Mathematics seminars 2004
Below is a list of seminars presented during 2004 in the Seminar Program of the then Department of Mathematics at La Trobe University's campus in Bendigo, Victoria.
Bob Anderssen
Playing Mathematics with the Stuart Piano, by Dr Bob Anderssen (CSIRO Mathematical and Information Sciences, Canberra)
Scheduled: 12 noon, Friday 12 November 2004, in Room B2.30
Abstract: Prior to 1800, the vibrating length of a string on a piano copied the arrangement on the harpsicord. One end of the vibrating length was determined by an 11 degree bend through a horizontal degree zig-zag clamp attached to the bridge on the soundboard. The other end was determined by an 11 degree bend around a fixed pin located between the de Capo bar and the tuning pin. This primitive arrangement was effective for the relatively gentle plucking motion of the harpsicord, but was unable to retain the strings in the proper position under the more powerful blows of the piano's hammer action. During the first decade of the 1800's, the famous piano and harp maker Erard of Paris, invented a brass stud (agraffe (staple)) with holes drilled through it to accommodate the triple, double or single strings of the tricords, bicords and the monocords. A thread on the base of the agraffe allowed it to be rigidly attached to the piano frame. By firmly resisting the upward motion of the hammer blow, the agraffe was an immediate success and central to the subsequent success of the piano as a musical instrument. It allowed the vibrations of the speaking length to radiate a clearer tone and a fuller sound with reduced impact noise. During the 19th and early 20th centuries, various attempts were made to duplicate this more rigid clamping system on the bridge. Expensive, but cumbersome, vertical zig-zag systems were found to give superior results. However, the cheaper and simpler historic system retained its dominance. The Australian piano maker, Wayne Stuart, commenced his search for a less expensive and more functional solution in the mid-1970's which resulted in his vertical zig-zag innovation of the late 1980's. (This is a excellent example of how long the innovative step that solves the specifics of a problem can lag behind the good idea on which it is based.) The new (grand) pianos that utilize the Stuart clamping are manufactured by Piano Australia Pty Ltd in Newcastle with the brand name Stuart & Sons. These pianos, as a direct consequence of the clamping, have an extradordinary clarity of tone, increased sustain and lower inharmonicity, when compared with the traditional grand pianos. Interestingly, for a rigorous explanation of the difference between horizontal and vertical zig-zag clamping, one must turn to an analysis of the non-linear vibrating string equation.
Peter Sullivan
Students' perceptions of factors contributing to successful participation in mathematics, by Professor Peter Sullivan, Dr Steve Tobias and Assoc Prof Vaughan Prain (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 22 October 2004, in Room B2.30
Abstract: This seminar is a report of a project investigating students' perceptions of the extent to which their own efforts influence their achievement at mathematics and their life opportunities. We conducted two hour interviews with over 50 students, as well as collecting other data. Even students who were confident, successful and persistent exhibited short term goals. It also seems that classroom culture may be an important determinant of under participation in schooling.
Vincent Rouillard
The use of intrinsic mode functions to characterise shocks and vibrations in the distribution environment, by Vincent Rouillard (School of Architectural, Civil and Mechanical Engineering, Victoria University)
Scheduled: 12 noon, Friday 15 October 2004, in Room B2.30
Abstract: This paper describes an innovative approach, based on the Instrinsic Mode Functions (IMF), to characterise the nature of mechanical shocks and vibrations encountered in transport vehicles. The paper highlights the importance of understanding the nature of transport shock and vibrations and shows that their accurate characterisation is essential for the optimisation of protective packaging. Although there have been numerous studies aimed at characterising random vibrations during transport, the majority of those have been limited to applying relatively conventional signal analysis techniques such as the average Power Spectral Density (PSD) for vibration data and probability distribution estimates for shock data. This paper investigates the benefits offered by the recently introduced Hilbert-Huang Transform when characterising non-stationary random vibrations in comparison with more traditional Fourier analysis based techniques. The paper describes the operation of the Hilbert-Huang Transform which was developed to assist in the analysis of non-Gaussian and non-stationary random data. The Hilbert-Huang transform is based on the Empirical Mode Decomposition technique used to produce a finite number of Intrinsic Mode Functions (IMF), which, as a set, provides a complete description of the process. It is shown how these Intrinsic Mode Functions are well suited to the application of the Hilbert transform to determine the magnitude and instantaneous frequency of each Intrinsic Mode Function. The technique is applied to various records of random vibration data collected from transport vehicles in order to illustrate the benefits of the method in characterising the nature of non-stationarities present in transport vibrations.
Terry Mills
How to draw a histogram, by Professor Terry Mills (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 8 October 2004, in Room B2.30
Abstract: The histogram is a simple graph that describes a statistical distribution, such as the age distribution of a population. The histogram conveys information readily, it is easy to read, and is one of the first ideas encountered in high school statistics. However, authors of elementary statistics books tend to skate over details about the question "How do you draw a histogram?". As is often the case, asking a simple question about a basic idea is like opening Pandora's box. In this seminar, we will see what is in the box!
Mirka Miller
New Results in the Topology of Interconnection Networks as Modelled by Graphs, by Mirka Miller (Professor of Computer Science, University of Ballarat)
Scheduled: 12 noon, Friday 24 September 2004, in Room B2.30
Abstract: Networks govern all aspects of society, including transportation, communication networks, computer networks, social networks, and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs.
