Symmetric and Asymmetric Gaps in Some Fields of Formal Power Series

2000 Mathematics Subject Classification: 03E04, 12J15, 12J25.

Discourse practice gaps in work life balance : comparative case studies in the Australian construction industry

Perspectives on work-life balance (WLB) reflected in political, media and organisational discourse, would maintain that WLB is on the agenda because of broad social, economic and political factors (Fleetwood 2007). In contrast, critical scholarship which examines work-life balance (WLB) and its associated practices maintains that workplace flexibility is more than a quasi-functionalist response to contemporary problems faced by individuals, families or organisations. For example, the literature identifies where flexible work arrangements have not lived up to expectations of a panacea for work-home conflicts, being characterised as much by employer-driven working conditions that disadvantage workers and constrain balance, as they are by employee friendly practices that enable it (Charlesworth 1997). Further, even where generous organisational work-life balance policies exist, under-utilisation is an issue (Schaefer et al, 2007). Compounding these issues is that many employees perceive their paid work as becoming more intense, pressured and demanding (Townsend et al 2003).

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Design of Mono-symmetric LiteSteel Beam Floor Joists with Web Openings

The new cold-formed LiteSteel beam (LSB) sections have found increasing popularity in residential, industrial and commercial buildings due to their lightweight and cost-effectiveness. They have the beneficial characteristics of including torsionally rigid rectangular flanges combined with economical fabrication processes. Currently there is significant interest in using LSB sections as flexural members in floor joist systems. When used as floor joists, the LSB sections require holes in the web to provide access for inspection and various services. But there are no design methods that provide accurate predictions of the moment capacities of LSBs with web holes. In this study, the buckling and ultimate strength behaviour of LSB flexural members with web holes was investigated in detail by using a detailed parametric study based on finite element analyses with an aim to develop appropriate design rules and recommendations for the safe design of LSB floor joists. Moment capacity curves were obtained using finite element analyses including all the significant behavioural effects affecting their ultimate member capacity. The parametric study produced the required moment capacity curves of LSB section with a range of web hole combinations and spans. A suitable design method for predicting the ultimate moment capacity of LSB with web holes was finally developed. This paper presents the details of this investigation and the results

Community food security gaps in surveillance and monitoring

This paper describes the gaps in monitoring and surveillance identified while conducting Community Food Security assessments in three geographical areas located in south-east Queensland, Australia

Bahrain skills gaps study : tourism, construction, and education skills plans

The tourism, construction, and education plans and skills strategies (embedded in project reports) were developed as part of a nation-wide comprehensive research project covering current, emerging and future skills deficiencies and requirements in Bahrain’s labour market. The research covered the majority of economic sectors and activities in the Kingdom and will serve as a basis for formulating industry and occupational outlooks as well as career guidance and awareness activities by academic and training institutions across Bahrain. It will provides foundation work for industry skills councils in order to conduct and achieve a uniform system of occupational standards across industries, occupations and job levels.

Single-layer decoupling networks for large circulant symmetric arrays

In this paper, the authors propose a new structure for the decoupling of circulant symmetric arrays of more than four elements. In this case, network element values are again obtained through a process of repeated eigenmode decoupling, here by solving sets of nonlinear equations. However, the resulting circuit is much simpler and can be implemented on a single layer. The corresponding circuit topology for the 6-element array is displayed in figure diagrams. The procedure will be illustrated by considering different examples.

Attitudes towards inclusion : gaps between belief and practice

General education teachers in the Republic of Korea were investigated regarding their participation in programs to include students with disabilities in general education settings. Previous studies have shown that even general education teachers with positive attitudes towards inclusion are reluctant in practice to have students with disabilities in their classrooms. This study examines 33 Korean general education teachers from three primary schools in Seoul regarding their attitudes towards, and willingness to accommodate, the needs of a student with a disability. The results show that 41.37% of general education teachers had positive attitudes towards inclusion programs, while 55.16% were unwilling to actually participate. Quantitative data obtained through a questionnaire was supplemented by qualitative data obtained through interviews. The interviews focused on the positive and negative effects of inclusion, as well as problems in implementing inclusive education programs. The findings will be discussed in the light of previous international research and will highlight links between the age and teaching experience of general education teachers and their negative attitudes towards inclusion.