# Research Publications for 1990

## Books

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

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

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

A3. Reichel A (1990) Out of the Crucible Conference Proceedings. CHAST, Sydney.

## Chapters in Books

B1. Butler G and Cannon JJ (1990) 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, 10–19.

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

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

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

B1. Zheligovsky VA (1990) 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, 161–181.

## Journal Articles

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

C1. Bennett MR and Robinson J (1990) 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, 329–358.

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

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

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

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

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

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

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

C1. Deligne P and Dimca A (1990) Filtrations de Hodge et par l'ordre du $$p$$ le pour les hypersurfaces singulières. Annales Scientifiques de l'École Normale Supérieure, Quatrième Série, 23 MR1078856

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

C1. Dimca A and Choudary ADR (1990) 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, 145–147. MR91e:14017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

C1. Monro GP (1990) A note on the performer's conception of space. Journal for the Anthropological Study of Human Movement, 6(2), 63–71. (actually appeared in 1991)

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

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

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

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

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

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

C1. Reichel A (1990) Chapters in Australian science. Quadrant, 34(266) MR1082702

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

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

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

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

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

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

C1. Thompson RS and Trudinger BJ (1990) 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, 449–458.

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

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

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

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