Newsletters Index       Centrefolds Index

Number 93     April 2005

NEWSLETTER

OF THE

NEW ZEALAND MATHEMATICAL SOCIETY (INC.)

Contents

ISSN 0110-0025

CENTREFOLD

BOB LONG

Robert Stephen Long is a very good candidate for a long-service medal for his contributions to mathematics in this country, and his career illustrates with great clarity the development of the subject in the past half-century.

Bob turned up at Canterbury University College in 1942, with a University Entrance Scholarship, from St Andrews College. At this time, the mathematics staff of C.U.C. numbered four, and was headed by Professor Sadler, a Scottish geometer, who had been appointed in 1930. Bob did well as an undergraduate—in 1944, at the end of his BSc course, he was awarded a Sir George Grey Scholarship, and the Haydon Prize in physics—and he went on to study for an MSc in mathematics. In the third term of the 1945 year, he went down with pneumonia, from which he had barely recovered by the time of his examinations, and he was awarded second class honours, rather than the first that he and his teachers no doubt had expected.

He treated this set-back with the stubborn determination that anyone who has ever played tennis or badminton against him would recognize; he returned to his old school, St Andrews, as a mathematics master, to earn and save enough money to take him to Cambridge on his own account. (During this time he first encountered the young Roy Kerr, whom he remembers as being very brisk in dealing with set work in class.) By the middle of 1946, he had saved enough, and sailed off to England and Cambridge. As was the practice at Cambridge in those days, he was obliged to study for a BA; and he completed this in two years, and was awarded first class honours. His course was largely in applied mathematics, which in these days would seem rather to be classical continuum mechanics/theoretical physics, and he was tutored by the astronomer R A Lyttelton, of the famous Hoyle–Bondi–Lyttelton trio, whom he recalls as being capable of giving an elegant solution to almost any problem in the field he studied.

He stayed at Cambridge for another year, taking advanced courses; but the money inevitably ran out (despite some assistance from Canterbury U C) and he returned to New Zealand in 1952, and took a position as lecturer in the Mathematics Department at CUC. Sadler was still the head; but now there were five other members of staff. Research was no longer actively discouraged (see, if you can't believe that this once was the case, Karl Popper's autobiographical "Unended Quest") but as the Hughes Parry report of 1959 indicated—CUC was invidiously cited in this for its amazingly economical use of staff in mathematics teaching—the time which could be devoted to it was constrained by a very high teaching load. In these earlier years of his university teaching career, Bob was called on to give honours courses in five subjects; Electricity & Magnetism, Hydrodynamics, Quantum Mechanics, Optimal Control, and Analysis.

With the retirement of Sadler, and the arrival of Derek Lawden as HoD, the atmosphere if not the resources for research improved a great deal, and through the 1960s Bob wrote and published a series of papers, largely on one of the topics that Lawden had pioneered, that of orbital transfer. He was promoted to a readership in 1968.

Throughout his time in the department, Bob took more than his share of administrative work, and of the teaching of first-year and engineering mathematics courses, and is rightly remembered for his patience and thoroughness.

On his retirement at the end of the 1980s, Bob became involved in (perhaps "was inveigled into" suits the case better) the NZ International Mathematical Olympiad movement, and set up the weekly coaching sessions which are open to candidate olympians in Christchurch. He is still in charge, and the number of this country's best young mathematicians who have passed through his hands, and who owe a real debt to him for patient instruction, encouragement and inspiration, grows by the year.

Bob's activities beyond the department and mathematics were, and are, for he still pursues them, very much those of the model twentieth century New Zealand man. He plays tennis, and played badminton, with zeal and tenacity. He delights in tramping in the back-country, and has done many of the classic hard tramps of the South Island. He was until very recently an enthusiastic skier. He is a meticulous gardener. And a pivotal point in his life occurred in the early fifties, when at a tennis club afternoon he was allocated a mixed doubles partner, no doubt by some random process: This of course a classic mid-twentieth way of meeting one's future wife, and indeed he and Betty, the young woman concerned, celebrate fifty years of marriage this month. A number of his Christchurch friends will share this celebration; and I am sure that many more of his colleagues and friends in the NZMS will wish them well, and will also celebrate BobÕs career, so far, of patient and well-judged service to mathematics and the world at large, and wish it to long continue.

Brian Woods

Centrefolds Index

NEW COLLEAGUES

Professor Mark Meerschaert

"I joined the Department of Mathematics and Statistics at the University of Otago in February 2005 as the new Chair of Applied Mathematics. The previous chair, Vernon Squire, is now serving as Pro-Vice-Chancellor of the Division of Sciences. Prior to that, I spent 12 years in the Departments of Mathematics & Statistics and Physics at the University of Nevada, and before that, 8 years at Albion College, a small liberal arts college in Michigan USA. I also worked in industry for several years as a Systems Analyst in Operations Research. I was born and raised in Michigan and received my BS, MS, and PhD degrees from the Mathematics Department at the University of Michigan, where I specialized in limit theorems in Probability and Mathematical Statistics.

I decided to study mathematics because I could not manage to limit my interests to just one area of science or engineering. My current research interests reflect that. Partial differential equation models that use fractional derivatives are useful to model flow and transport of contaminants in ground water and surface water. Heavy tailed stochastic processes describe the microscopic behavior of these phenomena. Numerical methods for fractional partial differential equations require a new approach, since the fractional derivative operator is non-local. These numerical methods are important for applications in which physical parameters, like groundwater velocity, vary over space and time, so that analytical solutions are not available. Heavy tailed time series analysis is useful for modeling river flows when the flow volume is highly variable. Statistical models for heavy tailed phenomena require novel parameter estimation methods, since the outliers we usually discard are now the main items of interest. Applications include floods, droughts, and large price jumps (up or down) in financial markets."

AITKEN PRIZE 2004

The Aitken Prize for best student talk at the New Zealand Mathematics Colloquium was awarded in 2004 to Joanne Mann of Massey University, Albany, for her talk presented below.

TO VACCINATE OR NOT TO VACCINATE?
Joanne Mann

Vaccination and immunisation are two of the most cost effective ways to combat an infectious disease. You may be choose to vaccinated to prevent being infected and passing the infection to others around you, and it may be the "cheaper" option. However, you may choose not be vaccinated due to concerns about any adverse side effects from the vaccine or concerns about the vaccine efficiency; and some people believe that natural immunity is better than imposed immunity.

Assume that there is a constant cost associated with being vaccinated, C_V, which includes the actual cost of the vaccine, the possible side effects caused by the vaccine and the time taken to be vaccinated. This cost could be quite low if you think of the sore arm you get after an influenza vaccination, or quite high when you consider that smallpox vaccination causes 1 -  2 deaths per million. We also assume a constant cost associated with being infected, C_I, that includes the effects of the infection, the cost of the treatment for the infection, the time required off work for recovery and any lasting side effects caused by the infection—for example the scars left from chicken pox or the loss of limbs from meningitis. The idea of these two costs was presented in Bauch et. al. (2003).

Individuals have two options: remain susceptible and risk infection, or be vaccinated. The expected cost of remaining susceptible depends on the proportion of the population who are vaccinated, as this affects the probability of infection. The individual will choose whichever option they perceive to present the lowest cost to them, and we assume that everyone in the population has access to the same information and understands it in the same manner. The expected cost to the community depends on the proportion of individuals choosing to be vaccinated, and the costs associated with the two strategies.

We determine what proportion of the population needs to be vaccinated to minimize the cost to the community as a whole and compare this with the optimal solution for the individual. We consider two vaccination scenarios: an epidemic infection, such as influenza where vaccination is required yearly; and an endemic infection, such as tuberculosis.

Epidemic Infections
To measure the spread of an infection in a population we use the basic reproduction ratio, R₀, defined as "the number of secondary cases that occur from a primary case in a fully susceptible population" (Anderson & May, 1992). If R₀ > 1 then there will be an epidemic, and if R₀ < 1 the infection will not persist in the population. If a proportion v of the population is vaccinated, then there will be an epidemic if:

We calculate the basic reproduction ratio from:

The number of new cases of infection, or incidence of infection i(t), as shown in Diekmann & Heesterbeek (2000) is:

where S(t) is the size of susceptible population, and the accounts for the initial case of infection in the population. The incidence of infection is the same as the negative rate of change of S(t); hence we gain the final size equation:

where is the proportion of the population who remain susceptible after an epidemic, and S(0) is the initial proportion of the population who are susceptible. When the proportion of the population vaccinated reaches there will no longer be an epidemic, so we can let decrease linearly with v, and we do not solve the non-linear equation. The maximum value of s(v) is and is reached at the critical point v = .

Individuals either have the cost associated with vaccination, or the expected cost associated with remaining susceptible:

The expected cost to the community is proportional to a linear combination of the expected costs of the two individual strategies

The two individual strategies have a break even point when:

The community's best strategy is found by minimising the cost function for the community. Assuming that the cost associated with vaccination is less than the cost associated with being infected, the minimum occurs when v = .

Figure 1  When the expected cost of remaining susceptible is greater than the expected cost of being vaccinated, we see that the individual's best strategy is to be vaccinated, until v reaches the break even point where all three lines intersect; after this point the best strategy is to remain susceptible. The best strategy for the community is to vaccinate the proportion of the population equal to , which is greater than the individual's break even point. Hence the optimum vaccination coverage for the community results in some individuals being vaccinated when their best strategy would be not to. R₀ = 5 for this example.

Endemic Infections
We now consider an infection that is endemic in the population, for example tuberculosis. We assume that if a person chooses to be vaccinated it is at birth or near to birth, and they are not included in the susceptible population prior to vaccination. We use a susceptible, infected, and removed model (SIR). The demography of the population now has to be considered, so we include a constant birth/death term in the model.

The expected cost to an individual depends on the probability of being infected at some point during their lifetime, which we can calculate using the endemic steady state of the SIR model (note that R₀ has a different mathematical expression, but the same biological meaning as in the epidemic situation):

The expected costs to an individual are:

The individuals break even point now occurs when

The community's expected cost is a combination of the two individual expected costs:

Minimising the above function, we find the expected cost for the community is at its lowest when v = , assuming that the cost associated with vaccination is less than the cost associated with being infected.

Conclusion
For both scenarios, the minimum expected cost to the community is reached when v = . This is greater than the proportion of the population that is vaccinated at the individual's break even point. If the choice of vaccination is left to the individual, and they behave rationally, the community will incur a higher cost as too few will choose vaccination and there will be an epidemic. If the expected cost to the community is minimised individuals will incur a higher cost, but there will not be an epidemic. As an individual, the best strategy is to be not vaccinated, and to make sure that every one around you is!

References
Anderson, R. M. & May, R. M. (1992). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford.

Bauch, C. T., Galvani, A. P., & Earn, D. J. J. (2003). Proceedings of the National Academy of Sciences, 100(18), 10564-10567.

Diekmann, O. & Heesterbeek, J. A. P. (2000). Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. John Wiley and Sons Ltd, Chichester.

T. M. CHERRY PRIZE 2005

The T. M. Cherry Prize for best student talk at ANZIAM was awarded in 2005 to Jason Looker of the University of Melbourne, for his talk presented below.

Introduction

The transport of electrolyte through porous media is a classical multiscale phenomenon with numerous applications in geophysics and bio-porous materials modeling. Phenomenological equations relating the transport of ions and solvent to electrical potential, pressure and concentration gradients have achieved widespread acceptance in the literature (Adler, 2001; Coelho et al., 1996; de Groot and Mazur, 1969; Edwards, 1995; Gross and Osterle, 1968; Marino et al., 2000, 2001; Revil and Leroy, 2004). These equations are assumed to be valid on the scale of the porous body (the macroscopic or Darcy-scale) and represent an average, in some sense, of the pore-scale (or microscopic) equations. Attempts at deriving macroscopic transport equations from microscopic equations have been successful under various somewhat restrictive assumptions (Edwards, 1995; Gross and Osterle, 1968; Moyne and Murad, 2002, 2003; Revil and Leroy, 2004). Furthermore, the precise form of these equations varies between authors. In this paper, Darcy-scale transport equations are derived with minimal assumptions using homogenization theory. Without any additional assumptions, we rigorously prove that the transport coefficient tensors obey certain fundamental thermodynamic requirements, namely, Onsager's reciprocal relations and the positive definiteness of the diagonal coefficient tensors (de Groot and Mazur, 1969).

