# Research Publications for 1996

## Books

A4. Phipps MC and Quine MP: A Primer of Statistics, Second Edition. Prentice Hall, NSW Australia, 1996, ISBN 0 7248 0946 5, iv + 141 pages.

## Chapters in Books

B1. Fackerell ED: Remarks on the Yilmaz and Alley papers, Proceedings of the First Australasian Conference on General Relativity and Gravitation. Australasian Conference on General Relativity and Gravitation, Institute for Theoretical Physics, University of Adelaide, Adelaide, 1996, ISBN 0 86396 430 3, 117–131.

B1. Henyey FS and Macaskill C: Sound through the internal wave field, Stochastic Modelling in Physical Oceanography. Progress in Probability, 39, Birkhäuser, Boston, 1996, ISBN 0-8176-3798-2, 141–184. MR96k:76106

B1. Hu BL and Matacz A: Quantum Noise in Gravitation and Cosmology, Fluctuations and Order: The New Synthesis. Springer, New York, 1996, ISBN 0-387-94602-0, 429–454. MR98c:83046

B1. Shannon AG, Loh RP, Melham RS and Horadam AF: A search for solutions of a functional equation, Applications of Fibonacci numbers. 6, Kluwer Academic Publishers, Dordrecht, 1996, 431–441. MR1393476

## Journal Articles

C1. Bennett MR, Farnell L and Gibson WG: Quantal transmitter release at somatic motor-nerve terminals: stochastic analysis of the subunit hypothesis. Biophysical Journal, 70 (1996), 654–668.

C1. Bennett MR, Farnell L and Gibson WG: Quantal transmitter release onto different patterns of receptor distributions at somatic neuromuscular junctions. Journal of Theoretical Biology, 183 (1996), 231–236.

C1. Bennett MR, Robinson J, Phipps MC, Karunanithi S, Lin YQ and Cottee L: Quantal components of spontaneous potentials at visualised varicosities. Journal of Autonomic Nervous System, 56 (1996), 161–174.

C1. Bloom SL, Sabadini N and Walters RFC: Matrices, machines and behaviors. Applied Categorical Structures, 4 (1996), 343–360. MR98a:68049

C1. Bolsinov AV, Dullin HR and Wittek A: Topology of energy surfaces and existence of transversal Poincaré sections. J. Phys. A,, 29 (1996), 4977–4985.

C1. Bosma W and Stevenhagen P: On the computation of quadratic 2-class groups. Journal de Théorie des Nombres, 8 (1996), 283–313. MR98e:11129a

C1. Bosma W and Stevenhagen P: Density computations for real quadratic units. Mathematics of Computation, 65 (1996), 1327–1337. MR96j:11171

C1. Brown G, Koumandos S and Wang KY: Positivity of Cotes numbers at more Jacobi abscissas. Monatshefte für Mathematik, 122 (1996), 9–19. MR97k:33006

C1. Brown G, Koumandos S and Wang KY: Positivity of more Jacobi polynomial sums. Mathematical Proceedings of the Cambridge Philosophical Society, 119 (1996), 681–694. MR97d:33002

C1. Brown SF: Formation of coronal loops with temperatures between $$10^5$$ and $$10^6$$ K. Astronomy and Astrophysics, 305 (1996), 649–659.

C1. Buchen PW and Ben Hador R: Free-mode surface wave computations. Geophysical Journal International, 124 (1996), 869–887.

C1. Buchen PW and Kelly MF: The maximum entropy distribution of an asset inferred from option prices. Journal of Financial and Quantitative Analysis, 31 (1996), 143–159.

C1. Cannon JJ and Playoust CE: Magma: a new computer algebra system. Euromath Bulletin, 2 (1996), 113–144. MR1413180

C1. Cao D, Dancer EN, Noussair ES and Yan S: On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems. Discrete and Continuous Dynamical Systems, 2 (1996), 221–236. MR96m:35095

C1. Carboni A and Janelidze G: Decidable (=separable) objects and morphisms in lextensive categories. Journal of Pure and Applied Algebra, 110 (1996), 219–240. MR97d:18001

C1. Carboni A, Janelidze G and Magid AR: A note on Galois correspondence for commutative rings. Journal of Algebra, 183 (1996), 266–272. MR97g:13009

