# Research Publications for 1990

## Books

**A1.**
Lai KF and Lan YZ**:**
*Representation Theory of \(\mathrm{GL}(2)\) and theory of automorphic forms.*
Peking University Press,
1990.

**A2.**
Hutchinson TP and Lai CD**:**
*Continuous Bivariate Distributions, Emphasising Applications.*
Rumsby Scientific Publishing, Adelaide,
1990.
MR1070715

**A2.**
Wehrhahn KH**:**
*Combinatorics — An Introduction.*
Undergraduate Lecture Notes in Mathematics,
**1**
Carslaw Publications, Sydney,
1990.

**A3.**
Reichel A**:**
*Out of the Crucible Conference Proceedings.*
CHAST, Sydney,
1990.

**A5.**
Bosma W and van der Hulst MPM**:**
*Primality proving with cyclotomy.*
Universiteit van Amsterdam,
1990,
(Proefschrift).

## Chapters in Books

**B1.**
Butler G and Cannon JJ**:**
The design of Cayley — a language for modern algebra,
*Design and Implementation of Symbolic Computation Systems.*
Miola A (ed.),
Lecture Notes in Computer Science,
**429**,
Springer,
1990,
10–19.

**B1.**
Dancer EN and Hess P**:**
Behaviour of a semilinear periodic-parabolic problem when a parameter is small,
*Functional analytic methods for partial differential equations.*
Springer-Verlag, Berlin,
1990,
(Kato 60th birthday volume 12–19)
MR1084598

**B1.**
Myerscough MR, Maini PK, Murray JD and Winters KH**:**
Two dimensional pattern formation in a chemotactic system,
*Dynamics of Complex Interconnected Biological System.*
Vincent TL, Mees AI, Jennings LS (ed.),
Birkhauser, Boston,
1990,
65–83.
MR1104228

**B1.**
Rees DE**:**
Stokes Polarimetry of Sunspots,
*Interior and Atmosphere of the Sun.*
Cox AN, Livingston WC, Matthews MS (ed.),
Uni of Arizona,
1990,
(Section III of Chapter 23. Invited review.)

**B1.**
Zheligovsky VA**:**
On magnetic field generation by a flow of a conducting medium with an internal scale,
*Computer analysis of geophysical fields.*
Computational Seismology,
**23**,
Nauka, Moscow,
1990,
161–181.

## Journal Articles

**C1.**
Barnes DW**:**
Finitely sorting Lie algebras.
*Journal of the Australian Mathematical Society*,
49
(1990),
354–363.
MR91i:17027

**C1.**
Bennett MR and Robinson J**:**
Probabilistic secretion of quanta from nerve terminals of synaptic sites on muscle cells: non-uniformity, autoinhibition and the binomial hypothesis.
*Royal Society of London. Proceedings*,
Series B,
239
(1990),
329–358.

**C1.**
Bosma W**:**
Approximation by mediants.
*Mathematics of Computation*,
54
(1990),
421–434.
MR90m:11119

**C1.**
Bosma W**:**
Canonical bases for cyclotomic fields.
*Applicable Algebra in Engineering, Communication and Computing*,
(1990),
125–134.
MR95k:11135

**C1.**
Bosma W and Kraaikamp C**:**
Metrical theory for optimal continued fractions.
*Journal of Number Theory*,
34
(1990),
251–270.
MR91d:11095

**C1.**
Choo KG and Sun SH**:**
Some new cardinal inequalities involving a cardinal function less than the spread and the density.
*Commentationes Mathematicæ Universitatis Carolinæ*,
31
(1990),
395–401.
MR92b:54005

**C1.**
Dancer EN**:**
Certain weakly nonlinear partial differential equations on annuli.
*Nonlinear Analysis. Theory, Methods and Applications*,
14
(1990),
441–442.
MR1041507

**C1.**
Dancer EN**:**
The effect of domain shape on the number of positive solutions of certain nonlinear equations II.
*Journal of Differential Equations*,
87
(1990),
316–339.
MR91j:35034

**C1.**
Dancer EN and Toland JF**:**
Degree theory for orbits of prescribed period for flows with a first integral.
*Proceedings of the London Mathematical Society*,
60
(1990),
549–580.
MR91a:58152