We consider an N-component electrolyte in a dilute Newtonian solvent flowing through a rigid porous body with a periodic microstructure, where the geometry of the porous medium ensures that the Reynolds number of the flow is much less than unity. The electrolyte flows in response to a static (d.c.) electric field and a constant surface charge density on the pore walls. The magnitude of the applied field is assumed to be sufficiently small to permit the linearization of the ionic transport (electrokinetic) equations. In addition, we utilize the standard approximation , where is the dielectric constant of the solid part of the porous medium, and is the dielectric constant of the fluid. This approximation enables the electric potentials in the fluid and solid parts of the porous body to be decoupled.

Gross and Osterle (1968) derived Darcy-scale transport equations for the case of a capillary model for charged wide-pore membranes. This simple geometry allowed for a complete analytical solution of the electrokinetic equations, without linearizing the Poisson-Boltzmann equation, including the establishment of the Onsager relations. By assuming a very thin double layer on the pore walls, Edwards (1995) employed a volume averaging approach to derive macroscopic transport equations for a periodic porous body. However, Edwards did not succeed in establishing Onsager's reciprocal relations. The paper by Marino et al. (2001) studies a periodic porous medium subjected to an external electric field, a pressure gradient and a concentration gradient. The well-known phenomenological equations are assumed to hold and, starting from the electrokinetic equations on the pore-scale, the transport coefficient tensors are calculated numerically for a number of different microstuctural geometries. Moyne and Murad (2002, 2003) also considered a periodic porous medium but in addition, they permitted the porous body to swell. No linearization of the pore-scale Nernst-Planck equation was carried out. However, by assuming the Peclet number to have the same order of magnitude as the microscopic length scale, they effectively neglected pore-scale ionic convection. Under the assumption that the ionic concentrations in the pore water obey the Donnan distribution, Revil and Leroy (2004) used volume averaging to derive macroscopic transport equations from linearized microscopic equations. The Onsager relations were established under these conditions. In all of the aforementioned articles, only a 1-1 electrolyte was considered.

In this paper, no assumptions are made about the double layer thickness or Peclet number and the equilibrium concentrations obey the Boltzmann distribution. Consequently, our analysis includes the effects of pore-scale ionic convection. No assumptions are made regarding the microstructure. Although we assume periodicity of the porous domain, there exists an equivalence between periodic and statistically homogeneous random porous media (Beliaev and Kozlov, 1996; Espedal et al., 2000).

This work is stimulated by the author's interest in developing a theory for the electroacoustic characterization of suspensions of porous particles (O'Brien, 1988). To determine the electrophoretic motion of a porous particle, we need to specify the governing equations outside the particle, inside the particle and the boundary conditions coupling the two domains. The governing equations exterior to the particle are the well-known electrokinetic equations (Hunter, 1987Ð1989; Lyklema, 1991). It is therefore natural to upscale the electrokinetic equations to obtain a Darcy-scale model inside the particle. The authors have used scaling arguments in conjunction with recent results in homogenization theory to develop a model for the hydrodynamics of an oscillating porous particle (Looker and Carnie, 2004), since electroacoustic experiments generate oscillatory flows. To be consistent with this work, we choose to employ homogenization theory to upscale the electrokinetic equations.

Homogenization
Homogenization theory exploits the fact that transport phenomena in porous media occur on two disparate length scales: a macroscopic} scale (the scale of the reservoir, L) and a microscopic} scale (the pore scale, ). Transport phenomena can then be characterized via the small dimensionless parameter . In practice we only observe macroscopic transport phenomena and it is sufficient for information regarding the microstructure to be retained purely in the form of averaged quantities, such as porosity and permeability. The homogenization process transforms equations on the microscopic scale to effective equations on the macroscopic scale by determining the limiting behavior of the microscopic equations as . For an extensive coverage of homogenization and porous media, see Hornung (1997).

We briefly describe the construction of a periodic porous domain with period . A complete description of periodic porous media can be found in Espedal et al. (2000). A standard cell consists of a three dimensional cube C containing a standard obstacle S where the fluid part of the cell is , with boundary . This cell is extended periodically, with period , to all of three dimensional space. A domain is then intersected with the periodically extended standard cells to give the periodic porous domain. The fluid part of the periodic porous domain is given the symbol , with boundary . The limit corresponds to the size of the cells becoming progressively smaller and greater in number until the fluid part is annihilated (or, the pore size goes to zero).

Under the assumptions stated in the introduction, the scaled linearized microscopic equations are for (O'Brien and White, 1978):

     (11) to (18)

The ionic parameters , and represent the valency, drag and the (scaled) bulk ionic number density of the jth ionic species, respectively. The physical constant is the (scaled) surface charge density and is the applied electric field. The functions are the equilibrium electric potential, equilibrium number density of the jth ionic species, ionic potential of the jth ionic species, velocity of the solvent, and the partial pressure of the solvent. The vector denotes the outward unit normal to . The dependence of these functions on the characteristic microscopic length scale is signified by the superscript . Observe that the boundary conditions are applied on the boundary of the pore walls, not} on the boundary of the macroscopic domain C. For convenience, all functions and variables in the above equations refer to dimensionless quantities. We shall adopt this convention for the remainder of the paper.

To study the limit as of equations 11 to 18 above, we postulate that have formal two-scale asymptotic expansions of the form, where the with respect to the microscopic (or fast) variable . A function has the same value on each opposite face of The two different length scales imply that the derivatives must be transformed according to,

The asymptotic expansions for are substituted into equations 11 yo 18 and terms of the same order of magnitude are compared, generating a cascade of equations. Solutions are sought in terms of products of macroscopic forcing terms and cell functions. Cell functions are defined only in and are required to be

Non-Equilibrium Thermodynamics
After homogenization of the microscopic equations and integration over a cell, it is shown in Looker and Carnie (2005) that the macroscopic fluid velocity and ionic flux of the jth species can be expressed as:

     (19) (20)

where and are the effective electrochemical potential and pressure, respectively. The electrochemical potential is a thermodynamic measure of how much work is required to return a system to equilibrium (Lyklema, 1991); it is related to the ionic potential via,

The tensors and are coupling tensors, is the permeability tensor, is a self electrodiffusion tensor and accounts for cross electrodiffusion effects. Note that Our aim is to establish the validity of these macroscopic equations. This shall be accomplished by rigorously proving, without any additional assumptions, that our macroscopic system obeys one of the fundamental laws of non-equilibrium thermodynamics: Onsager's reciprocal relations. The primary reference for this section is de Groot and Mazur (1969).

Onsager's reciprocal relations are essentially a statement of time reversal invariance. That is, if a small perturbation to a system in some reference state is sent back in time, then the system will return to that reference state. If the system is expressed in the following format,

     (21)

where is a vector representing the fluxes and a vector of the independent thermodynamic forces, Onsager proved that the tensor must obey , that is, must be symmetric. Recasting Eqns 19 and 20 into the form of Eqn 21 gives,

Symmetry of the coefficient tensor requires that:

     (22)

must be true for each if the Onsager relations are to hold.

A necessary condition ensuring the entropy production of the system remains positive, is the positive definiteness of the diagonal tensors in . Therefore the permeability tensor and the self electrodiffusion tensor are required to be positive definite.

It is rigorously proven in Looker and Carnie (2005) that Eqns 22 hold and the permeability and self electrodiffusion tensors are positive definite, for the transport coefficient tensors defined in this paper. The proof follows directly from the ionic and fluid cell problems.

Discussion
Note that Eqns 19 and 20 are formally the same as the Darcy-scale equations modelling ionic transport in porous shales derived by Revil and Leroy (2004), and are identical to the phenomenological transport equations presented in de Groot and Mazur (1969). Explicit expressions for the transport coefficient tensors in terms of solutions to cell problems are presented in Looker and Carnie (2005), where it is shown that all of the transport coefficient tensors have been influenced by the inclusion of pore-scale ionic convection in the present model.

This paper constitutes a theoretical framework for a greater understanding of the assumptions underlying the phenomenological equations and similar models describing transport phenomena in porous media; however more work is required. For instance, computing the transport coefficient tensors numerically by solving the ionic and fluid cell problems will elucidate the relative importance of the terms in Eqns 19 and 20. Furthermore, making the formal mathematical calculations presented in this paper rigorous by establishing the two-scale convergence (Hornung, 1997) of the microscopic functions to their homogenized counterparts will further clarify the assumptions upon which Eqns 19 and 20 are based, and may be of independent mathematical interest.

References
Adler, P. M.: 2001 Macroscopic electroosmotic coupling coefficient in random porous media, Math. Geol. 33(1), 63–93.

Beliaev, A. Yu. and Kozlov, S. M.: 1996, Darcy equation for random porous media, Comm. Pure Appl. Math. 49, 1–34.

Coelho, D., Shapiro, M., Thovert, J. F., and Adler, P. M.: 1996, Electroosmotic phenomena in porous media, J. Colloid Interface Sci. 181, 169–190.

de Groot, S. R. and Mazur, P.: 1969, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam.

Edwards, D. A.: 1995, Charge transport through a spatially periodic porous medium: electrokinetic and convective dispersion phenomena, Phil. Trans. R. Soc. Lond. A. 353, 205–242.

Espedal, M. S., Fasano, A. and Mikelic, A.: 2000, Filtration in porous media and industrial application, Vol. 1734 of Lecture notes in mathematics, Springer-Verlag, Berlin, pp. 127–214.

Gross, R. J. and Osterle, J. F.: 1968, Membrane transport characteristics of ultrafine capillaries, J. Chem. Phys. 49(1), 228–234.

Hornung, U. (ed.): 1997, Homogenization and porous media, Vol. 6 of Interdisciplinary applied mathematics, Springer-Verlag, Berlin.

Hunter, R. J.: 1987–1989, Foundations of colloid science, Vol. 2, Oxford University Press.

J. R. Looker and S. L. Carnie, 2004, The hydrodynamics of an oscillating porous sphere, Phys. Fluids, 16 (1), 62–72.

Looker, J. R., and Carnie, S. L.: 2005, Homogenization of the ionic transport equations in periodic porous media, Transport in Porous Media, submitted.

Lyklema, J.: 1991, Fundamentals of interface and colloid science, Vol. 1, Academic Press, London.

Marino, S., Coelho, D., Békri, S. and Adler, P. M.: 2000, Electroosmotic phenomena in fractures, J. Colloid Interface Sci., 223, 292–304.

Marino, S., Shapiro, M., and Adler, P. M.: 2001, Coupled transports in heterogeneous media, J. Colloid Interface Sci. 243 391–419.

Moyne, C. and Murad, M.: 2002, Electro-chemo-mechanical couplings in swelling clays derived from a micro/macro-homogenization procedure, Int. J. Solids Structures. 39, 6159–6190.

Moyne, C. and Murad, M.: 2003, Macroscopic behavior of swelling porous media derived from micromechanical analysis, Transport in Porous Media. 50, 127–151.

O'Brien, R. W.: 1988, Electro-acoustic effects in a dilute suspension of spherical particles, J. Fluid Mech. 190, 71–86.

O'Brien, R. W. and White, L. R.: 1978, Electrophoretic mobility of a spherical colloidal particle, Journal of the Chemical Society, Faraday Trans. 74(2), 1607–1626.