C1. Dancer EN: Some remarks on classical problems and fine properties of Sobolev spaces. Differential and Integral Equations, 9 (1996), 437–446. MR97e:35057

C1. Dancer EN: A counterexample on competing species equations. Differential and Integral Equations, 9 (1996), 239–246. MR97d:35220

C1. Dancer EN: Domain variation for certain sets of solutions and applications. Topological Methods in Nonlinear Analysis, 7 (1996), 95–113. MR97m:35079

C1. Dancer EN and Du Y: The generalized Conley index and multiple solutions of semilinear elliptic problems. Abstract and Applied Analysis, 1 (1996), 103–135. MR97i:35048

C1. Dancer EN and Toland JF: Real transformations with polynomial invariants. Journal of Geometry and Physics, 19 (1996), 99–122. MR97c:58120

C1. Daners D: Domain perturbation for linear and nonlinear parabolic equations. Journal of Differential Equations, 129 (1996), 358–402. MR97h:35071

C1. Dullin HR, Richter PH and Wittek A: A two parameter study of the extent of chaos in a billiard system. Chaos,, 6 (1996), 43–58.

C1. Easdown D and Gould V: Commutative orders. Proceedings of the Royal Society of Edinburgh, 126A (1996), 1201–1216.. MR97m:20069

C1. Easdown D and Gould V: Orders in power semigroups. Glasgow Mathematical Journal, 38 (1996), 39–47.. MR97a:20112

C1. Forbes LK, Gray BF and Sidhu HS: Periodically forced hydrocarbon oxidation in a CSTR. Bifurcation and Chaos, 6 (1996), 12.

C1. Fraser WB, Clark JD, Ghosh TK and Zeng Q: The effect of a control ring on the stability of the ring-spinning balloon. Royal Society of London. Proceedings, Series A. Mathematical and Physical Sciences, 452 (1996), 47–62.

C1. Gopalsamy K and He XZ: Dynamics of an almost periodic logistic integrodifferential equation. Methods in Applied Analysis, 2 (1996), 38–66.

C1. Graham JJ and Lehrer GI: Cellular algebras. Inventiones Mathematicae, 123 (1996), 1–34. MR97h:20016

C1. Gray BF, Forbes LK and Sidhu HS: A detailed study of the effects of forcing a hydrocarbon oxidation reaction. Mathematical Computation and Modelling, 24 (1996), no.8, 65–88.

C1. Gray BF and Jones JC: Futher evidence of anomolies in the self heating temperature histories of solid substrates. Journal of Fire Science, 14 (1996), 91–94.

C1. Gray BF, Mercer GN, Weber RO and Watt SD: Combustion pseudo-waves in a system with reactant consumption and heat loss. Mathematical Computation and Modelling, 24 (1996), no.8, 29–38. (Special issue: Nonlinear Dynamics of Combustion Systems) MR1422953

C1. Halburd RG and Joshi N: The coalescence limit of the second Painlevé equation. Studies in Applied Mathematics, 97 (1996), 1–15. MR1393931

C1. Hammer J: Orthogonal designs and generalised Fourier-Walsh transforms. Utilitas Mathematica, 50 (1996), 113–125.

C1. He XZ: Stability and delays in a predator-prey system. Journal of Mathematical Analysis and Applications, 198 (1996), 355–370. MR97a:92009

C1. Hillman JA: Embedding homology equivalent 3-manifolds in 4-space. Mathematische Zeitschrift, 223 (1996), 473–481. MR97h:57044

C1. Holst L, Quine MP and Robinson J: A general stochastic model for nucleation and linear growth. Annals of Applied Probability, 6 (1996), 903–921. MR97i:60093

C1. Hu H and Tholen W: A note on free regular and exact completions, and their infinitary generalizations. Theory and Applications of Categories, 2 (1996), 113–132. MR98e:18001

C1. Iltyakov AV: On rational invariants of the group $$E_6$$. Proceedings of the American Mathematical Society, 124 (1996), 3637–3640. MR97b:13008

C1. Iltyakov AV and Shestakov IP: On invariants of $$F_4$$ and the center of the Albert algebra. Journal of Algebra, 179 (1996), 838–851. MR96m:17058