**C1.**
Deligne P and Dimca A**:**
Filtrations de Hodge et par l'ordre du \(p\) le pour les hypersurfaces singulières.
*Annales Scientifiques de l'École Normale Supérieure*,
Quatrième Série,
23
(1990)
MR1072821

**C1.**
Dimca A**:**
Betti numbers of hypersurfaces and defects of linear systems.
*Duke Mathematical Journal*,
60
(1990),
285–298.
MR91f:14041

**C1.**
Dimca A and Choudary ADR**:**
Singular complex surfaces in \(\mathbb{P}^3\) having the same \(\mathbb{Z}\)-homology and \(\mathbb{Q}\)-homotopy type as \(\mathbb{P}^3\).
*The Bulletin of the London Mathematical Society*,
22
(1990),
145–147.
MR91e:14017

**C1.**
Donati JF, Semel M, Rees DE, Taylor K and Robinson RD**:**
Detection of a magnetic region on HR 1099.
*Astronomy and Astrophysics*,
232
(1990),
L1–L4.

**C1.**
Du J**:**
Cells in the affine Weyl group of type \(\tilde D_4\).
*Journal of Algebra*,
128
(1990),
384–404.
MR91a:20052

**C1.**
Edelman D**:**
An inequality of optimal order for the tail probabilities of the \(t\)-statistic under symmetry.
*Journal of the American Statistical Association*,
85
(1990),
120–122.
MR1137357

**C1.**
Edelman D**:**
A confidence interval for the center of an unknown unimodal distribution based on a sample size of 1.
*American Statistician*,
44
(1990),
285–287.

**C1.**
Edelman D**:**
A note on uniformly most powerful two-sided tests.
*American Statistician*,
44
(1990),
219–220.
MR1130913

**C1.**
Field MJ and Golubitsky M**:**
Symmetric Chaos.
*Computers in Physics*,
4
(1990),
470–479.

**C1.**
Field MJ and Richardson RW**:**
Symmetry breaking in equivariant bifurcation problems.
*Bulletin of the American Mathematical Society*,
22
(1990),
79–84.
MR90e:58017

**C1.**
Glasby SP and Slattery MC**:**
Computing intersections and normalizers in soluble groups.
*Journal of Symbolic Computation*,
9
(1990),
637–651.
MR91j:20044

**C1.**
Hartfield DJ and Seneta E**:**
A note on semigroups of regular stochastic matrices.
*Linear Algebra and its Applications*,
141
(1990),
47–51.
MR91m:15031

**C1.**
Hillman JA and Plotnick SP**:**
Geometrically fibred 2-knots.
*Mathematische Annalen*,
287
(1990),
259–273.
MR91g:57023

**C1.**
Hoppe FM and Seneta E**:**
Bonferroni-type inequalities and the methods of indicators and polynomials.
*Advances in Applied Probability*,
22
(1990),
241–246.
MR91e:60052

**C1.**
Hoppe FM and Seneta E**:**
A Bonferroni-type identity and permutation bounds.
*International Statistical Review*,
58
(1990),
253–261.

**C1.**
Jones CA, Roberts PH and Galloway DJ**:**
Compressible convection in the presence of rotation and a magnetic field.
*Geophysical and Astrophysical Fluid Dynamics*,
53
(1990),
145–182.

**C1.**
Joshi N**:**
An explicit one-soliton solution of the (2+1) dimensional generalized Sine-Gordon equations.
*Letters in Mathematical Physics*,
20
(1990),
261–270.
MR1077957

**C1.**
Kasangian S and Walters RFC**:**
The duality between flow charts and circuits.
*Bulletin of the Australian Mathematical Society*,
42
(1990),
71–79.
MR91j:68033

**C1.**
Kokic PN and Weber NC**:**
An Edgeworth expansion for \(U\)-statistics based on samples from finite populations.
*The Annals of Probability*,
18
(1990),
390–404.
MR91e:60068

**C1.**
Kotz S and Seneta E**:**
Lenin as a statistician: a non-Soviet view.
*Journal of the Royal Statistical Society*,
Series A. Statistics in Society,
153
(1990),
73–94.