Revil, A. and Leroy, P.: 2004, Constitutive equations for ionic transport in porous shales, J. Geophys. Res. 109, B03208.

¹ A longer paper of the same name has been submitted to Transport in Porous Media.

² Author to whom correspondence should be addressed. Electronic mail: jrlooker@ms.unimelb.edu.au

³ Electronic mail: carniesl@ms.unimelb.edu.au

NZMS LECTURER

The NZMS lecturer Professor Eugene Seneta with Jeff Hunter and Mick Roberts at the 14th International Workshop on Matrices and Statistics, Massey University, Albany.

LEADING MATHEMATICIAN RETIRES

Professor Alastair John Scott is one of New Zealand's leading mathematical scientists and one who has contributed greatly to the health and international profile of mathematical sciences in New Zealand.

After graduating in Mathematics from The University of Auckland in 1961, Alastair started his career in the Applied Mathematics Division of the DSIR, before undertaking graduate study in statistics at the University of Chicago.

After his time in Chicago he joined the Department of Statistics at the London School of Economics before returning to the Mathematics Department at the University in 1972. Alastair was head of the Department of Mathematics and Statistics on two occasions before the (amicable) divorce of the two departments in 1994, and became the founding head of the Department of Statistics.

Alastair has made many fundamental contributions to the analysis of survey data, often in collaboration with J.N.K. Rao and T.M.F. Smith. His 1981 paper with Jon Rao in the Journal of the American Statistical Association was selected as one of the 19 landmark papers in the history of survey sampling for the 2001 IASS (International Association of Survey Statisticians) centenary volume. He has guided the official statistics agencies in Australia and Canada as well as Statistics New Zealand. He has also made fundamental contributions to many other areas of statistics, including the design and analysis of retrospective studies extending classical results for case control studies with applications in medicine and many other fields.

Amongst the honours bestowed upon him are fellowships of the Royal Society of New Zealand, the American Statistical Association, and the Institute of Mathematical Statistics. He is an elected member of the International Statistical Institute, and a past president and one of only four honorary life members of the New Zealand Statistical Association.

He has also served on the board of directors of the American Statistical Association and as a member of the council and as scientific secretary of the International Association of Survey Statisticians. In April 2005 this association is sponsoring a satellite conference of the 55th Session of the International Statistical Institute to celebrate Alastair's distinguished career.

As well as all this achievement, Alastair has become a much loved figure in the University; he has always been happy to advise research students and colleagues across the University. Many have benefited from his collaboration; his list of publications includes joint papers with members of five different faculties of the University.

He has served on many University committees, chaired several departmental reviews and for a time was a board member of the Environmental Risk Management Authority (ERMA).

His retirement will allow him spend more time with his grandchildren in the holiday house at the head of Leigh Harbour, which he owns jointly with other members of the department that he founded.

Professor Chris Wild (Statistics) andAssociate-Professor Chris Triggs (Statistics—Tamaki

SPEECH TO MATHEMATICS IN INDUSTRY STUDY GROUP
Hon Dr Michael Cullen, Deputy Prime Minister
Delivered 24 January 2005, Massey University, Albany Campus, Auckland

I am very pleased to open this year's Mathematics in Industry Study Group. The Study Group is exactly the kind of cross-fertilisation between academia and industry that we need to sustain growth in our economy and to build a vigorous tertiary education system.

I would like to commend the leadership of Professor Graeme Wake and the work of his colleagues at Massey University in bringing this event together

It is a little known fact that I am the only New Zealand finance minister in history (and, I believe, the only New Zealand member of parliament) to have had a degree in mathematics. I would like to say that this training has been instrumental in achieving a series of strong fiscal surpluses in the last five years. However, the truth is that managing government expenditure and revenue is primarily an exercise in understanding and accounting for human behaviour, in which the hard sciences play something of a handmaidÕs role.

However, it is certainly my ambition, when I retire, to attempt to develop a set of algorithms which explain mathematically the behaviour of ministers of the Crown and MPs in a parliamentary democracy. This work will have to compete with my ambition to undertake a detailed analysis of my golf swing, and I expect both of these endeavours will need to draw considerably on the mathematics of chaos theory if they are to come to any conclusion.

While my own academic career in mathematics took a turn towards social statistics and merged with the study of history, I see an important common principle in the approach of the Mathematics in Industry Study Group. That is the conviction that even the purest and most abstract forms of mathematical theory can shed light on real life problems, even if takes some time for that to occur.

After all what attracts most of us into the study of mathematics is the realisation that numbers explain things, be they natural phenomena such as the growth of plants, the swarming of insects or the changes in weather patterns, or aspects of the human environment such as the design of hard structures, the manipulation of chemistry or biology, the transmission of energy or the management of information.

Linking the advanced study of mathematics to the challenges of industry (the challenges of managing risk, streamlining production and creating new value) not only benefits industry and hence the community, but also provides fresh intellectual challenges to mathematicians and thereby extends the boundaries of the discipline.

I think this gives the lie to the kind of reductionist utilitarian view of academic endeavour, the view that says that research that has no immediate commercial application should not receive public funding. This is certainly not the approach that drives the governmentÕs tertiary education and research policies.

We are certainly looking to foster a tertiary sector that is engaged with its community. We want to see tertiary institutions that provide education and training that is relevant to the needs and aspirations of students, and that is delivered in ways that aid their learning and fire their enthusiasm.

We expect tertiary institutions to show leadership in forming partnerships with industry, both in terms of fine tuning the kind of education programmes they provide so as to meet the long term skill needs of the economy, and in terms of building a portfolio of research that extends New ZealandÕs reputation as a nation of innovators.

These are more than vague ambitions. For the past five years we have worked with the research community and the business community to develop a Growth and Innovation Framework which focuses resources on the ways in which new knowledge generates growth in the New Zealand economy, and on the key points in the value-chain where we need to build our capacity or to clear away roadblocks.

Alongside of this we have increased government expenditure on research, with a significant proportion of the new expenditure targeted to research partnerships involving key growth industries.

However, none of this alters our commitment to maintaining a strong tradition of liberal education within our tertiary system. We see academic freedom as an essential value, and want to sustain a system in which researchers are able to pursue knowledge for its own sake.

This commitment can be seen in the way we have increased public expenditure on scientific research year or year, and have created funding mechanisms that use public resources to attract more private resources into research partnerships. Looking ahead, we are increasing government's investment in research by $212 million over the next four years. Again, a large portion of this increase has been targeted at research ventures involving CRIs and industries where public and private investment work hand in hand.

It is also reflected in the Performance-Based Research Fund, which rewards institutions which undertake research that is recognised as world-class, and scholars who are active and valued contributors to international networks of researchers.

What we don't want is for the process to stop there. If we are to create a vibrant `knowledge economy' then we need a more disciplined approach to the transmission and dissemination of knowledge. And as a small country, we one of those disciplines is to make strategic choices about where to focus our efforts so as to build on our competitive advantages and create strong and sustainable niche industries.

Inevitably this means change. One thing that has to go is the cherished myth of the amateur; the individual who retreats to the garden shed, constructs an unlikely piece of sophisticated equipment, and produces something world-beating. It is time we put this little romance to bed.

As management theorists like Peter Drucker and Peter Senge have argued, innovation is not an art; it is a set of disciplines that can be learned, practiced and taught.

With hindsight we can trace the history of the computer through three centuries, from the development of binary theory in the seventeenth century, Charles Babbage's calculating machines in the 1820s and 1830s, the invention of the punchcard by Herman Hollerith in 1890, through Bertrand Russell and Alfred North Whitehead's work on symbolic logic, the invention of the audion tube, the transistor, the microchip and so on. The question for us is: how can we speed up this process whereby advances in mathematics and technology are combined to create innovations that serve humanity and create wealth?

There is no law that requires new discoveries in mathematics to take three centuries to find practical applications.

A true knowledge economy needs more than just smart people. It depends upon the quality of relationships between those people, and a culture that supports the sharing of information and collaboration across disciplines.

These things do not arise spontaneously; they have to be consciously designed and created, and they need energetic people to drive them. The interests of all have to be understood and respected. Issues such as intellectual property need to be worked through, and common understandings are required around best practice collaboration. We need this kind of interchange to be a regular, ongoing activity, and not just a periodic one.

The Mathematics in Industry Study Group is an excellent example of collaboration between academics and industry. Over the next few days you will take part in an extended process of intellectual `fermentation'.

This not only provides an opportunity to dig deep into the underlying causes of the problems you will consider. It also builds the kind of relationships that assist better transmission of new research into industry and guide future research. And it enables you to explore questions that may at first seem tangential, but which may lead to new discoveries, or at least to new questions and problems that deserve attention in the future.

Reading the feedback from previous study groups, the over-riding theme is one of surprise at how valuable the process can be. I trust that this year's experience will be the same.

This is the kind of endeavour that signals where New Zealand businesses should be heading in terms of harnessing technology to increase value, and of what New Zealand universities should be doing to engage with business.

My chief regret in opening this event is that my schedule does not allow me to stay and witness the proceedings.

Thank you.

BOOK REVIEWS

Information has been received about the following publications. Anyone interested in reviewing any of these books should contact

Bruce van Brunt
Institute of Fundamental Sciences
Massey University
(email: B.vanBrunt@massey.ac.nz)

SPRINGER-VERLAG PUBLICATIONS

Bullo, F , Geometric Control of Mechanical Systems. (Texts in Applied Mathematics, Vol. 49) 726pp.
Chambert-Loir, A , A Field Guide to Algebra. (Undergraduate Texts in Mathematics) 195pp.
Chen, Mu-Fa , Eigenvalues, Inequalities, and Ergodic Theory. (Probability and its Applications) 228pp.
Edwards, HM , Essays in Constructive Mathematics. 180pp.
Ischebeck, FG , Ideals and Reality. (Springer Monographs in Mathematics) 336pp.
Jungnickel, D , Graphs, Networks and Algorithms. (Algorithms and Computation in Mathematics, Vol. 5) 611pp.
Kaipio, J , Statistical and Computational Inverse Problems. (Applied Mathematical Sciences, Vol. 160) 344pp.
Kuzmin, D , Flux-Corrected Transport. (Scientific Computation) 301pp.
Marsh, D , Applied Geometry for Computer Graphics and CAD. (2nd ed. Springer Undergraduate Mathematics Series) 352pp.
Murty, MR , Problems in Algebraic Number Theory. (Graduate Texts in Mathematics, Vol. 190) 352pp.
Ruiz-Tolosa, JR , From Vectors to Tensors. (Universitext) 670pp.
Strocchi, F , Symmetry Breaking. (Lecture Notes in Physics, Vol. 643) 203pp.
Stroock, DW , An Introduction to Markov Processes. (Graduate Texts in Mathematics, Vol. 230) 171pp.
Yin, GG , Discrete-Time Markov Chains. (Stochastic Modelling and Applied Probability, Vol. 55) 347pp.

