Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Perpetuating Racism: Legal Education, Race and Social Justice

By presenting the results of a content analysis of Australian undergraduate legal education, this paper examines the extent to which issues of race, ethnicity, discrimination, and multiculturalism feature within this component of the moral, ethical, and professional development of legal professionals. It will demonstrate that instead of encouraging a deep, critical and contextual understanding of such issues, legal education provides a relatively superficial one, which has important implications for the role that legal professionals play in overcoming injustices such as institutional racism, and the kinds of social reform that they are likely to undertake.

The epistemology that maintains white race privilege, power and control of Indigenous Studies and Indigenous peoples' participation in universities

This paper represents my attempt to turn the gaze and demonstrate how Indigenous Studies is controlled in some Australian universities in ways that witness Indigenous peoples being further marginalised, denigrated and exploited. I have endeavoured to do this through sharing an experience as a case study. I have opted to write about it as a way of exposing the problematic nature of racism, systemic marginalisation, white race privilege and radicalised subjectivity played out within an Australian higher education institution and because I am dissatisfied with the on-going status quo. In bringing forth analysis to this case study, I reveal the relationships between oppression, white race privilege and institutional privilege and the epistemology that maintains them. In moving from the position of being silent on this experience to speaking about it, I am able to move from the position of object to subject and to gain a form of liberated voice (hooks 1989:9). Furthermore, I am hopeful that it will encourage others to examine their own practices within universities and to challenge the domination that continues to subjugate Indigenous peoples.

Race and equity in higher education : A harder path for Indigenous academics

Our experiences as Indigenous academics within universities often reflects the experiences we have as Indigenous people in broader society, yet I am still surprised and angered when it is others working in higher education who espouse notions of justice and equity with whom we experience tension and conflict in asserting our rights, values and cultural values. At times it is a constant struggle even when universities have Reconciliation Statements as most of them do now, Indigenous recruitment or employment strategies and university wide anti-racism and anti-discrimination policies and procedures.

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.