**C1.**
Lehrer GI and Dyer MJ**:**
On positivity in Hecke algebras.
*Geometriæ Dedicata*,
25
(1990),
115–125.
MR91h:20062

**C1.**
Lehrer GI and Shoji T**:**
On flag varieties, hyperplane complements and Springer representations of Weyl groups.
*Journal of the Australian Mathematical Society*,
(Series A),
49
(1990),
449–485.
MR91k:20050

**C1.**
Luckock HC and McKane AJ**:**
Path Integrals and non-Markov Processes: III. Calculation of the Escape-Rate Prefactor in the Weak-Noise Limit.
*Physical Review. A*,
42A
(1990),
1982–1996.
MR91k:82006

**C1.**
Mack JM**:**
FORUM: Survey of Entry Level Courses.
*Australian Mathematical Society Gazette*,
17
(1990),
177–180.

**C1.**
Madan DB and Seneta E**:**
The variance gamma (v.g.) model for share market returns.
*Journal of Business*,
63
(1990),
511–524.

**C1.**
Madan DB and Seneta E**:**
On the monotonicity of the labour-capital ratio in Sraffa's model.
*Journal of Economics (Zeitschrift für Nationalökonomie)*,
51
(1990),
101–107.
MR1054199

**C1.**
McKane AJ, Luckock HC and Bray AJ**:**
Path Integrals and non-Markov Processes: I. General Formalism.
*Physical Review. A*,
41A
(1990),
644–656.
MR91b:82032

**C1.**
Monro GP**:**
A note on the performer's conception of space.
*Journal for the Anthropological Study of Human Movement*,
6
(1990),
no.2,
63–71.
(actually appeared in 1991)

**C1.**
Myerscough MR**:**
Propagation of a standing wave pattern in a chemotactic system.
*Australian Mathematical Society Gazette*,
17
(1990),
1–4.
MR1037098

**C1.**
Nelson AM**:**
A Generalized Cyclotomic Identity.
*Advances in Mathematics*,
83
(1990),
1–29.
MR92h:05010

**C1.**
Palmer WD**:**
Generalized Bhaskar-Rao designs with two association classes.
*Australasian Journal of Combinatorics*,
1
(1990),
161–180.
MR92g:05036

**C1.**
Parusiński A**:**
Gradient homotopies of gradient vector fields.
*Studia Mathematica*,
XCVI
(1990),
73–80.
MR91g:58086

**C1.**
Peiris MS**:**
Analysis of multivariate ARMA processes with nonstationary innovations.
*Communications in Statistics. Theory and Methods*,
19
(1990),
2847–2852.
MR92b:62135

**C1.**
Quine MP and Robinson J**:**
A linear random growth model.
*Journal of Applied Probability*,
27
(1990),
499–509.
MR91i:60068

**C1.**
Reichel A**:**
Chapters in Australian science.
*Quadrant*,
34
(1990),
no.266

**C1.**
Robinson J, Hoglund T, Holst L and Quine MP**:**
On approximating probabilities for small and large deviations on \(\mathbb{R}^d\).
*The Annals of Probability*,
18
(1990),
727–753.
MR91i:60069

**C1.**
Rosenberg S, Weber NC, Crocq MR, Duval F and Macher JP**:**
Random number generation by normal, alcoholic and schizophrenic subjects.
*Psychological Medicine*,
20
(1990),
953–960.

**C1.**
Seneta E**:**
Karamata's iteration theorem and normed regularly varying sequences in a historical light.
*Publications de l'Institut Mathématique, Académie Serbe des Sciences*,
48
(1990),
45–51.
(New series)
MR1105138

**C1.**
Sun SH**:**
Remarks on quantic nuclei.
*Mathematical Proceedings of the Cambridge Philosophical Society*,
108
(1990),
257–260.
MR91j:81011

**C1.**
Taylor DE**:**
A natural proof of the cyclotomic identity.
*Bulletin of the Australian Mathematical Society*,
42
(1990),
185–189.
MR92g:05021

**C1.**
Thompson RS, Aldis GK and Linnett IW**:**
Doppler ultrasound spectral power density distribution: measurement artefacts in steady flow.
*Med. & Biol. Eng. & Comput.*,
28
(1990),
60–66.

**C1.**
Thompson RS and Trudinger BJ**:**
Doppler waveform indices and resistance, pressure and flow in the umbilical placental circulation: an investigation using a mathematical model.
*Ultrasound in Medicine and Biology*,
16
(1990),
449–458.