C1. Ivanoff BG and Weber NC: Some characterisations of partial exchangeability. Journal of the Australian Mathematical Society, (Series A), 61 (1996), 345–359. MR97k:60099

C1. James GD and Mathas A: Hecke algebras of type A with q=-1. Journal of Algebra, 184 (1996), 102–158. MR97h:20017

C1. Joarder AH and Hossain MA: On the characteristic function of the multivariate Pearson type II distribution. Statistica, LVI 3 (1996), 313–319. MR1476909

C1. Joarder AH and Hossain MA: Estimation of the eigenvalues of the scale matrix of a class of elliptical distributions. Statistica Neerlandica, 56 (1996), no.3, 313–319. MR1476909

C1. John RD and Robinson J: Rates of convergence to normality for samples from a finite set of random variables. Journal of the Australian Mathematical Society, (Series A), 60 (1996), 355–362. MR97d:60040

C1. Johnstone PT: Remarks on quintessential and persistent localizations. Theory and Applications of Categories, 2 (1996), 90–99. MR97j:18004

C1. Joshi N and Petersen JA: Complex blow-up in Burgers' equation: an iterative approach. Bulletin of the Australian Mathematical Society, 54 (1996), 353–362. MR1419597

C1. Ku S and Seneta E: Quenouille-type theorem on autocorrelations. Annals of the Institute of Statistical Mathematics, 48 (1996), 621–630. MR98f:62259

C1. Kuchel PW, Lennon AJ and Durrant CJ: Analytical solutions and simulations for spin-echo measurements of diffusion of spins in a sphere with surface and bulk relaxation. Journal of Magnetic Resonance, Series B, 112 (1996), 1–17.

C1. Lavers TG: The monoid of ordered partitions of a natural number. Semigroup Forum, 53 (1996), 44–56. MR97b:20093

C1. Lehrer GI: A vanishing theorem for hyperplane cohomology. Bulletin of the Australian Mathematical Society, 53 (1996), 361–368. MR97d:52024

C1. Lehrer GI: The space of invariant functions on a Lie algebra. Transactions of the American Mathematical Society, 348 (1996), 31–50. MR96f:20070

C1. Ma C: Multivariate survival functions characterized by constant product of mean remaining lives and hazard rates. Metrika, 44 (1996), 71–83. MR98b:62183

C1. Ma C: A class of multivariate survival distributions characterized by minimum and marginal distributions. Biometrical Journal, 38 (1996), 647–652. MR98f:62025

C1. Macaskill C and Cao P: A new treatment of rough surface scattering. Royal Society of London. Proceedings, Series A. Mathematical and Physical Sciences, 452 (1996), 2593–2612. MR1427927

C1. Macaskill C and Ewart TE: Numerical solution of the fourth moment equation and comparison with the MATE data. Journal of the Acoustical Society of America, 99 (1996), 1419–1429.

C1. Macintosh AC and Gray BF: Self-heating of combustible vapour in porous material when the fibres are entirely covered by fluid. Combustion Science and Technology, 113–114 (1996), 503–515.

C1. Malin SRC and Winch DE: Annual variation of the geomagnetic field. Geophysical Journal International, 124 (1996), 170–174.

C1. Mathas A: On the left cell representations of Iwahori-Hecke algebras of finite Coxeter groups. Journal of Algebra, 54 (1996), 475–488. MR97h:20008

C1. Myerscough MR, Darwen MJ and Hogarth WL: Stability, persistence and structural stability in a classical predator-prey model. Ecological Modelling, 89 (1996), 31–42.

C1. Papadima S and Paunescu L: Reduced weighted complete intersection and derivations. Journal of Algebra, 183 (1996), 595–604. MR97e:13013

C1. Peiris MS: Improving the precision of forecasting. Microelectronics and Reliability, 36 (1996), 1375–1378.

C1. Peiris MS and Singha N: Predictors for seasonal and nonseasonal fractionally integrated arima models. Biometrical Journal, 38 (1996), 741–752. MR99c:62260

C1. Phipps MC and Robinson J: Non-randomness in time-ordered neurobiological data. Theory of Stochastic Processes, 2 (1996), 234–240.

C1. Poznanski RR and Peiris MS: Subthreshold response to white-noise current input in a tapering cable model of a neuron. IMA Journal of Mathematics Applied In Medicine and Biology, 13 (1996), 207–222.

