1.**
Winch DE**:**
The earth's magnetic field.
*Journal of the Royal Society of London. Proceedings of New South Wales*,
122
(1989),
1–9.

**C4.**
Trudinger BJ, Cook CM, Giles WB, Connelly AJ and Thompson RS**:**
Low dose aspirin and twin pregnancy.
*Lancet*,
ii
(1989),
1214.

## Conference Proceedings

**E1.**
Easdown D
(1989)
Biordered sets : a tool for constructing semigroups.
*Monoids, Semigroup Theory and Applications, Proceedings to the Berkeley Workshop on Monoids*,
World Scientific Publishing Company

**E1.**
Easdown D
(1989)
Minimal faithful permutation and transformation representations of groups and semigroups.
*Proceedings of the International Conference on Algebra in Honour of A.I. Malcev*

**E1.**
Fackerell ED and Kersten PHM
(1989)
Vacuum Einstein fields with a single non-null Killing vector.
*Proceedings of the fifth Marcel Grossman Meeting on General Relativity*,
Blair DG, Buckingham MJ (ed.) ,
World Scientific,
515–519.
MR1056911

**E1.**
Mack JM
(1989)
What are the purposes of a mathematical education?
*MANSW Annual Conference, Mudgee*,
Kumar M, et al. eds (ed.) ,
Reflections,
MANSW, Sydney,
**14**(4),
9–13.
(Invited address)

**E1.**
Pecker JC and Wilson PR
(1989)
Systematic observations of the Sun.
*Proc. of 20th General Assembly of Intern. Astron. Union, (Baltimore)*
MR1110821

**E1.**
Phan D
(1989)
Axisymmetric vacuum Einstein fields.
*Proceedings of the 5th Marcel Grossman Meeting on General Relativity*,
Blair DG, Buckingham MJ (ed.) ,
World Scientific,
545–548.

**E1.**
Rees DE
(1989)
Synthesis and Inversion of Stokes Profiles in Sunspots.
*Proc. Atelier Transfert*,
Frisch H, Mein N eds (ed.) ,
l'Observatoire de Paris,
33–41.
(Invited Review)

**E1.**
Ryan AJ
(1989)
Domains of holomorphy as initial data for Dirac equations in \(\mathbb{C}^n\).
*Seventeenth International Congress on Differential Geometric Methods in Theoretical Physics, Chester 15–19 August 1998*,
World Scientific,
281–291.
MR1124434

**E1.**
Seneta E
(1989)
Ukrainians in the 1986 census.
*Fourth Conference, Sydney 1988*,
*Ukrainian Settlement in Australia*,
Gordijew I, Koscharsky H eds (ed.) ,
88–93.

**E3.**
Zheligovsky VA
(1989)
On magnetic field generation by a class of flows of conducting fluid.
*Abstracts of the VI Seminar ``Non-linear problems of the theory of hydrodynamic stability''*,
Moscow University Press,
25.

## Computer Software

**G1.**
Cannon JJ and others
(1989)
Cayley V3.7.
(As for V3.6 plus soluble groups and number theory; 280,000 lines of C code.)
.

## Other Output

**OT.**
Bosma W
(1989)
Notes on primality testing and factoring.
Laboratoire de Mathématiques Marseille,
**89**

**OT.**
Fackerell ED
(1989)
Einstein vacuum field equations with a single non-null Killing vector.
(Seminar presented to Phys. Dept. Brigham Young Uni. Utah, USA)

## Unpublished Conference Proceedings

**UN.**
Durrant CJ
Solar physics and the large Earth-based solar telescope.
*AAS/ASA scientific discussion meeting, Canberra 1989*
.

**UN.**
Durrant CJ and Galloway DJ
The solar analogue.
*CSIRO stellar workshop, Sydney 1989*
.

**UN.**
Fackerell ED
Ricci collineations and new potentials for vacuum spacetimes with one Killing vector.
*12th International Conference on General Relativity and Gravitation, University of Colorado, Boulder, Colorado July 1989*
.

**UN.**
Galloway DJ
Kinematic dynamo action and stability of the ABC flows.
*Conference on Small-diffusivity dynamos and dynamical systems, Nice, France 1989*
.

**UN.**
Gibson WG
Hopfield networks.
*Workshop on foundation of connectionist modelling, UNSW July 1989*
.

**UN.**
Phan D
Exact solutions for axisymmetric vacuum spacetimes where the killing vector is hypersurface orthogonal.
*12th Conference on General Relativity Colorado, USA 1989*
.

**UN.**
Quine MP
A linear random growth model.
*Singapore Probability Conference, June 1989*
.

**UN.**
Quine MP
Models for nucleation and growth on a line.
*Symposium on Applied Probability, Sheffield, England August 1989*
.

**UN.**
Quine MP and Robinson J
A Poisson process with inhibition.
*International Conference on Recent Developments in Statistical Data Analysis and Inference, Neuchâtel, Switzerland, August 1989*
.

**UN.**
Robinson J
Approximating probabilities for small and large deviations.
*47th Session of the International Statistical Institute Paris, France, September 1989*
.

**UN.**
Wilson PR
The reversal of the solar polar magnetic fields.
*Solar cycle workshop: 3rd meeting, Sydney 1989*
.

**UN.**
Wilson PR
The extended solar cycle.
*Solar-terrestrial forecast workshop, Leura 1989*
.

**UN.**
Wilson PR
The origin of the large-scale fields.
*Solar-terrestrial forecast workshop, Leura 1989*,
Poster paper
.

**UN.**
Winch DE
Sydney-Auckland cable voltage analysis.
*25th Austr. Appl. Maths. conference, Ballarat, Vic. 1989*
.

**UN.**
Winch DE
Displaced daygraphs for the presentation of geomagnetic data.
*IAGA 6th scientific assembly Exeter, UK 1989*
.

**UN.**
Winch DE and others
Geoelectric potentials measured by ocean cables.
*IAGA 6th scientific assembly, Exeter, UK 1989*
.

**UN.**
Winch DE and others
Eastward and westward moving components of \(S_q\) and \(L\).
*IAGA 6th scientific assembly Exeter, UK 1989*
.