**C1.**
Wehrhahn KH and Varadarajan K**:**
Aperiodic rings, necklace rings and Witt vectors.
*Advances in Mathematics*,
81
(1990),
1–29.
MR91f:05012

**C1.**
Wilson PR, Donnelly RF and Wilkinson P**:**
Solar cycle workshop: Third meeting (a review).
*Solar Physics*,
125
(1990),
159.

**C1.**
Wilson PR, McIntosh PS and Snodgrass HB**:**
The reversal of the solar polar magnetic fields I.
*Solar Physics*,
127
(1990),
1–9.

**C1.**
Winters KH, Myerscough MR, Maini PK and Murray JD**:**
Tracking bifurcating solutions of a model biological pattern generator.
*Impact of Computing in Science and Engineering*,
2
(1990),
355–371.

## Conference Proceedings

**E1.**
Bosma W and van der Hulst MPM
(1990)
Faster primality proving.
*Advances in Cryptology — EUROCRYPT '89*,
Goos G, Hartmanis J eds (ed.) ,
Springer, Berlin,
652–656.

**E1.**
Durrant CJ
(1990)
Outstanding theoretical problems.
*Solar photosphere: Structure, Convection and Magnetic Fields*,
Stenflo JO (ed.) ,
Kluwer, Dordrecht,
489–499.
(IAU Symposium)

**E1.**
Fraser WB
(1990)
The unwinding problem: a moving boundary value problem.
*Mini-conference on approximate methods for boundary value problems*,
Centre for Mathematical Analysis, ANU,
(December 1990)
MR1123673

**E1.**
Galloway DJ
(1990)
Dynamo action and stability of the ABC chaotic flows.
*Chaos in Australia, UNSW*,
(February 1990)
MR1038611

**E1.**
Gibson WG, Robinson J and Bennett MR
(1990)
Probabilistic Secretion of Transmitter at Granule Cell Synapses: A Role in Pattern Separation and Activity Regulation.
*Australian Conference on Neural Networks, Sydney (January, 1990)*,
*Proceedings of the First Australian Conference on Neural Networks*,
132–133.

**E1.**
Lehrer GI
(1990)
Group representations, geometry and topology.
Lecture Notes in Mathematics,
Springer,
**1456**,
14–31.
MR92d:20058

**E1.**
Mack JM
(1990)
Mathematics Education towards 2000.
*Australian Academy of Science Annual Symposium, April 1990*
MR1147470

**E1.**
Mack JM
(1990)
What are the purposes of a mathematical education?
*Mathematical Turning Points : Strategies for the 1990s, Vol. 1. Hobart*,
Milton K, McCann H eds (ed.) ,
81–92.
(Proceedings of the Australian Association of Mathematics Teachers 13th Biennial Conference)

**E1.**
Suffern KG and Fackerell ED
(1990)
Interval methods in computer graphics.
*Proc. AUSGRAPH 90*,
Gigante M (ed.) ,
Aust. Comp. Graphics Assoc. Inc., Melbourne,
35–44.

**E1.**
Wall GE
(1990)
Dependence of Lie relators for Burnside varieties.
Lecture Notes in Mathematics,
Springer-Verlag, Berlin,
**1456**,
191–197.
MR1092233

**E1.**
Wilson PR
(1990)
The extended solar activity cycle.
*Proceedings of the Solar-Terrestrial Predictions Workshop, Leura, 1989*,
257–263.

**E1.**
Wilson PR and McIntosh PS
(1990)
The origin of the large-scale fields.
*Proceedings of the Solar-Terrestrial Predictions Workshop, Leura, 1989*,
650–657.

## Computer Software

**G1.**
Cannon JJ and Richardson JS
(1990)
Blockhandler V1.3.
(5,000 lines of C code.)
.

## Other Output

**OT.**
Fackerell ED
(1990)
Einstein vacuum field equations with a single non-null Killing vector.
(Seminar presented to Phys. Dept. Uni. of Utah, Utah, USA)

## Creative Works

**OT.**
Fredericks I, Lee R, Monro GP and Ryan M
(1990)
Strange Attractors.
(Presented at the 1990 WATT concerts (4 concerts), Seymour Centre, Sept 1990)

## Unpublished Conference Proceedings

**UN.**
Brown SF
Coronal loops in solar active regions.
*Conference on solar terrestrial and space physics, Melbourne 1990*
.