BIRKHÄUSER PUBLICATIONS

Amann, H, Analysis 1. 448pp.
Andersson, M, Complex Convexity and Analytic Functionals. (Trends in Mathematics) 176pp.
Andreu-Vaillo, F, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. (Progress in Mathematics) 356pp.
Arendt, W, Nonlinear Evolution Equations and Related Topics. 822pp.
Ashino, R, Advances in Pseudo-Differential Operators. (Operator Theory: Advances and Applications, Vol. 155) 244pp.
Baird, P, Variatational Problems in Riemannian Geometry. (Progress in Nonlinear Differential Equations, Vol. 59) 128pp.
Da Prato, G, Kolmogorov Equations for Stochastic PDEs. (Advanced Courses in Mathematics—CRM Barcelona) 192pp.
Eidelman, SD, Analytic Methods in the Theory of Differential and Pseudo-differential Equations of Parabolic Type. (Operator Theory: Advances and Applications, Vol. 152) 400pp.
Falk, M}, Laws of Small Numbers: Extremes and Rare Events. 392pp.
Galdi, P, Contributions to Current Challenges in Mathematical Fluid Mechanics. (Advances in Mathematical Fluid Mechanics) 160pp.
Gil, JB, Aspects of Boundary Problems in Analysis and Geometry. (Operator Theory: Advances and Applications, Vol. 151) 576pp.
Gilding, BH, Travelling Waves in Nonlinear Diffusion-Convection-Reaction. (Progress in Nonlinear Differential Equations, Vol. 60) 220pp.
Gray, A, Tubes. 2nd ed. (Progress in Mathematics) 296pp.
Janas, J, Spectral Methods for Operators of Mathematical Physics. (Operator Theory: Advances and Applications, Vol. 154) 254pp.
Koen Thas, Symmetry in Finite Generalized Quadrangles. (Frontiers in Mathematics) 240pp.
Kreck, M, The Novikov Conjecture. (Oberwolfach Seminars, Vol. 33) 288pp.
Lagnese, JE, Domain Decomposition Methods in Optimal Control of Partial Differential Equations. (International Series of Numerical Mathematics, Vol. 148) 460pp.
Palamodov, V, Reconstructive Integral Geometry. (Monographs in Mathematics, Vol. 98) 176pp.
Qian, T, Advances in Analysis and Geometry. (Trends in Mathematics) 392pp.
Walczak, P, Dynamics of Foliations, Groups and Pseudogroups. (Monografie Matematyczne, New Series, Vol. 65) 240pp.}

ALGEBRAIC TRANSFORMATION GROUPS AND ALGEBRAIC VARIETIES
Proceedings of the Conference on Interesting Algebraic Varieties Arising in Algebraic Transformation Group Theory held in Vienna, October 22–26, 2001.
Edited by Vladimir L. Popov.
Encyclopaedia of Mathematical Sciences, 132. Invariant Theory and Algebraic Transformation Groups, III. Springer-Verlag, Berlin, 2004. xii+238 pp. ISBN 3-540-20838-0

This collection of articles deals with relationships between algebraic transformation groups and algebraic varieties. Here the varieties in question are mostly projective algebraic varieties over an algebraically closed field k of characteristic zero and the groups are linear algebraic groups over k — subgroups of a general linear group GL_n(k) defined by polynomial equations in the matrix entries. Linear algebraic groups are varieties of a very special kind; nonetheless all sorts of surprising interactions have been discovered between the theory of algebraic groups and algebraic geometry as a whole.

One link comes from geometric invariant theory, which asks the following question. Suppose a linear algebraic group G acts on a variety V. Under what circumstances can one form a reasonable quotient variety V/G? Hilbert's 14th Problem was to show that if V is affine then the subring of invariants k[V]^G of the co-ordinate ring k[V] is finitely generated as a k-algebra. Nagata in 1958 gave a celebrated counter-example; Hilbert himself proved that if G is reductive then k[V]^G is finitely generated, so one can define V/G to be the affine variety with k[V]^G as its co-ordinate ring. The article of Snow investigates the question of when a coset space G/H (where H is a closed subgroup of G) is affine. The article of Mukai gives further counterexamples to Hilbert's problem by a geometric construction involving the cohomology groups of certain projective varieties.

A rich source of interesting varieties comes from the representation theory of semisimple algebraic groups. Let G be such a group, let v be an irreducible representation of G and let . Let [V] denote the image of V in the projectivisation P(V). The orbits G·v in v and G·[v] in P(V), and their closures, have been much-studied. De Concini in his article looks at the normalisation of orbit closures; Popov and Tevelev in theirs consider self-dual projective varieties arising from nilpotent orbit closures in the projectivised adjoint representation of G.

If G/V are as above then there is a unique closed orbit G·v in P(V). This orbit is of the form G/P, where P is a parabolic subgroup of G; here G acts transitively on G/P by left translation. Projective varieties of the form G/P are called homogeneous varieties. Several of the articles in this collection involve the geometry of homogeneous varieties: that of Hwang and Mok proves a rigidity result when G is of type F₄, that of Tevelev is motivated by a question involving vector bundles on G/P, while that of Landsberg and Manivel looks at the local structure of homogeneous varieties.

An important theme in projective algebraic geometry is classification: to describe or list all projective varieties of a certain type. Suitable invariants such as dimension and degree are helpful here. Zak in his article generalises the notion of determinant of a matrix to arbitrary projective varieties, giving new invariants.

The collection is rounded off by three articles (the two of Ciliberto and Di Gennaro and the one of Krashen and Saltman), which have little or no input from algebraic groups, on the geometry of varieties.

This book gives a good flavour of some current research in algebraic transformation groups and their applications. It is not well-suited to beginners: many of the articles are very technical. Several of the authors, however, have written clear introductions and/or included expository sections. I found the article of Landsberg and Manivel particularly readable; it brings together ideas from projective geometry, representation theory, Jordan algebras and knot theory.

The contents are as follows: Ciro Ciliberto and Vincenzo Di Gennaro, Factoriality of certain hypersurfaces of P⁴ with ordinary double points; Ciro Ciliberto and Vincenzo Di Gennaro, Boundedness for low codimensional subvarieties; Corrado De Concini, Normality and non normality of certain semigroups and orbit closures; Jun-Muk Hwang and Ngaiming Mok, Deformation rigidity of the 20-dimensional F₄-homogeneous space associated to a short root; Daniel Krashen and David J. Saltman, Severi-Brauer varieties and symmetric powers; Joseph M. Landsberg and Laurent Manivel, Representation theory and projective geometry; Shigeru Mukai, Geometric realization of t-shaped root systems and counterexamples to Hilbert's fourteenth problem; Vladimir L. Popov and Evgueni A. Tevelev, Self-dual projective algebraic varieties associated with symmetric spaces; Dennis Snow, The role of exotic affine spaces in the classification of homogeneous affine varieties; Evgueni A. Tevelev, Hermitian characteristics of nilpotent elements; Fyodor L. Zak, Determinants of projective varieties and their degrees.

Ben Martin
University of Canterbury

INTRODUCTORY OPERATIONS RESEARCH
by Harvir S. Kasana and Krishna D. Kumar,
Springer-Verlag, 581pp, US $79.95. ISBN 3-540-40138-5

Kasana and Kumar provide an introductory text for the theory and applications of operations research. The book will be of interest to engineers, managers and students of statistics looking for a self-contained text. The book consists of eighteen chapters and an appendix. There is much material and many examples provide for interesting reading. The book may be used as a one-year course. Each chapter contains exercises and answers to the exercises are given at the end of the book. The authors suggest the book be used as an undergraduate or graduate level textbook. I agree and also feel the book provides an excellent source of reference material.

Chapter 1 introduces linear programming and optimization in general. One example: how should a patient select food items to minimize cost subject to fulfilling minimum daily requirements. Chapter 2 provides a geometric interpretation of the linear programming problem (LPP). If a linear programming problem has n₂ constraints then the LPP has a 2-dimensional representation. The authors discuss extreme points, basic feasible solutions (BFSs) and the objective function. In chapter 3 the authors develop the theory of the simplex method to solve linear programming problems. First start at some BFS and then move to another so that the value of the objective function is improved. After a few steps the desired BFS is reached where the optimal solution exists. Two other methods discussed are slight variants of the simplex method known as the big-M method and the two-phase method. Plenty of examples are given. Chapter 4 considers the dual linear problem, where for each linear program there corresponds another with the same set of data. The dual of a minimization problem is a maximization problem. An important result is that if either the original or dual LPP has a finite optimal solution then both achieve the same optimal objective value. Chapter 5 continues with more advanced techniques. The revised simplex algorithm is described, where instead of finding the next iteration by row operation, the next iteration is computed by using the product form to invert the basis matrix. Other techniques include the bounded variable technique, the decomposition algorithm and the Karmarkar interior point algorithm. In chapter 6 the linear programming problem produces a solution that may need refinement at a later time to find a new optimal solution. Small changes that will have an effect on the objective function value and solution require the use of sensitivity analysis. Chapter 7 discusses a special type of LPP, the transportation problem. Material is transported from different sources to different destinations. Five methods are described: 1) the North-west rule; 2) the least cost method; 3) the Vogel approximation method; 4) the Russell approximation method; and 5) the u - v method. The process of transshipment and the assignment problem are included. The Hungarian method to solve the assignment problem is outlined. Chapter 8 is concerned with networks. The minimal spanning tree algorithm calculates the minimum distance between nodes connected directly or indirectly. The authors analyze the minimum distance between two specified nodes connected through various feasible paths. The authors next consider the maximal flow problem and give an example of two wells which supply crude oil to refineries. Chapter 9 examines the critical path method for managing the successful completion of a project. Chapter 10 evaluates the sequence that should be taken to minimize the time needed for a finite number of jobs processed on a finite number of machines. This is the sequencing problem. Chapter 11 examines the integer linear programming problem, where decision variables are positive integer values. The traveling salesman and the cargo-loading problem are described. Chapter 12 introduces dynamic programming. Recursive relations, the continuous and the discrete case are considered. Dynamic programming is compared to linear programming. Chapter 13 presents nonlinear programming when the objective function includes several variables and any type of constraints. Two methods are described. These are the Lagrange multiplier method for nonlinear problems with equality constraints and the Kuhn–Tucker theory for nonlinear problems with inequality constraints. Chapter 14 considers the unconstrained optimization of nonlinear problems. The authors use the Fibonacci search method, the Golden section method, the steepest descent method, and the conjugate gradient method. Chapter 15 examines different types of geometric programming problems. Chapter 16 introduces goal programming when more than one objective function is to be optimized. Chapter 17 introduces games theory and compares it to linear programming. Chapter 18 concludes with the description of various special topics. The topics include the extremum difference method, generalized transportation and assignment problems and the multi-objective transportation problem. The appendix lists objective type questions.

I liked the book. The book makes a worthwhile addition for those interested in operations research. The book contains much reference material and is well written. The book contains an extensive subject index. The examples, summaries, discussions and conclusions are well presented. The authors in my opinion should have added additional material, perhaps even a chapter, discussing various computer packages and/or software for use in solving such problems. I liked the useful exercises at the end of each chapter. I recommend this book. It makes a worthwhile addition to a mathematics/statistics library.

Paul Johnson
Davis, California

MATHEMATICS HANDBOOK FOR SCIENCE AND ENGINEERING (Fifth edition)
by Lennart Räde and Bertil Westergren, 562pp, £ 38.50, SFr88.50, US $59.95. ISBN 3-540-21141-1.

My dictionary defines a handbook as a "concise manual or reference book providing specific information or instruction about a subject or place." Most of my previous experience with mathematical handbooks has involved trying to find obscure integrals in the likes of Gradshteyn and Ryzhik, so I was interested to see how useful the book under review (which is much more widely ranging than that weighty tome) would be. It contains much information—and a little instruction—which adds greatly to its usefulness. Not surprisingly, it is not a book to read for instruction alone, but rather one in which to look up those things you know that you know but can't remember off the top of your head and don't want to derive from scratch. But rather than just being lists of expressions and equations, we have these interspersed with short explanations, notes and examples. These serve to jog the memory, explain notation, or provide examples of the concepts being discussed (with answers given for comparison).

The book is organised into 19 chapters, starting from discrete mathematics (logic, algebraic structures, graph theory, etc.) and ending with statistics (point estimation, factorial experiments, a glossary, etc.). Along the way, algebra, geometry, calculus, transforms, complex analysis, optimisation and more are covered, and it includes 30 pages of definite and indefinite integrals. Each chapter is divided into about eight sections in a logical fashion.