C1. Quine MP and Law JS: Exact results for a secretary problem. Journal of Applied Probability, 33 (1996), 630–639. MR97k:60127

C1. Ramagge J: How to make life hell for the judges of the B.H. Neumann Prize. The Gazette of the Australian Mathematical Society, 23 (1996), 186–187.

C1. Ramagge J and Robertson G: Triangle Buildings and Actions of Type $$III_{1/q^2}$$. Journal of Functional Analysis, 140 (1996), 472–504.

C1. Rannard R: Incompressible surfaces in Seifert fibered spaces. Topology and its Applications, 72 (1996), 19–30. MR97g:57023

C1. Richter PH, Dullin HR, Waalkens H and Wiersig J: Spherical pendulum, actions and spin. J. Phys. Chem.,, 100 (1996), 19124–19135.

C1. Sabadini N, Vigna S and Walters RFC: A note on recursive functions. Mathematical Structures in Computer Science, 6 (1996), 127–139. MR97e:03061

C1. Seneta E: Markov and the birth of chain dependence. International Statistical Review, 64 (1996), 255–263.

C1. Seneta E and Chen TH: Frechet optimality of upper bivariate Bonferroni-type bounds. Theory of Probability and Mathematical Statistics, 52 (1996), 147–152. MR98a:60020

C1. Shneerson LM and Easdown D: Growth and existence of identities in a class of finitely presented inverse semigroups with zero. International Journal of Algebra and Computation, 6 (1996), 105–121. MR96m:20093

C1. Singh S, Joarder AH and King ML: Regression analysis using scrambled responses. The Australian Journal of Statistics, 38 (1996), 201–211. MR99c:62191

C1. Solomon AI: Catalan monoids, monoids of local endomorphisms and their presentations. Semigroup Forum, 53 (1996), 351–368. MR98c:20104

C1. Stump DM and Fraser WB: A simplified model of fabric drape based on ring theory. Textile Research Journal, 66 (1996), no.8, 506–514.

C1. Stump DM and Fraser WB: Transient solutions of the ring-spinning balloon equations. Journal of Applied Mechanics, 63 (1996), 523–528.

C1. Thavaneswaran A and Peiris MS: Nonparametric estimation for some nonlinear models. Statistics and Probability Letters, 28 (1996), 227–233. MR97e:62113

C1. Thomas CM, Gibson WG and Robinson J: Stability and bifurcations in an associative memory model. Neural Networks, 9 (1996), 53–66.

C1. Thompson MJ, Toomre J, Burtonclay D and Wilson PR: Differential Rotation and Dynamics of the Solar Interior. Science, 272 (1996), 1300–1305.

C1. Thompson RS and Aldis GK: Effect of a cylindrical refracting interface on ultrasound intensity and the CW Doppler spectrum. IEEE Transactions on Biomedical Engineering, 43 (1996), 451–459.

C1. Thompson RS and Wilson LS: The effect of variations in transducer position and sound speed in intravascular ultrasound: A theoretical study. Ultrasound in Medicine and Biology, 22 (1996), 719–734.

C1. van de Ven RJ and Weber NC: Percentile related bounds and estimator for the mean of the negative binomial distribution. Statistics, 27 (1996), 345–352. MR97k:60099

C1. Warren D and Seneta E: Peaks and eulerian numbers in a random sequence. Journal of Applied Probability, 33 (1996), 101–114. MR97b:60060

C1. Wilson PR: On the inference of the solar rotation profile from frequency splitting data. Bulletin of the Astronomical Society of India, 24 (1996), 251–260.

C1. Wilson PR, Burtonclay D and Li Y: On the inference of the solar internal rotation profile from frequency-splitting data. Astrophysical Journal, 470 (1996), 621–628.

C1. Wilson PR, Burtonclay D and Li Y: Calculations of the solar internal angular velocity for 1986-1990. Astrophysical Journal, 457 (1996), 440–446.

C3. Monro GP: Digital power - cheap. Sounds Australian, 14 (1996), 18–20. (This contribution to "Sounds Australian" was invited by the guest editor for the issue.)

