Science, Technology and Engineering

Department of Mathematics and Statistics, Bendigo

Mathematics Seminars 2003

Below is a list of seminars presented during 2003 in the Seminar Program of the then Department of Mathematics at La Trobe University's campus in Bendigo, Victoria.

Baorui Song

Topics in Rational Interpolation, by Associate Professor Baorui Song (Shanghai Jiao Tong University, China)

Scheduled: 12 noon, Friday 24 October 2003, in Room B2.15

Abstract: In this seminar, I will talk about the definition and basic properties, numerical algorithms and the convergence problems of rational interpolation. Some generalizations and applications of rational interpolation are briefly mentioned.

Daniel Alpay

Reproducing Kernel Hilbert Spaces and the Theory of Linear Systems, by Professor Daniel Alpay (Ben-Gurion University of the Negev, Israel)

Scheduled: 12 noon, Friday 10 October 2003, in Room B2.15

Abstract: In this seminar, I will review the relationships between the theory of linear systems and reproducing kernels. Then we can discuss a related inverse scattering problem. I will also explain how the reproducing kernel approach allows one to tackle more general situations such as non-stationary systems.

Ashley Dyson

Quadratic Equations, by Ashley Dyson (Girton Grammar School, Bendigo)

Scheduled: 12 noon, Friday 15 August 2003, in Room B2.15

Abstract: Ashley has been a work experience student in the Department of Mathematics for the past fortnight. During this time, he has been investigating quadratic equations, including their history, applications, and connections with other areas of mathematics. In this seminar he will present some of his findings.

Hendrik Lenstra

Coin-flipping by Telephone, by Professor Hendrik Lenstra (Universiteit Leiden, The Netherlands, and University of California, Berkeley) – Professor Lenstra is the 2003 Mahler Lecturer of The Australian Mathematical Society

Scheduled: 12 noon, Monday 30 June 2003, in Room B2.15

Abstract: This conveys the essential point of applying number theory to cryptography to a perfectly general mathematical audience. True math, but elementary and expository.

Hendrik Lenstra, who holds appointments at the University of California at Berkeley, and the University of Leiden, the Netherlands, is widely regarded as the world's premier algorithmic number theorist. He is responsible for two of the most famous algorithms in 20th century number theory: the LLL lattice basis reduction algorithm (along with his brother, Arjen Lenstra, and Laszlo Lovasz) and the elliptic curve factoring algorithm.

Jason Giri

The Convoluted World of Optimization, by Jason Giri (University of Ballarat)

Scheduled: 11 am, Friday 27 June 2003, in Room B1.30

Abstract: The field of constrained mathematical optimization is one of the most practically applicable areas of mathematics. It has been used successfully to solve problems in a wide range of areas including economics, communications and computational chemistry. A key technique in the solution of many of these types of problems is the method of Lagrange multipliers. This elegant and powerful method has been used since the eighteenth century, but an important generalization which was made around the middle of the twentieth century has significantly extended the utility of the technique. This seminar will discuss the details of these traditional Lagrangian methods and introduce some recent results which generalize the technique even further.

Whole of Hospital Simulation, by Philip Cooper and Christopher Bain (Clinical Epidemiology and Health Service Evaluation Unit, Melbourne Health, and Iridium Consulting, Royal Melbourne Hospital) [Co-author: Don Campbell]

Scheduled: 12 noon, Friday 30 May 2003, in Room B2.30

Abstract: Managing a modern large hospital, which provides a complex range of services, involves optimising patient access, throughput and resource use, and constitutes an enormous challenge. This must be done in the face of increasing demand for emergency and surgical elective patient access and reduced bed availability. In addition, managers face difficulties in attracting and retaining sufficient nurses and escalating health service costs. Inevitably undesirable events occur, which include bed block, ambulance bypass, long waits for elective surgery and elective theatre list cancellations.

There are significant difficulties in planning and instituting changes in a hospital because of flow-on effects that are difficult to predict. In addition, the internal allocation of resources within a hospital is complex to the point where it exceeds human ability to understand the system-wide implications of individual resourcing decisions. In the absence of appropriate data to guide management decision making the "loudest" opinion often prevails when resource allocation decisions are made. The management policies that will optimise the numbers of patients treated and still maintain an acceptable quality of service will demand new approaches to service provision and patient management, based on an understanding of factors affecting optimal movement of patients through a complex dynamic system.

Around the world, potential solutions to the current problems are increasingly drawing on an understanding of hospital systems as dynamic, complex entities. One means of exploring these issues is through simulation modelling. There have been various attempts at modelling some aspects of health care both at institutional and system levels. This talk will outline the development and use of a discrete event simulator at Melbourne Health. It is believed that this is a world first since it models the whole of a hospital, in a significant amount of detail, and can be configured to represent any hospital.

Terry Mills

Reproducing Kernel Hilbert Spaces and Probability, by Professor Terry Mills (La Trobe University, Bendigo)

Scheduled: 12 noon, Friday 28 March 2003, in Room B2.05

Abstract: The theory of reproducing kernel Hilbert spaces was established in a seminal paper by Nachman Aronszajn in 1950. Since then, these spaces have proved to be useful in many different branches of mathematics. In this seminar, I will explain how they arise in probability theory.

Rainer Loewen

Surfaces Supporting Line Geometries, by Professor Rainer Loewen (Technische Universität Braunschweig, Germany)

Scheduled: 12 noon, Friday 21 February 2003, in Room B2.15

Abstract: We suppose we are given a connected surface endowed with a system of curves (the "lines") such that any two distinct points are joined by a unique line, which depends continuously on the pair of points. Also we assume that intersection points exist for an open set of line pairs and again depend continuously on the line pair. We shall give some examples and explain the first steps in the theory of such surface geometries, e.g., why a compact line has to intersect every other line. We outline a proof of the result that the point surface can only be a disk, a Moebius strip, or a sphere with one cross cap (the real projective plane).