This book is in its fifth edition, so one would have expected that obvious typos would have been edited out by now. However, I found a few: "condradiction" (p. 10, which was also there in the third edition), "intervall" (p. 135) and "respektively" (p. 236). On p. 71 we have k defined as the curvature of a circle and r its radius, but then find the formula k = 1/r, and on p. 432 the expected value E[X] should be E[Y]. These are minor, but on p. 113 several lines of text from p. 112 appear again, which could lead to confusion.

There were several other things that I originally thought were typos, but turned out to be more involved than that. The authors consistently use ^alog instead of log_a to denote "log to the base a". I have never seen this notation elsewhere, and it makes their definition of entropy, for example, which contains a term of the form ²log f(x) instead of log₂ f(x), look unusual. The authors also use "artanh", "arcosh" and "arsinh" to denote the inverses of the hyperbolic functions tanh, cosh and sinh, respectively, seemingly replacing "arc" with "ar". Apparently, this is the usual spelling in some European countries (the authors are from Sweden). These terms can be derived from the Latin "area tangentis hyperbolicae", "area cosini hyperbolici" and "area sini hyperbolici," respectively. This was a revelation to me, as I had always assumed that "arc" was just a way of indicating an inverse.

Having said that, the text is well laid-out and many useful diagrams are included. The index is sufficiently detailed to be useful (it is 16 pages long) and there is some cross-referencing within the text, so finding what one is looking for in a reasonable time is not too difficult. I don't recommend that you rush out to buy this book, but it is certainly a handy one to have within reach.

Carlo Laing
Massey University, Albany

RUSSIAN MATHEMATICIANS IN THE 20TH CENTURY
Yakov Sinai (editor)
World Scientific, Singapore, 2003 ISBN 981-02-4390-1

This large book (700 pages) has chapters about 33 Russian mathematicians, each of whom was one of the important mathematicians of the 20th century—but there is no perceptible ordering in that list, neither chronological nor alphabetical. The mathematicians considered are (in alphabetic order): A. D. Aleksandrov, P. S. Aleksandrov, S. N. Bernstein, N. N. Bogoliubov, N. G. Chebotaryov, B. N. Delone, D. F. Egorov, D. K. Faddeev, I. M. Gelfand, A. O. Gelfond, L. V. Kantorovich, M. V. Keldysh, A. Ya. Khinchin, A. N. Kolmogorov, M. G. Krein, M. A. Lavrentev, Yu. V. Linnik, L. A. Liusternik, N. I. Luzin, A. M. Lyapunov, A. I. Malcev, A. A. Markov, D. E. Menshov, P. S. Novikov, I. G. Petrovsky, L. S. Pontryagin, V. A. Rokhlin, V. I. Smirnov, S. L. Sobolev, V. A. Steklov, A. N. Tikhonov, P. S. Urysohn, I. M. Vinogradov. Israil Moiseevich Gelfand is the only one still living. Remarkably, no women are included—I would certainly have expected a chapter about O. A. Ladyzhenskaya; and each of V. N. Faddeeva, P. Ya. Kochina, L. V. Keldysh and O. A. Oleinik had a strong claim to be included. \par Each chapter starts with a brief biography by the Editor, with photograph and dates of birth and death. None of those biographical articles cites any source, except for D. K. Faddeev. (But there is no photograph of D. K. Faddeev, and no date is given for his death.) The texts of the biographies mostly occupy 1 to 2 pages: but the entire biographical text for L. A. Liusternik (p. 469) consists of the sentence "Lazar Liusternik was a corresponding Member of the Division of Physical-Mathematical Sciences since 4 Dec 1946".

The Editor's biography is followed by a biographical article (in Russian) for V. A. Steklov, and by 3 biographical articles (1 in Russian, 2 in English) for D. F. Egorov. Each of the other 31 chapters reprints one or more articles by that mathematician (in Russian or French or German or English, or in English translation from Russian or from French), and in some chapters another biographical article is reprinted (in English translation from Russian, or in English).

This anthology of mathematical writings contains many very significant works, including I. M. Vinogradov's renowned papers on primes [1,2], A. O. Gelfond on Hilbert's 7th problem [4], A. Ya. Khinchin's classic little book Three Pearls of Number Theory [5], A. N. Kolmogorov on turbulent fluids [6,7,8,9], S. L. Sobolev on functional analysis [11], I. G. Petrovsky on partial differential equations [12], L. V. Kantorovich's pioneering papers (written in English) on linear programming [13,14], and A. A. Markov (\textsl{junior}) on algorithms [15].

Many of the reprints of articles lack bibliographic details, and so the reader needs to consult the list of Contents (pp.vii-xi)—but some bibliographic information is missing there. The articles by A. M. Lyapunov [17,18] are printed in English translation (typewritten), but the Contents ascribes those translations only to Collected Papers [19], with no further information. The article [20] about V. A. Steklov is a speech (in Russian) given by N. M. Gyunter at a memorial meeting of the Leningrad Physical-Mathematical Society on 9 October 1926, and the Contents identify the source only as Uspekhi, Vol.1, new series, No.4. In fact, Gyunter's speech was first published as pp.49–77 in the book In Memory of V. A. Steklov (in Russian), a collection of papers published by the Academy of Sciences of the USSR at Leningrad in 1928. It was reprinted in Uspekhi Matem. Nauk (new series) 1, No. 3–4 (1946), 23–43, and that reprint is reproduced in this book. I. M. Vinogradov's renowned papers [1,2] on primes are published in English translations, which are not identified as coming from his Selected Works [3].

The 3 chapters of A. Ya. Khinchin's classic little book Three Pearls of Number Theory are reproduced from the English translation ([5], pp.11–64) published by Graylock Press—but the publication date (1952) is not stated. And Khinchin's very significant preface A Letter to the Front: March 24, 1945 is not reproduced from pages 9–10. He addressed that to a former student (for one year) who had been wounded after 3 years of fighting against the Nazi invaders, and had written from a hospital to his former professor asking him to send "some little mathematical pearls". After several days of deliberation, Khinchin selected "the three theorems of arithmetic which I am sending you, to be genuine pearls of our science". He explained that "They have all been solved quite recently, and there are two remarkable common features in their history. First, all three problems have been solved by the most elementary arithmetical methods (do not, however, confuse elementary with simple: as you will see, the solutions of all three problems are not very simple, and it will require not a little effort on your part to understand them well and assimilate them). Secondly, all three problems have been solved by very young, beginning mathematicians, youths of hardly your age, after a series of unsuccessful attacks on the part of `venerable' scholars. Isn't this a spur full of promise for future scholars like you? What an encouraging call to scientific daring!

The work of expounding these theorems compelled me to penetrate more deeply into the structure of their magnificent proofs, and gave me great pleasure."

A. N. Kolmogorov's 4 papers on turbulence in fluids [6,7,8,9] are published in English translations, which are not identified as coming from Volume 1 of his Selected Works [10]. L. S. Pontryagin's papers [21,22,23,24] are published in English translations, which are not identified as coming from Volume 1 of his Selected Works [25].

The paper [26] by M. Krein and D. Milman (in English with Ukrainian summary, pp.457-462) was published in the Polish journal Studia Mathematica t.9, but the highly significant date of publication (1940) is not indicated. L. A. Liusternik's survey article [27] is attributed to Uspekhi, new series, Vol.1, No.1 with no date given: actually it was published in Vol.1 No.11 (1946), 30-56. The very brief biographical article (p.599) about Andrei Andreyevich Markov (1856-1922) tells that "Markov had a son (of the same name) who was born on September 9, 1903 and followed his father in also becoming a renowned mathematician". But the following articles [15,16] were both written by the younger Andrei Andreyevich Markov! M. A. Lavrentev's paper [28] is attributed to J. d'analyse Mathematique 19; which should be J. d'Analyse Mathématique 19 (1967), 217-225. A. N. Tikhonov's paper [29] is attributed to Math. Ann. 102, but the date of publication (1930) is not indicated; and P. S. Aleksandrov's paper The principal topological discoveries of A. N. Tikhonov [30] is misnamed in the Contents (p.xi) as The principal mathematical discoveries of A. N. Tikhonov.

There are several further misprints, including (on p.viii) "Scienes" for "Sciences", "P. S. Alexdrov" for "P. S. Aleksandrov" and "Petreovski" for "Petrovsky".

This book is a valuable anthology of mathematical writings—but it should have been edited with greater care.

References
[1] Vinogradov, Ivan Matveevich, Representation of an odd number as the sum of three primes, [pages 191-194], Doklady Akademii Nauk SSSR 15
No.6-7 (1937) 291-294, translated by P. S. Naidu, [3] 129-132,
[2] Vinogradov, Ivan Matveevich, Estimates of certain simple trigonometric sums with prime numbers, [pages 195-221]. Izvestiya Akademii Nauk SSSR Ser. Mat.3 No.4 (1939) 371-398, translated by P. S. Naidu, [3] 133-159.
[3] Vinogradov, Ivan Matveevich, Selected Works (translated by P. S. Naidu), Springer-Verlag, Berlin, 1985.
[4] Gelfond, Aleksandr Osipovich, Sur le septième problème de Hilbert, [pages 254-265], Izvestiya Akademii Nauk SSSR, Ser. Mat. (1934) 623-634.
[5] Khinchin, Aleksandr Yakovlevich, Three Pearls of Number Theory, [pages 269-322], (translated by F. Bagemihl, H. Komm, & W. Seidel), Graylock Press, Rochester N.Y., 1952, 11-64.
[6] Kolmogorov, Andrey Nikolaevich, Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers, [pages 325-331].Doklady Akademii Nauk SSSR 30:4 (1941) 299-301, translated by V. M. Volosov, [10] 312-318.
[7] Kolmogorov, Andrey Nikolaevich, On the degeneration of isotropic turbulence in an incompressible viscous fluid, [pages 332-336], Doklady Akademii Nauk SSSR 31:6 (1941) 538-541, translated by V. M. Volosov, [10] 319-323.
[8] Kolmogorov, Andrey Nikolaevich, Dissipation of energy in isotropic turbulence, [pages 337-340], Doklady Akademii Nauk SSSR 32:1 (1941) 19-21, translated by V. M. Volosov, [10] 324-327.
[9] Kolmogorov, Andrey Nikolaevich, Equations of turbulent motion in an incompressible fluid, [pages 341-343], Doklady Akademii Nauk SSSR Ser. Fiz. 6:1-2 (1942) 56-58, translated by V. M. Volosov, [10] 328-330.
[10] Kolmogorov, Andrey Nikolaevich, Selected Works (translated from Russian by V. M. Volosov), Kluwer Academic Publishers, Dordrecht, 1991.
[11] Sobolev, Sergei Lvovich, On a theorem of functional analysis, [pages 383-412], translated by J. R. Brown in Amer. Math. Soc. Trans., Series 2 34 (1963), 39-68.
[12] Petrovsky, Ivan Georgievich, On some problems of the theory of partial differential equations, [pages 414-454], Russian Mathematical Surveys 4, 3-43. Translated from Uspekhi Matem. Nauk (N.S.) 1, No.3-4 (1946), 44-70.
[13] Kantorovich, Leonid Vitalyevich, A new method of solving of some classes of extremal problems, [pages 551-554], Doklady Akademii Nauk SSSR 28 No.3 (1940) 211-214.
[14] Kantorovich, Leonid Vitalyevich, On the translocation of masses, [pages 555-557], Doklady Akademii Nauk SSSR 37 No.7-8 (1942) 199-201.
[15] Markov, Andrey Andreyevich (\textsl{junior}), The theory of algorithms, [pages 600-613], American Mathematical Society Translations, Series 2 15 (1960), 1-14, translated by Edwin Hewitt.
[16] Markov, Andrey Andreyevich (\textsl{junior}), Foundations of the algebraic theory of tresses, [pages 614-621], Proc. Steklov Math. Inst. 16, 46-53.
[17] Lyapunov, Aleksandr Mikhailovich, A new case of integrability of differential equations of motion of a solid body in fluid, [pages 3-7], Reports of the Kharkov Mathematical Society, Series 2, 4 No.1-2 (1893), 81-85. Translation from [19] 329-333.
[18] Lyapunov, Aleksandr Mikhailovich, A general proposition of probability theory, [pages 8-9], Comptes Rendus de l'Acad{émie des Sciences, 132 (1901), 814-815. Translation from [19] 161-162.
[19] Lyapunov, Aleksandr Mikhailovich, Collected Papers (no details).
[20] Gyunter, Nikolai Maksimovich, The work of V. A. Steklov in mathematical physics (in Russian), [pages 39-59], In Memory of V. A. Steklov (in Russian), Academy of Sciences of the USSR, Leningrad 1928, 49-77. Reprinted from Uspekhi Matem. Nauk (new series) 1, No. 3-4 (1946), 23-43.
[21] Pontryagin, Lev Semenovich, Characteristic cycles of manifolds, [pages 347-351], Doklady Akademii Nauk SSSR 35 No.2 (1942) 35-39, translated by P. S. Naidu, [25] 283-287.
[22] Pontryagin, Lev Semenovich, Characteristic cycles, [pages 352-356], Doklady Akademii Nauk SSSR 47 No.4 (1945) 246-249, translated by P. S. Naidu, [25] 341-345.
[23] Pontryagin, Lev Semenovich, Rough systems, [pages 357-362], Doklady Akademii Nauk SSSR 14 No.5 (1937) 247-250, translated from French by P. S. Naidu, [25] 159-164.
[24] Pontryagin, Lev Semenovich, Homotopic classification of an (n+2)-dimensional sphere into an n-dimensional sphere [pages 363-366], Doklady Akademii Nauk SSSR 70 No.6 (1950) 957-959, translated by P. S. Naidu, [25] 477-480.
[25] Pontryagin, Lev Semenovich, Selected Works (translated by P. S. Naidu), Gordon & Breach, New York, 1986.
[26] Krein, Mark Grigorievich & Milman, D.I., On extreme points of regular convex sets, [pages 457-462], Studia Mathematica 9 (1940), 133-138.
[27] Liusternik, Lazar Aronovich, Topology and the calculus of variations (in Russian) [pages 470-496], Uspekhi Matem. Nauk, new series 1 No.11 (1946), 30-56.
[28] Lavrentev, Mikhail Alekseevich, On the theory of quasi-conformal mappings of three-dimensional domains, [pages 624-632], J. d'Analyse Mathématique 19 (1967), 217-225.
[29] Tikhonov, Andrei Nikolaevich, {Über die topologische Erweiterung von Raumen, [pages 635-652], Math. Ann. 102 (1930), 544-561.
[30] Aleksandrov, Pavel Sergeevich, The principal topological discoveries of A. N. Tikhonov, [pages 653-655], Russian Mathematical Surveys 31:6 (1976), 13-15. Translated by D. Mathon from Uspekhi Matem. Nauk 31:6 (1976), 13-16.