Such a network (graph) consists of a number of nodes and some connections (either unidirectional or bidirectional) between nodes. An interesting measure related to the performance of a network is its diameter which is the maximum distance between any two nodes of the network. Given a limited number of connections (degree) available at any node and given the desired value of the network's diameter, the following problem has been of interest:
Degree/diameter problem: Given maximum degree and diameter, what is the largest possible number of nodes in a network?
In this talk we give an overview of the degree/diameter problem and we present some recent new results.
Angela Pezic
Modelling Internal Migration in Bendigo and Warrnambool, by Ms Angela Pezic (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 9 September 2004, in Room B1.30
Abstract: In many Australian regional centres, internal migration is the principal influence on population growth. In this paper we explore some of the determinants of internal migration using the most recent census data with attention restricted to the regional centres of Bendigo and Warrnambool in Victoria. To facilitate this we use geographically weighted regression (GWR) to estimate the effect of factors such as age, unemployment, housing affordability and other socio-economic variables on the internal migration measure. A major advantage of GWR over the traditional (global) regression methods is that it provides spatially varying estimates of model parameters. The resulting parameter spaces can then be thematically mapped thus providing a useful graphical representation of spatially varying relationships. For example, a somewhat surprising result of our work is found in the effect of relative house price on in-migration to Bendigo. The thematic map of the house price parameter space shows that an increase in house prices (relative to Bendigo) in some northern and central Victorian areas has a positive effect on the in-migration measure. However for other areas and in particular, metropolitan areas, the effect is much smaller. This observation seems to run counter to the "conventional wisdom" of some in local government and the regional media who predict an influx of residents who, upon selling their metropolitan home, settle in regional centres using the residual of their asset to fund retirement.
Pietro Cerone
On bounds for the Euler zeta function, by Assoc Prof Pietro Cerone (School of Computer Science and Mathematics, Victoria University)
Scheduled: 12 noon, Friday 27 August 2004, in Room B2.09
Abstract: Accurate bounds are obtained for estimating the Euler zeta function at odd integer values in terms of known zeta function values at even integers. This is accomplished from an identity involving the zeta function at a distance of one apart. Upper bounds for odd Euler zeta functions are also obtained using a technique involving the Chebyshev functional.
Theo Tuwankotta
Coupled oscillators with widely separated frequencies and energy-preserving nonlinearity, by Dr J. M. Tuwankotta (A.R.C. Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics, La Trobe Unversity, and Mathematics Department, Bandung Institute of Technology, Indonesia)
Scheduled: 1 pm, Friday 13 August 2004, in Room B2.09
Abstract: We present an analysis of a system of coupled oscillators suggested by atmospheric dynamics. We assume two conditions to be satisfied by the system. The first is that the frequencies of the characteristic oscillations are widely separated. The second is that the nonlinear part of the vector field preserves the energy which is represented by the distance to the origin. Using normal form theory, we have contructed an approximation for the system. Due to the nature of the problem, the normal form can be seen as an sphere-preserving three-dimensional system which is linearly perturbed. Finally, we present some numerical bifurcation analysis of the three dimensional system.
John Schutz
Non-Euclidean geometry and space-time, by Assoc Prof John Schutz (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 5 August 2004, in Room B2.30
Abstract: During my recent Outside Studies Program which involved visits to the Australian Mathematical Sciences Institute, the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) and the Technical University of Braunschweig, I investigated non-Euclidean geometry and space-time structure. In one completed article, ellipsoids are characterised in projective geometry by the property of isotropy. This result is then used in a second article to present a particularly simple system of axioms for hyperbolic geometry. The investigations into space-time structure are continuing. In the seminar, aspects of these geometries and results will be presented so as to be accessible to a general audience.
Graeme Byrne
Internal Migration and Regional Population Growth, by Dr Graeme Byrne and Ms Angela Pezic (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 10 June 2004, in the Lecture Theatre, Ironbark Centre [This seminar is also part of the Seminar Program of the School of Business and Technology.]
Abstract: In regional centres such as Bendigo the main determinant of population growth is internal migration. Unlike natural growth, internal migrants present local government with special problems due to their demographic characteristics. In this talk we examine the most recent census data and report on some of these characteristics as well as discuss the likely implications for Bendigo and its satellite communities. We also explore a new method of estimating the effect of factors such as age, unemployment and housing affordability on internal migration.
Dr Graeme Byrne is a Senior Lecturer and Ms Angela Pezic is a Doctoral student working on a demographic project whose methods and conclusions will have interesting implications for town planning and the provision of urban and social infrastructure.
Terry Mills
A Mathematician Goes to Hospital, by Professor Terry Mills (Department of Mathematics, Faculty for Regional Development, La Trobe University, and Collaborative Health Education and Research Centre, Bendigo Health Care Group)
Scheduled: 12 noon, Thursday 25 March 2004, in Room B2.28-29 [This seminar is also part of the Seminar Program of the School of Business and Technology.]
Abstract: La Trobe University, Bendigo is a key component in the University's effort to realise its mission in regional engagement. In recent years, our Faculty has developed a strong focus on encouraging interaction between La Trobe University and regional Victoria. While it is easy to imagine how academics in some disciplines could contribute to community-university interaction, it is more difficult to imagine how those in other disciplines (such as mathematics) can be so involved. As a mathematician in the Faculty for Regional Development, I have chosen to make a contribution to health care in the region. Over the last five years I have been able to blend my skills as an academic mathematician with the needs of the Bendigo Health Care Group (BHCG). In this presentation I will describe the projects at BHCG in which I am involved, and their impact on my work in undergraduate teaching, course development, and research. Also, I will mention some challenges associated with community engagement and the key factors that have led to my experience being both exciting and rewarding.