**UN.**
Easdown D
The free semigroup on a biordered set.
*Conference/Workshop on Semigroups, Formal Languages and Applications, Sydney, July 17–20 1990*
.

**UN.**
Eyland RW and Sharp B
The differentiability of convex functions on topological linear spaces.
*Australian Mathematical Society Annual Meeting, Townsville, June 29 – July 2 1990*
.

**UN.**
Eyland RW and Sharp B
The Frechet differentiability of convex functions on \(C(S)\).
*Miniconference on Analysis, Townsville, July 3–8 1990*
.

**UN.**
Eyland RW and Sharp B
A generalization of Mazur's theorem and other results.
*Miniconference on Convex Analysis, Newcastle, June 11–25 1990*
.

**UN.**
Eyland RW and Sharp B
A factor theorem for locally convex differentiability spaces.
*Workshop on Convex Analysis, Newcastle, June 11–25 1990*
.

**UN.**
Eyland RW and Sharp B
Duality results for locally convex differentiability spaces.
*Workshop on Convex Analysis, Newcastle, July 16–30 1990*
.

**UN.**
Field MJ
Symmetry breaking.
*Conference on Computational Algebra in honour of G E Wall Sydney, November 7–9 1990*
.

**UN.**
Keener RW, Kmenta J and Weber NC
Estimation of the covariance matrix of the least square regression coefficients when the disturbance covariance matrix is of unknown form.
*6th World Congress of the Econometric Society, Barcelona*
.

**UN.**
Kelly GM
Finitely enriched monads and their presentations.
*International Summer Conference in Category theory, Como, July 22–28 1990*
.

**UN.**
Kuo TC
Some ideas of Thom and their outcome.
*Conference of Stratification et singularités d'applications. Luminy, May 21–25 1990*
.

**UN.**
Lehrer GI
Hecke algebras and related topics.
*Workshop on Algebraic Groups, Berkeley, October 1990*
.

**UN.**
Lehrer GI
Geometry of conjugacy classes.
*Conference on Group Theory, in honour of GE Wall, Sydney, November 10–11 1990*
.

**UN.**
Monro GP
Interpolation methods in the computer manipulation of sound.
*Australian New Music Conference, Brisbane, August 1990*
.

**UN.**
Peiris MS
Multivariate ARMA processes with nonstationary innovations.
*10th Australian Statistical Conference, University of NSW*
.

**UN.**
Rees DE
Biomagnetism-the Next Frontier in Medical Imaging.
*Mathematical Association of NSW, Talented Students Day (July 1990)*
.

**UN.**
Rees DE, Rennie CJ, Gordon E and Barn G
Dynamics of electrical brain activity in schizophrenia.
*Chaos in Australia, UNSW 1990*,
Poster Paper
.

**UN.**
Reichel A
Substance abuse syndrome.
*Out of the Crucible, Sydney, December 1990*
.

**UN.**
Reichel A
Fostering the cognitive turn.
*Australian Association of History, Philosophy and Social Studies of Science, September 1990*
.

**UN.**
Taylor DE
Two graphs and doubly transitive groups.
*Eighth Annual Algebra Conference of Victoria, Melbourne. September 27 and 28 1990*
.

**UN.**
Taylor DE
Solomon algebras.
*16th Australasian Conference on Combinatorial Mathematics and Computing, Massey University, New Zealand, December 2–7 1990*
.

**UN.**
Walters RFC
An imperative language based on distributive categories.
*International Summer Conference in Category Theory, Como, July 22–28 1990*
.

**UN.**
Walters RFC
The Todd Coxeter procedure and the computation of left Kan extension.
*Conference on Computational Algebra in honour of GE Wall, Sydney, November 7–9 1990*
.

**UN.**
Wehrhahn KH
Aperiodic rings, necklace rings and Witt vector.
*International Conference on Commutative Algebra and Combinatorics Nagoya, August 1990*
.

**UN.**
Wehrhahn KH
The cyclotomic identity and combinatorial species.
*International Congress of Mathematicians, Kyoto, August 1990*
.