Garry J. Tee
The University of Auckland

CONFERENCES

REPORT ON NZIMA MEETING IN LEIGH
30 November–3 December, 2004

Last year's NZIMA thematic programme on Dynamics Systems and Numerical Analysis came to a triumphant close in December with a meeting at the Goat Island Marine Reserve in Leigh. Around 30 of us gathered at the reserve for 2½ days of talks. The definite highlight was almost 3 hours of presentation by Jerry Marsden from Caltech, who showed us what we can only aspire to in our most vainglorious dreams, with reports of a huge variety of work in discrete mechanics, variational integrators, and optimal control.

In addition to Jerry, two invited speakers, Jeroen Lamb from Imperial College & our own Robert McLachlan gave extended presentations. Jeroen, a veteran of the NZIMA programme since he also talked at the Raglan meeting, talked about bifurcations in the presence of symmetry. He also brought a number of his PhD students from the UK. Robert kicked off the scientific programme with a general introduction to geometric numerical integration.

The rest of the scientific presentations came from talks from the audience, and covered a wide variety of themes, from bifucation analysis to image registration, via inverse problems and the rotating shallow water equations. There was a good mix of talks by students and academics. The full program, and links to the slides for some of the talks are available at http://www.math.waikato.ac.nz/ rua/dsna/leigh/speakers.html

However, I couldn't possibly write this review without mentioning the facilities provided for us by the Marine Reserve. They fed us admirably, and provided a wonderful location. While it was still rather cold for snorkelling—my first December in New Zealand wasn't the sun-drenched wonder I'd imagined from the Northern Hemisphere winter the previous year—a number of us did brave the water to see a wide variety of fish, and a great many could also be seen from the safety of the rocks. Furthermore, the Wednesday afternoon free time enabled the organisation of a trip on the `Glass-Bottomed Boat', a Leigh innovation for those wishing to see underwater without freezing. Pretty much the whole group, and assorted hangers-on and families joined the trip around Goat Island, with the skipper providing a commentary of marine life we were seeing below the boat, while his assistant spent her time vigorously polishing the glass to stop it from misting up.

In conclusion, I'd like to thank the organisers, Vivien Kirk, Rua Murray, and Robert McLachlan for an extremely interesting, stimulating, and enjoyable workshop—I'm looking forward to some future follow-up meeting already.

REPORT ON THE 2004 NEW ZEALAND MATHEMATICS COLLOQUIUM
6–8 December 2004

The 2004 New Zealand Mathematics Colloquium was held at the University of Otago from 6–8 December 2004. It incorporated the Annual General Meetings of the New Zealand Mathematical Society and ANZIAM (NZ branch).

There was a welcoming reception at Unicol on Sunday evening 5 December, and the programme included a SIAM (South Island Applied Mathematics) Day on the Tuesday and an Education Day on the Wednesday. The invited speakers were:

Rod Gover (University of Auckland), "Overdetermined PDEs, the Einstein equations and conformal geometry."
Peter Cameron (Queen Mary College), "The Rado graph and the Urysohn space."
James Sneyd (The University of Auckland), "Neither an ant nor a spider be: historical vignettes in mathematical physiology."
Bill Currie (Fisher & Paykel), "Simulation and appliance design: using applied maths to get better outcomes faster."
Carsten Thomassen (Technical University of Denmark), "Rendezvous numbers and von Neumann's mini-max theorem."

There were 103 registrants and 53 contributed talks. The Aitken prize for the best student talk was awarded to Joanne Mann of Massey University at Albany for her talk To vaccinate or not to vaccinate.

Following afternoon tea on Tuesday afternoon there was an excursion to Natures Wonders—a bus trip down the Otago peninsular in a bracing wind and showery weather, not inhospitable to the albatross. This was followed by the Colloquium dinner at Glenfalloch. In recognition of its thirty year anniversary the NZMS presented Life memberships to the four longest serving office bearers: Marston Conder, Rob Goldblatt, Gillian Thornley and Graeme Wake. The NZMS Research Award to Eamonn O'Brian was formally presented (in Eamonn's absence) though it had been announced earlier in the year at a Royal Society function.

The Colloquium Business Meeting agreed to depart once again from the "Peterson cycle" on account of possible forthcoming combined meetings with the American Mathematical Society at Victoria and with the Australian Mathematical Society at Canterbury over the next four years. The 2005 Colloquium will therefore be hosted by Massey University at Palmerston North.

We are grateful to our sponsors, the NZMS and ANZIAM (NZ branch) for their financial support. We thank the Otago organising committee for a well run Colloquium and the typical southern hospitality.

Gillian Thornley
Massey University, Palmerston North

DLT'04: Short Presentation
12–17 December 2004

In December 2004 the Eighth International Conference "Developments in Language Theory" (DLT'04) was held at Massey University at Albany; it was jointly organized with the Centre for Discrete Mathematics and Theoretical Computer Science of the University of Auckland, under the auspices of the European Association for Theoretical Computer Science (EATCS), with the support of the New Zealand Royal Society. Together with the satellite workshops, the International "Workshop on Automata, Structures and Logic", and the International Workshop "Tilings and Cellular Automata", DLT'04 had about 100 participants from 17 different countries from all continents.

The main subjects of the DLT conference series—the main international conference in formal language theory—are formal languages, automata, conventional and unconventional computation theory, and applications of automata and language theory.

A panel of distinguished theoretical computer scientists have selected selected 30 papers (out of 50) to be presented at DLT'04 (which includes a record number of papers written by graduate students: 5); they were complemented by five invited lectures given by the well-known experts Bruno Courcelle (Bordeaux, France), Rodney Downey (Wellington, NZ), Nata\v sa Jonoska (Tampa, USA), Anca Muscholl (Paris, France) and Grzegorz Rozenberg (Leiden, Holland). The proceedings of the conference have been published as the volume 3340 of the Lecture Notes in Computer Science series of Springer, Heidelberg (2004, 442 pp).

A detailed presentation of DLT'04 will appear in the Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 85, S(2005).

Elena Calude

REPORT ON 2004 NZIMA CONFERENCE IN COMBINATORICS AND APPLICATIONS
13–18 December 2004

The conference was held in conjunction with The 29th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing and was held at Copthornes-Manuels Hotel in Taupo from 13 to 18 December 2004. About 150 participants from 22 countries attended the conference. Massey's participants were Charles Little, Serguei Norine, Bhalchandra Thatte, and Kee Teo. I have never met so many world-reknowned researchers at a combinatorics conference before. I was particularly pleased to meet Alan Sokal and Carsten Thomassen, whom I have communicated with in the past. The talks given by the invited speakers and most speakers were outstanding. The invited speakers were Dan Archdeacon, Rosemary Bailey, Richard Brualdi, Darryn Bryant, Peter Cameron, Maria Chudnovsky, Bruno Courcelle, Jim Geelen, Bert Gerards, Catherine Greenhill, Bojan Mohar, Bruce Richter, Neil Robertson, Paul Seymour, Alan Sokal, Robin Thomas, Carsten Thomassen, Tom Tucker, Mark Watkins and Dominic Welsh.

The conference excursion included the Huka Falls and the Taupo Prawn Farm and ended at Orakei Korako Thermal Park. I could hear a lot of oohs and aahs about this truly unique geothermal wonderland.

Paul Bonnington and his committee must be congratulated for organising such a great and successful conference.

Kee Teo
Massey University, Palmerston North

NZ MATHEMATICS RESEARCH INSTITUTE SUMMER WORKSHOP 2005
9–15 January 2005

The workshop this year was held in sunny Napier from 9th–15th January at the Napier War Memorial Conference Centre. It was sponsored by the New Zealand Institute for Mathematics and its Applications as one of the key events in the Geometry Program which runs from January to June 2005. The theme of the meeting was Geometry: Interaction with Algebra and Analysis and was interpreted broadly, indeed few parts of mathematics were left untouched by the star-studded line-up of invited speakers.

The meeting attracted over 80 participants, including students and post-docs, and over 40 accompanying persons. The weather behaved, the vineyards sparkled, the climb of Mt Kaweka succeeded and the gannets put on a grand show. One blemish—the breeze was too light for wind-surfing.

Speakers in the main session (each gave three lectures) were Ben Andrews (Camberra) who discussed the recently announced proof of the Poincaré conjecture, Craig Evans (Berkeley) who presented weak KAM theory and non-linear PDEs (here is the formula but what does it mean!), Martin Liebeck (Imperial) who presented probabilistic group theory with a kiwi connection, Alex Lubotzky (Jerusalem) who showed how counting groups, manifolds and primes can be related and Peter Sarnak (Princeton) who discussed eigenvalues and eigenfunctions in the context of analysis and arithmetic on locally symmetric spaces.