C4. Phipps MC: The existence of an efficient estimator. Mathematical Scientist, 21 (1996), 129–131. MR97g:62036

## Reviews

D. Fraser WB: Ring spinning. Textile Horizons, April/May (1996), 37–39. (Review article contributed by invitation from the editor)

D. Gibson WG: Review of Neural Networks: An Introduction (second edition), by Muller, Reinhardt and Strickland. Australian and New Zealand Physicist, 33 (1996), 83–84.

## Conference Proceedings

E1. Charlton BG, Gray BF, Le BT, Jones JC and Foulds GA (1996) The use of a jet stirred CSTR to study the gas phase partial oxidation of methane to methanol. Fourth Natural Gas Conversion Symposium, Proceedings, Fourth Natural Gas Conversion Symposium, Elsevier, 00–00.

E1. Fraser WB (1996) A mathematical model of textile yarn ring-spinning. Australian Engineering Mathematics Conference 1996, Proceedings of the Second Biennial Australian Engineering Mathematics Conference, W.Y.D. Yuen, P. Broadbridge, J.M. Striner (ed.) , Institution of Engineers, Australia, ISBN 0 85825 653 3, 371–377.

E1. Fraser WB and Fackerell ED (1996) Modelling optical fibre cable. Mathematics-in-industry Study Group 1996, Proceedings of MISG96, John Hewitt (ed.) , MISG, ISBN 0 646 28979 9, 92–102.

E1. Gibson WG, Bennett MR and Farnell L (1996) Monte Carlo simulation of quantal transmission at purinergic junctions. Fourth Annual Computatinal Neuroscience Meeting, Monterey, CA, Computational Neuroscience: Trends in Research 1995, JM Bower (ed.) , Academic Press, 15–20. (Already reported as an unpublished conference paper (1995))

E1. Gibson WG, Bennett MR and Farnell L (1996) Synaptic conductances for neural networks. The Seventh Australian Conference on Neural Networks, ACNN96: Proceedings of the Seventh Australian Conference on Neural Networks, P. Bartlett, A. Burkitt, R.C. Williamson (ed.) , Australian National University, ISBN 0 7315 2429 2, 62–66.

E1. Gibson WG, Bennett MR and Robinson J (1996) Modeling the spontaneous release of quanta at active zones of varicosities, boutons and endplates. Fourth Annual Computational Neuroscience Meeting, Computational Neuroscience. Trends in Research 1995, JM Bower (ed.) , Academic Press, 9–14. (Aleady reported as an unpublished conference paper (1995))

E1. Joshi N and Vassiliou PJ (1996) Lie symmetries and linearizations of analytic discrete dynamical systems. Symmetries and Integrability of Difference Equations, Symmetries and Integrability of Difference Equations, Decio Levi, Luc Vinet and Pavel Winternitz (ed.) , CRM Proceedings & Lecture Notes, AMS, ISBN 0-8218-0601-7, 163–171. MR1416836

E1. Luckock HC (1996) Quantum cosmology, supersymmetry, and the problem of time. Australasian Conference on General Relativity and Gravitation, Proceedings of the First Australasian Conference on General Relativity and Gravitation, David L. Wiltshire (ed.) , Institute for Theoretical Physics, University of Adelaide, ISBN 0 86396 430 3, 175–190.

E1. Macaskill C and Cao P (1996) Numerical solution of the second kind integral equation for random rough surfaces with extreme RMS height. 3rd International Conference on Industrial and Applied Mathematics ICIAM 95, ZAMM Z.angew.Math.Mech. volume 76, Supplement 1: ICIAM/GAMM 95 Numerical Analysis, Scientific Computing, Computer Science, G.Alefeld, O.Mahrenholtz, R.Mennicken (ed.) , Akademie Verlag, ISBN 3-05-501761-7, 461–462. (This should REPLACE the 1995 entry under ICIAM 95 for Macaskill and Cao)

E1. Seneta E and Weber NC (1996) Time-series diagnostics and explosive processes. First Ukranian-Scandinavian conference on stochastic dynamical systems: theory and applications, Proceedings of the First Ukranian-Scandinavian conference on stochastic dynamical systems: theory and applications, Vladimir Korolyuk, Gunnar Kulldorff, Oleg Klesov, Dmitrii Silvestrov (ed.) , TBiMC Scientific Publishers MR1473291

E1. Tholen W (1996) Objects with dense diagonals. Workshop on Categorical Topology, Proceedings of the Workshop on Categorical Topology, Kluwer Academic Publishers, 213–220. MR1412586

E1. Thompson RS, Aldis GK and Wilson LS (1996) The effect on ultrasound intensity of refraction at a curved surface. 22nd International Symposium on Acoustical Imaging, Acoustical Imaging, P Tortoli, L Masotti (ed.) , Proceedings of the Twenty-Second International Symposium, Plenum Press, ISBN 0-306-45364-9, 371–376.

