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This thesis is about data mining in automotive warranty analysis, with an emphasis on modeling the mean cumulative warranty cost or number of claims (per vehicle). In our study, we deal with a type of truncation that is typical for automotive warranty data, where the warranty coverage and the resulting warranty data are limited by age and mileage. Age, as a function of time, is known for all...

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Reduced-order models for micro-electromechanical structures possess several attractive features when compared to computational approaches using e.g. finite element packages. However, also within the business of reduced-order modeling there are different approaches which yield different results. The efficiency of such approaches has to be judged according to, first, the purposes and aims of the... [Journal Article]

The time varying flow in which fluid is withdrawn from a reservoir through a point sink of variable strength beneath a free surface is considered. Asymptotic techniques are used to derive an approximate solution to the flow that is valid at intermediate times, giving a simple rational approximation to track changes in the free surface for any temporal variations in the sink strength.... [Journal Article]

The unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has...This article has been published in the journal: ANZIAM Journal. © 2005 Australian Mathematical Society. [Journal Article]

Withdrawal of a fluid through an isolated line sink (for planar flow) or a point sink (for axi-symmetric flow in three dimensions) is considered. A linearized solution is presented in both cases, under the assumption that the sink strength is small and the sink is turned on gradually. The results show that the behaviour for small times is as if an image source were present above the surface....This is an author’s version of an article published in Journal of Engineering Mathematics. © 2008 Springer. The original publication is available at www.springerlink.com. [Journal Article]

An EQ-monoid A is a monoid with distinguished subsemilattice L with 1 2 L and such that any a, b 2 A have a largest right equalizer in L. The class of all such monoids equipped with a binary operation that identifies this largest right equalizer is a variety. Examples include Heyting algebras, Cartesian products of monoids with zero, as well as monoids of relations and partial maps on sets. The...This is an author's final draft verison of an article published in the journal: Acta Sci. Math. (Szeged). © ACTA Scientiarum Mathematicarum [Journal Article]

This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the...This is an author’s version of an article published in Journal of Algebra. © 2003 Elsevier. [Journal Article]

The stochastic model of solute transport describes the motion of fluid elements in a porous medium as stochastic variation of the fluid velocity, produced by pore wall impacts. This gives a stochastic differential equation for fluid displacements, and solute transport is obtained as the cumulative effect over all realisations of the stochastic path. It is shown that applying Dynkin’s equation... [Thesis or Dissertation]

The sap beetle genus Carpophilus Stephens (Coleoptera: Nitidulidae) is a large genus consisting of over 200 species and are found worldwide. Several species are important pests of crops and stored products, and are frequently intercepted as part of biosecurity operations. The genus is poorly known taxonomically, and there are several species groups that are challenging to identify by... [Thesis or Dissertation]

A metapopulation is defined as a set of potential local populations among which dispersal may occur. Metapopulation theory has grown rapidly in recent years, but much has focused on the mathematical properties of metapopulations rather than their relevance to real systems. Indeed, barring some notable exceptions, metapopulation theory remains largely untested in the field. This thesis... [Thesis or Dissertation]

The back circulant latin square of order n is the latin square based on the addition table for the integers modulo n. A critical set is a partial latin square that has a unique completion to a latin square, and is minimal with respect to this property. In this note we show that the size of a critical set in the back circulant latin square of order n is at least n ⁴/³/2 - n - n²/³/2 +...This article has been published in the Australasian Journal of Combinatorics. Used with permission. [Journal Article]

This thesis presents the findings of a project that explored the ways in which primary school children developed understandings about mathematics, mathematical 'learning' and 'knowing' and themselves as learners of mathematics. The research aimed to describe the children's mathematical learning environments, to explore the ways in which children made meaning about...

The earlier constitutive model of Fang & Owens (Biorheology, vol. 43, 2006, p. 637) and Owens (J. Non-Newtonian Fluid Mech. vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the... [Journal Article]

This thesis investigates structures that are presentable by finite automata working synchronously on tuples of finite words. The emphasis is on understanding the expressiveness and limitations of automata in this setting. In particular, the thesis studies the classification of classes of automatic structures, the complexity of the isomorphism problem, and the relationship between definability... [Thesis or Dissertation]

The structure completion problem in fiber diffraction is addressed from a Bayesian perspective. The experimental data are sums of the squares of the amplitudes of particular sets of Fourier coefficients of the electron density. In addition, a part of the electron density is known. The image reconstruction problem is to estimate the missing part of the electron density. A Bayesian approach is... [Conference Item]

The restoration of an incomplete image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation problem. This problem is motivated by the structure completion problem in x-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained.... [Conference Item]

In this paper we consider the capacity of the cognitive radio (CR) channel in a fading environment under a “low interference regime”. This capacity depends critically on a power loss parameter, alpha, which governs how much transmit power the CR dedicates to relaying the primary message. We derive a simple, accurate approximation to alpha which gives considerable insight into system... [Conference Paper]

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2 we investigate a concept of invertibility and the invertibility of the composition of random functions. In Section 3 we resolve some questions concerning the number of samples required to ensure the accuracy of parametric maximum likelihood estimation (MLE). A... [Journal Article]

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2 we investigate a concept of invertibility and the invertibility of the composition of random functions. In Section 3 we resolve some questions concerning the number of samples required to ensure the accuracy of parametric maximum likelihood estimation (MLE). A... [Journal Article]

Agathe Keller's latest publication, Expounding the Mathematical Seed, is an ambitious two- volume work which provides a translation and detailed commentary on a mathematical text composed in the 7th century by the Indian mathematician Bhāskara I, the content of which is itself a commentary that elucidates and clarifies the mathematical section of a 5th-century work by Indian... [Journal Article]

This thesis concerns the study of geometric numerical integrators and how they preserve phase space structures of Hamiltonian ordinary differential equations. We examine the invariant sets of differential equations and investigate which numerical integrators preserve these sets, and under what conditions. We prove that when periodic orbits of Hamiltonian differential equations are discretized... [Thesis or Dissertation]

The current of development in 20th century logic bypassed Peirce’s existential graphs, but recently much good work has been done by formal logicians excavating the graphs from Peirce’s manuscripts, regularizing them and demonstrating the soundness and completeness of the alpha and beta systems (e.g. Roberts 1973, Hammer 1998, Shin 2002). However, given that Peirce himself considered the...© Copyright 2009 C. Legg [Conference Item]

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dual-hop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios... [Journal Article]