The Thursday was devoted to celebrating Fred Gehring's 80^th year with a set of additional speakers having a close relationship to Fred. They were Kari Astala (Helsinki) who discussed Quasiconformal methods in impedance tomography, Tadeusz Iwaniec (Syracuse) - Extremal mappings of finite distortion, Peter Jones (Yale) - Some random homeomorphisms in analysis and Stephan Rohde (Seattle) - The stochastic Schramm-Loewner evolution equation.

The day concluded with a fine banquet held at Clearview Estate Vineyard with Gaven Martin giving an outrageously funny after-dinner speech.

In addition, three after-dinner lectures, suitable in the main for a public audience, were given. John Conway (Princeton) - How to beat children at their own game, Michael Eastwood (Adelaide) - Complex analysis out of thin air and Peter Jones - Geometry meets the traveling salesman.

The contribution made to the success of the meeting by the organizers Gaven Martin and Eamonn O'Brien and the support of the NZIMA are gratefully acknowledged.

(Some photographs, including the gannets, Napier, the venue, and Ben Andrews completing the proof of the Poincare conjecture are at http://math.waikato.ac.nz/~kab and follow the link under NZMRI Napier 2005 Workshop.)

Kevin Broughan
The University of Waikato

REPORT ON VIC2005, INTERNATIONAL WORKSHOP ON ALGEBRA
9–10 February 2005

The VIC2005 Workshop took place at Victoria University of Wellington on February 9–10, 2005. The themes of the meeting included noncommutative geometry, quantum groups and representation theory. 15 participants from Europe, China, Israel and New Zealand attended the two day meeting; and nine interesting one hour talks were given by Professor Fred Van Oystaeyen (University of Antwerp), Dr Huixiang Chen (VUW), Dr Jianbei An (The University of Auckland), Professor Piotr Hajac (Mathematical Institute, Polish Academy of Science), Professor Mia Cohen (Ben Gurion University), Dr John Clark (University of Otago), Dr Ben Martin (University of Canterbury), Professor Stefaan Caenepeel (Free University of Brussels) and Professor Quanshui Wu (Fudan Univ). The programme can be viewed at www.mcs.vuw.ac.nz/events/VIC2005. Thanks to our School Manager Ginny Nikorima, who did most of the local organization (and drove the bus on the wine trail to Martinborough), the workshop ran very smoothly and successfully.

Yinhuo Zhang
Victoria University of Wellington

APPROXIMATION AND HARMONIC ANALYSIS
held at The University of Auckland, 8–11 February 2005

This was the third conference in a series the others having been held at the University of Canterbury in February 1999, and at Westport in February 2002.

The fields of Approximation and Harmonic Analysis were virtually identical in the time of Zygmund but have unfortunately grown apart in recent times. This conference aimed at fostering and highlighting cross connections between these fields. We believe that it succeeded in this, in that almost all the talks were very interesting to audience members of the "other" specialty. A highlight of the conference was the excursion to Tiritiri Matangi, an idyllic wildlife reserve off the coast of Auckland. This provided a beautiful setting for the all important informal interactions between delegates.

The following invited talks were given

John Benedetto, "Sigma Delta quantization and finite frames."
Len Bos, "Some remarks on Heisenberg Frames."
Pete Casazza, "Signal Reconstruction without Noisy Phase."
Xuan Duong, "New characterisations of BMO and Morrey-Campato spaces."
David Levin, "Moving Least Squares for Surfaces."
SL Lee, "Approximation of the Gaussian and its Properties."
Vilmos Totik, "Equilibrium Measures and polynomials."

There were participants from Australia, Canada, Hungary, Israel, Korea, Singapore, United States of America, and New Zealand.

The organisers Shayne Waldron (Auckland), Qui Bui and Rick Beatson (Canterbury) are grateful to The University of Auckland, the University of Canterbury and the New Zealand Institute for Mathematics and its Applications for their support of this successful conference.

Rick Beatson

NEW ZEALAND PHYLOGENETICS MEETING
February 13–17, Whitianga'05

This year it was Auckland University's turn to host the NZ Phylogenetics meeting—the rules are that hosts can't hold the meeting in their own city—so we headed off to Whitianga. As in previous years the talks were on a spectrum from the more mathematical to more biological (with a healthy dash of statistics and computer science thrown in). One session that stood out was devoted to talks on applying phylogenetic techniques to studying the "evolutionary relationships" of languages and manuscripts. Quentin Atkinson gave a talk on how techniques that are usually used to put dates on evolutionary trees of species can be used to put dates on the "evolutionary tree" of Indo-European languages. Their findings support the Anatolian farming hypothesis that Indo-European languages started to diversify about 10,000 years ago along with the spread of agriculture. Of the talks with a math/computer science flavour, the one that stood out was Benny Chor on `Maximum Likelihood of Evolutionary Trees is Hard'. The hardness proof for this method has been an open problem in phylogenetics for years (the intuitively easier method Maximum Parsimony was already known to be NP-Hard in 1986), so it was great to get the gist of how this has now been proven. Whitianga turned on beautiful sunshine for the week (making up for Whitianga'02 when the meeting got hit by a cyclone) and people took full advantage. Tuesday evening saw most of the attendees wallowing in the mud at Hot Water Beach, and the following day the walk around to Cathedral Cove was the most popular excursion. A tally of the list of attendees shows that 24 of the 47 came from overseas with the biggest component from Australia or the UK. It's great that these meetings are consistently able to encourage so many people to travel from overseas. Next year is Canterbury University's turn to host so we will be heading back to Kaikoura. Already looking forward to it.

Barbara Holland
Massey University, Palmerston North

GEOMETRY: INTERACTIONS WITH ALGEBRA AND ANALYSIS
14–18 February 2005

This conference, part of the NZIMA Thematic Program with the same title, attracted visitors from many countries, including Japan, Israel, Italy, Australia, Britain, the Netherlands and the United States. It was held at The University of Auckland. Most of the participants stayed in hotels or Halls of Residence an easy walk from the university, avoiding the need to struggle against the Auckland traffic.

The subject of the conference was very broad. Geometry is an elusive creature and almost every speaker seemed to have his or her own idea of what it means: differential geometry, geometric group theory, algebraic geometry, geometric invariant theory, the geometry of projective planes, .... I found the wide spread of topics attractive; it's a shame more New Zealanders (and students in particular) were not able to attend the meeting and learn from the visiting experts.

The conference was well run by the organisers, Eamonn O'Brien and Gaven Martin (no relation to this writer!). They arranged excursions to Rangitoto Island and Muriwai Beach on the free afternoon. Getting to the conference dinner became a struggle when the taxis, carefully booked in advance, mysteriously failed to appear, but it was worth it: everyone I spoke to thought the meal was magnificent.

I thoroughly enjoyed the meeting. It's great to have the chance to talk to collaborators from outside New Zealand without having to travel half way around the world! Many of the overseas visitors stayed on to explore the country further and visit other universities.

Ben Martin
University of Canterbury

Conferences in 2005

19–22 April 2005, at The University of Auckland: Mathematical Models for Optimizing Transportation Services.
https://secure.orsnz.org.nz/transportation/

5–7 December 2005, in Palmerston North: New Zealand Mathematics Colloquium.

5–9 December 2005, at the University of Queensland, Brisbane: Thirtieth Australasian Conference in Combinatorial Mathematics and Combinatorial Computing (30 ACCMCC).
website: http://www.maths.uq.edu.au/cdmc/30accmcc.html

Maths-in-Industry Study Group Director Professor Graeme Wake visited by invitation the Australian Mathematical Sciences Institute (AMSI) on Monday 4th April in Melbourne. Discussions were held about activities by AMSI in Industrial Mathematics and its relationship to the 20 year ANZIAM MISG, presently being run in Massey, Auckland. He is pictured seated on the right with AMSI Director Professor Garth Gaudry on the left. Behind them standing is Dr Tom Montague, the Industry Liaison person for AMSI. The penguin is the star of the reception foyer!

NOTICES

ERRATUM

One of the founding vice-presidents of the society was Professor William Davidson of the University of Otago. We apologize for incorrectly naming him in the list of council members in Newsletter Number 92.

CALL FOR NOMINATIONS FOR 2005 NZMS RESEARCH AWARD

This annual award was instituted in 1990 to foster mathematical research in New Zealand and to recognise excellence in research carried out by New Zealand mathematicians. Recipients to date have been John Butcher and Rob Goldblatt (1991), Rod Downey and Vernon Squire (1992), Marston Conder (1993), Gaven Martin (1994), Vladimir Pestov and Neil Watson (1995), Mavina Vamanamurthy and Geoff Whittle (1996), Peter Lorimer (1997), Jianbei An (1998), Mike Steel (1999), Graham Weir (2000), Warren Moors (2001), Bakhadyr Khoussainov (2002), Rod Gover (2003) and Eamonn O'Brien (2004).

Call for nominations 2005

Applications and nominations are invited for the NZMS Research Award for 2005. This award will be based on mathematical research published in books or recognised journals within the last five calendar years: 2000–2004. Candidates must have been residents of New Zealand for the last three years. Nominations and applications should include the following:

1. Name and affiliation of candidate.
2. Statement of general area of research.
3. Names of two persons willing to act as referees.
4. A list of books and/or research articles published within the last five calendar years: 2000–2004.
5. Two copies of each of the five most significant publications selected from the list above.
6. A clear statement of how much of any joint work is due to the candidate.

A judging panel of three persons shall be appointed by the NZMS Council. The judges may call for reports from the nominated referees and/or obtain whatever additional referee reports they feel necessary. The judges may recommend one or more persons for the award, or that no award be made. No person shall receive the award more than once. The award consists of a certificate including an appropriate citation of the awardee's work, and will be presented (if at all possible) at the RSNZ Awards Dinner in 2005.

All nominations (which no longer need to include the written consent of the candidate) and applications should be sent by 30 June 2005 to the NZMS President, Associate Professor Mick Roberts, Institute of Information and Mathematical Sciences, Massey University, Albany Campus, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand.

Please consider nominating any of your colleagues whose recent research contributions you feel deserve recognition!

NZMS ACCREDITATION

Applications are invited for NZMS Accreditation. The deadline for applications is Saturday 30 April 2005. If you would like to be considered or would like to nominate someone could you send for application forms to

The Accreditation Secretary
C/- Department of Mathematics and Statistics
University of Otago University P O Box 56
DUNEDIN
or email lgrant@maths.otago.ac.nz.

To help you understand better what each of the categories of membership are, I have added a copy of Article IV of the Constitution.

ARTICLE IV: OPTIONAL ACCREDITATION
An Ordinary Member (or Reciprocity Member) may apply to the Council to become a Graduate Member, Accredited Member, or Fellow. The Council shall make and issue, and may revise from time to time, Rules which shall give effect to the following requirements.

1. A Graduate Member shall have completed a degree or diploma at a recognised university or other tertiary institution, the studies for which shall include mathematics as a major component, and shall be currently employed or occupied in the development, application or teaching of mathematics.
2. An Accredited Member shall have completed a postgraduate degree in mathematics at a recognised university or other tertiary institution, or shall have equivalent qualifications, and shall have been employed for the preceding three years in a position requiring the development, application or teaching of mathematics.
3. A Fellow shall be a person who currently has or previously has had the qualifications of an Accredited Member and who, in addition, is deemed by the Accreditation Committee (see paragraph below) to have demonstrated a high level of attainment or responsibility in mathematics and to have made a substantial contribution to mathematics or to the profession of mathematician or to the teaching or application of mathematics.

An Honorary Member shall have the right to become a Fellow immediately upon application to the Council and without payment of a fee.

The Council shall establish an Accreditation Committee to consider applications for designation as a Graduate Member, Accredited Member or Fellow, and to administer the Rules described in the first paragraph of this Article. In its determinations, the Accreditation Committee shall discount interruptions to employment such as temporary unemployment and parental leave.