E1. Wen L, Chen Y and He XZ (1996) Asymptotic behavior of a class of fourth order nonlinear functional differential equation with delays. Differential Equations and Control Theory, Differential Equations and Control Theory, Zongqi Deng, Zhaojun Liang, Guang Lu and Shigui Ruan (ed.) , Marcel Dekker, ISBN 0-8247-9658-6, 371–376. MR96k:34156

E2. Edelman D and Gillespie T (1996) Improved volatility prediction using group analysis (empirical Bayes) methods. Workshop on Quantitative Methods in Finance, Financial Mathematics Research Report, E. Platen (ed.) , FMRR 008-96, The Australian National University, Volume 2, 345–354.

E2. Galloway DJ (1996) General Review of Dynamo Theory. Solar and Stellar Dynamos, Proceedings, third AFCOP meeting Solar and Stellar Dynamos'', J.-F. Donati (ed.) , Observatoire Midi-Pyrénées, 15–25.

E2. Galloway DJ (1996) Implications of Stellar Observations on Dynamo Theories. Solar and Stellar Dynamos, Proceedings, third AFCOP meeting Solar and Stellar Dynamos'', J.-F. Donati (ed.) , Observatoire Midi-Pyrénées, 117–122.

E2. Kelly MF and Buchen PW (1996) The simulation from option prices of joint distributions for asset prices, interest rates and volatility. ANU Workshop on Quantitative Methods in Finance, Financial Research Report, ANU Workshop on Quantitative Methods in Finance, Financial Research Report, FMRR-008-96, 329–344.

E2. Langton B and Fackerell ED (1996) Similarity reductions of the field equations for stationary axisymmetric rigidly rotating perfect fluids. Seventh Marcel Grossmann Meeting, The Seventh Marcel Grossmann Meeting, Robert T Jantzen, G. Mac Keiser (ed.) , World Scientific, ISBN 9810220642, 420–421.

E2. Luckock HC and Oliwa C (1996) Quantisation of Bianchi class A models in supergravity and the probability density function of the universe. The Seventh Marcel Grossman Meeting, The Seventh Marcel Grossman Meeting, Robert T Jantzen, G Mac Keiser and Remo Ruffini (ed.) , World Scientific Publishing Co. Pty Ltd, ISBN 9810220642, 1020–1022.

E3. Bennett MR, Farnell L, Gibson WG and Lavidis NA (1996) Synaptic transmission at visualized boutons on rat pelvic ganglion cells. Australian Neuroscience Society. Sixteenth Annual Meeting, Proceedings of the Australian Neuroscience Society, P. Pilowsky (ed.) , Australian Neuroscience Society, 86.

E3. Gibson WG (1996) Modelling some aspects of synaptic function in neurons. The 32nd Australasian Applied Mathematics Conference, ANZIAM'96 The 32nd Australasian Applied Mathematics Conference, G. Wake (ed.) , ANZIAM Conference Porceedings, Australian Mathematical Society: ANZIAM, ISBN 0725908696, (no pagination).

E3. Henery R, Gibson WG and Bennett MR (1996) Quantal currents and potential in the three-dimensional anisotropic bidomain of the vas deferens. Australian Neuroscience Society. Sixteenth Annual Meeting, Proceedings of the Australian Neuroscience Society, P. Pilowsky (ed.) , Australian Neuroscience Society, 148.

E3. Myerscough MR (1996) Bifurcations, structural stability and persistent populations—new insights into classical models with harvesting and stocking. The Nicholson Centenary Conference on Population Biology, Frontiers of Population Biology, R.B Floyd, A.W. Sheppard, P.J. de Barro (ed.) , CSIRO Publishing, ISBN 0 643 05781 1, 617–630.