A Graduate Member may use the abbreviation GNZMS, an Accredited Member may use the abbreviation MNZMS, and a Fellow may use the abbreviation FNZMS. These designations and the corresponding abbreviations are the rights of that class of Member only while the member remains a financial member of the Society and while the occupational requirements outlined in the first paragraph of this Article continue to be satisfied. The occupational requirements shall be deemed to be satisfied by Honorary Members and in the case of interruptions to employment such as temporary unemployment and parental leave, and they shall not be applied in the case of retirement or promotion to an administrative or other position.

A fee shall accompany each application to the Accreditation Committee. The fee shall be additional to the annual subscription charged by the Society and shall be the only charge for accreditation.

**********

If you have any queries could you please direct them to me at the above address or by email dholton@maths.otago.ac.nz.

Derek Holton
Chair, Accreditation Committee

LECTURER/SENIOR LECTURER IN MATHEMATICS
Institute of Fundamental Sciences
Massey University, Palmerston North

We wish to appoint a mathematician with a PhD in mathematics, proven research capabilities and excellent teaching skills. A significant component of the teaching responsibility for the Mathematics Discipline is in extramural (distance) teaching. The appointee would be expected to contribute to both internal and extramural teaching. The group also teaches graduate and research degrees, including PhD level. You would also be expected to make a significant contribution to the research activities of the Institute. You should also be an effective communicator who has demonstrated an ability to work as part of a team. Applications are particularly encouraged from those with research experience in one of the fields of Applied, Computational or Discrete Mathematics.

Enquiries of an academic nature should be addressed to Dr Kee Teo, Discipline Leader of Mathematics (telephone 356 9099 extension 3572, email K.L.Teo@massey.ac.nz). Further information regarding the Institute of Fundamental Sciences can be found at the following website: http://ifs.massey.ac.nz. Estimated closing date 30 May 2005.

OPPORTUNITY FOR POSTGRADUATE RESEARCH 2005–2007

A three-year PhD scholarship is available on "Efficient Operation of Bioreactors Using Nonlinear Dynamical Systems Theory." The scholarship is A$23,866 tax free p.a for 3 years. Australian residents or NZ Citizens who are prospective or previous honours graduates in Applied Mathematics, Physics, or Engineering (particularly
Chemical Engineering) are invited to submit a preliminary application by sending a curriculum vitae to: Dr Harvinder Sidhu, School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600. Tel: (02) 6268 8820, Fax: (02) 6268 8786, E-mail: h.sidhu@adfa.edu.au or Dr Mark Nelson, Department of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Tel:(02) 4221 4400, Fax:(02) 4221 4845, E-mail: mnelson@uow.edu.au

RECORDINGS FROM THE ANZIAM MATHEMATICS-IN-INDUSTRY STUDY GROUP 2005

The Centre for Mathematics in Industry at Massey University, Auckland, NZ has available a set of DVDs of the formal presentations of the Monday and Friday sessions of MISG2005. We can place bulk orders for these at just $NZ 24 + GST (= $NZ 27) for each set. They include the power point and video presentations of "Problems" and "Solutions" of the seven problems packaged together, and the opening ceremony. These were produced professionally. Four discs with two Problems & Solutions on each disc. They are excellent for promotional purposes. Orders to Professor Graeme Wake, Centre for Mathematics in Industry, Massey University at Albany, Private Bag 102904, North Shore MC, Auckland, New Zealand. Please include cheque (made out to Massey University) or Visa/MasterCard details with each order. E-mail g.c.wake@massey.ac.nz

MINUTES OF THE 30TH ANNUAL GENERAL MEETING
5-50 pm Monday 7 December 2004
Burns 7 LT, University of Otago

Present. Mick Roberts (Chair), Shaun Hendy, Tammy Smith, Rua Murray, Graeme Wake, Garry Tee, Peter Donelan, David Gauld, Mick Roberts, Robert McKibbin, Graeme Wake, Ivan Reilly, Bill Barton, Amal Amleh, Allison Heard, Igor Boglaev, Dennis McCaughan, John Curran, Peter Fenton, Peter Cameron (observer), Marston Conder, Kevin Broughan, Derek Holton, Gillian Thornley, ? Chacko, Gloria Olive, Dean Halford, Winston Sweatman, Carlo Laing, Michael Albert, Celine Cattoen, Stephen Joe, Stephen Goulter (observer).

1. Minutes of 29th Annual General Meeting.

   It was moved (Smith, Joe) that the minutes of the 29th Annual General Meeting of the NZMS be accepted. The motion was carried.

2. Matters arising from the minutes

   There were no matters arising.

3. Presidents report.

   (a) The report was delivered to the meeting and will appear in the NZMS newsletter.

   (b) It was moved (Albert, Smith) the report be accepted. The motion was carried.

4. Treasurer's report.

   (a) The Treasurer's report was delivered to the meeting and the financial statements were distributed to the members.

   (b) Tammy Smith summarised the report, noting that money received in subs was slightly down this year due to a drop in membership and late payment. Peter Donelan asked about how Council set its budget for student travel and research awards. Tammy Said that it was set in advance at $2500. In addition $1000 was budgeted for student assistance to attend MISG in 2005. Mick Roberts informed the meeting that the Council had decided to increase the amount of travel assistance that it awarded to individual students. Previously students were considered eligible for only one award of up to $500 during their time as student members. The Council would now award a total of up to $1000 over the duration of a students membership. For travel within New Zealand the maximum value of any one award would be $500 (for example this would allow the student to recieve two $500 grants for travel with NZ during their studies). For overseas travel the value of any one award would be for up to $1000.

   (c) It was moved (Roberts,Murray) that the statements be accepted. The motion was carried.

5. Membership Secretary's report and annual subscriptions.

   A report from the Membership Secretary, John Shanks, was tabled by Shaun Hendy. Mick Roberts noted that membership was slightly down and asked that members encourage students and new staff to join the Society. It was moved (Roberts, Hendy) that the report be accepted. The motion was carried.

   Mick Roberts informed the meeting that the Council had recommended that subs be fixed at current levels ($36 ordinary member, $18 reciprocal, $18 overseas student and $7.60 student). It was moved that subs be fixed at current levels (Roberts, Wake).

6. Nominations for four Council positions.

   (a) The terms of office of Shaun Hendy, Geoff Whittle and Rod Downey (outgoing VP) have ended. A new incoming VP and two other councillors were needed.

   (b) Nominations for Council received at closing date: Shaun Hendy (IRL), Winston Sweatman (Albany) and Gaven Martin (for incoming Vice-President, Albany).

   (c) Shaun Hendy and Winston Sweatman were unopposed and duly elected to the Council. Gaven Martin was also unopposed for the position of Vice-President and was duly elected.

7. Appointment of auditors.

   It was moved (Smith, Roberts) that the current auditors, McKenzie McPhail (4th floor, Farmers Mutual House, 68 The Square, Palmerston North), be reappointed for another year. The motion was carried.

8. New Zealand Journal of Mathematics.

   The report was circulated to the members. It was noted that Gaven Martin is the current editor. After some discussion, the meeting recommended that the NZJM committee give consideration into policies that encourage the submission of articles from New Zealand based mathematicians.

   It was moved (Roberts, Hendy) that the report be accepted. The motion was carried.

9. Forder Lecturer 2005.

   (a) Prof. Martin Bridson is the Forder Lecturer for 2003. Gaven Martin is coordinating his visit in April 2005.

   (b) Mick Roberts agreed to approach the British Council for support once a firm itinerary is in place for Prof Bridson's visit.

   (c) It was noted that each local department will be expected to provide some support for local expenses during Prof. Bridson's visit to their centre.

10. NZMS - American MS Joint Meeting 2007.

    Peter Donelan informed the meeting that he was organising a NZMS - American MS Joint Meeting to be held at Victoria in mid-December in 2007. Peter proposed that this meeting ought to incorporate the 2007 Maths Colloquium. It was moved (Donelan, Roberts) that the meeting endorse this proposal and recommend it to the Colloquium Business Meeting. The motion passed.

11. General Business.

    (a) Graeme Wake raised the possibility of replacing the NZMS Research Award with a medal. The meeting was largely in favour of this and recommended that the Council investigate this (and other options) and bring a proposal back to the AGM in 2005. Mick Roberts informed the meeting that nominations for the 2005 Research Award were now being called for.

    (b) It was moved (Roberts,Gauld) to formally thank Rod Downey, Geoff Whittle and Shaun Hendy for their contributions during their time on Council. The motion was carried.

    The meeting closed at 6-40pm.

MATHEMATICAL MINIATURE 26

Mathematicians and light bulbs

At the ANZIAM 2005 conference in Napier, a competition was held on the subject "How many mathematicians does it take to change a light bulb?". This Miniature contains the text of the winning entry with names changed to protect the identity of the mathematicians involved.

I feel I need to justify my lack of seriousness in writing about a subject to which Mathematics is not traditionally applied. More than 30 years ago, Martin Gardner announced a number of plausible but untrue results in his regular column in Scientific American, as what was later realised to be an April Fools joke. This will probably be the last Miniature I write for an April issue so, ever the rebel, this will be my last chance to say that if was good enough for Martin Gardner it is good enough for me. So I return to the light bulb question and I announce the answer and the steps which led to this conclusion.

The answer is |1| under certain conditions, otherwise it is .}

Before our group of mathematicians could tackle this question, we felt we needed some theory. Gav Mehrtens wanted some axioms and a definition of light bulb. Mast Candour thought that it wasn't an interesting question: better to ask whether the number being sought was actually integer, and if not whether it was rational, and if not whether it was algebraic.

Jam Snyder, showed his contempt for this line of discussion by asking, sarcastically, whether the number was even finite.

Axian Ford, thought we shouldn't hold back from using knowledge from Physics and that finiteness didn't matter too much because we could always extract the part of the result that was observable by applying renormalization, or some other such trick.

Jon Harpoon thought we were on quite the wrong track and that we needed a model. A considerable time was spent trying to agree on a model that everyone was happy with.

When we realised we weren't going to get any agreement on the model, we decided to follow a lead from Grim Hwayk and considered first the question:

"Could a single mathematicians change a light bulb?"

We all thought not, but how about a second attempt, in which the first mathematician is now joined by a second? If the answer had been yes, we still wouldn't have enough for a publishable paper so we decided to assume, for the moment, that the answer was "No", or possibly "Maybe".

Because we couldn't be really sure about this step, we decided to assign a probability to it. In the absence of any reliable evidence we set the probability that this second attempt would be successful as ½. There were now two cases known to the more general question:

"What is the probability that success will be achieved by n or fewer mathematicians?" Both known cases fitted into the formula

so this was assumed to be the answer for the general case.

We really wanted the value of p_n, the probability that exactly n mathematicians would be needed.

Davier Johannes offered to help with the calculations, which now involved probability and conditional probability. He came up with the formula

The next step was to find the expected value of n and he was also able to give this result

Jam Snyder now felt vindicated by his earlier scepticism, because this sum was infinite. Axian Ford also could now make a specific proposal, coming out of his experiemce as a Mathematical Physicist, and this was to subtract from an adjustment of  ln n, so that the limit was the Euler constant, given by

Mast Candour tried to determine whether this was rational or not but soon gave up. Gav Mehrtens, ever the logical conservative, now questioned the very first step. What if a single mathematician had been able to accomplish the task alone? We decided to offer an alternative answer to cover this case. However, there was a short debate as to why 1 can be assumed to be real and positive. To cover our backs we decided to write |1.

It was generally agreed that offering two answers, when we weren't really sure which was correct, was a mark of intellectual integrity. Furthermore, it offered us the opportunity of a second paper later, with a guaranteed citation of the first paper, and altogether a firm case for continued funding.

John Butcher, butcher@math.auckland.ac.nz

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