FracSym: automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented. © 2013 Elsevier B.V. All rights reserved.

The manifestation of varieties of blended learning pedagogy (BLP) : interplay between academic, institutional and global pedagogy

Despite the increased recognition of the potential use of online technologies to deliver flexible and student-centered learning environments in higher education, there are numerous critiques that its usage does not transform the daily practices of teaching and learning. This paper draws on some of the findings from three case studies that explored the manifestation of blended learning pedagogies (BLP). Six academics teaching at three different higher education contexts at two different countries, namely Australia and Malaysia were interviewed. The study aimed to interrogate the different manifestation of BLP at the different contexts of higher education, highlighting the complex interplay between the users (academics), technology and the specific socio-cultural contexts. Focusing on the academic identities that are shaped and reshaped within its socio-cultural context, this study demonstrated the complexity and fluidity of the manifestation of the different varieties of BLP. It contributes to further understanding the ways in which online technologies are used in teaching and learning within context of global knowledge economy that emphasizes flexibility and active co-production of knowledge.

A comparative study of some computer algebra packages which determine the lie point symmetries of differential equations

The study seeks to determine which of five computer algebra packages is best at finding the Lie point symmetries of systems of partial differential equations with minimal user intervention. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. A series of systems of partial differential equations are used in the study. The paper concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie point symmetries of systems of partial differential equations.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

FTIR and thermal analysis of cashmere and other animal fibres

In this paper, sereval varieties of animal fibres including cashmere and Australian fine Merino wool have been analysed by Fourier transform infrared microscope and differential scanning calorimeter. The results showed that both Chinese and Australian cashmere fibres started absorbing heat at a relatively higher temperature but were thermally degraded quicker than other animal fibres tested. However, the mass changes (within the temperature range of 200oC to 350oC) and associated onset temperatures varied among fibre varieties. From the attenuated total reflectance spectra, the Chinese cashmere was clearly different from Australian cashmere and wool in a peak near 1040 cm-1 wavelength for S-O stretching of cysteic acid residues. The Chinese cashmere presented a stronger absorption at 1019 cm-1 wavelength, while Australian cashmere and wool peaked at 1079 cm-1 wavelength and had a weaker absorption. Combined with thermal analysis, the normalised R-SO3 - content of cysteic acid residues to the amide II peak of the protein backbone may have potential use in identifying Australian fine Merino wool from Chinese cashmere.

A new broad composite model of regional economic development as a framework for research

The mechanism of regional economic development has been studied extensively by economists, geographers, town planners and other academics. The existing wide varieties of theories into regional economic development are insufficient on their own in explaining how a region can develop and prosper. Each theory has evaluated a few facets of regional economic development. Research from these different perspectives is narrow and prevents any cross-fertilization of research from all these diverse
theories.

Recognition of multiple factors affecting the development process has led the author to create a new broad composite model of regional economic development. The paper first sets out to describe and explain this broad composite model. Each of the components of this new model draws heavily upon seminal work in the field. This model proposes three rings. Each ring is at a different level of abstraction. The determinants of development described in each ring can influence each and every other determinant of development shown in the three ring structure. This model recognises that development in any centre, regional or urban, nascent or established is a composite end result of the complex interplay of all the determinants of development.

The paper then goes on to show how this model can provide a broad holistic approach to regional economic development that can assist researchers in their attempts to understand and link the various theories of regional economic development.

An epistemically distant God? a critique of John Hick's response to the problem of divine hiddenness

God is thought of as hidden in at least two ways. Firstly, God's reasons for permitting evil, particularly instances of horrendous evil, are often thought to be inscrutable or beyond our ken. Secondly, and perhaps more problematically, God's very existence and love or concern for us is often thought to be hidden from us (or, at least, from many of us on many occasions). But if we assume, as seems most plausible, that God's reasons for permitting evil will (in many, if not most, instances) be impossible for us to comprehend, would we not expect a loving God to at least make his existence or love sufficiently clear to us so that we would know that there is some good, albeit inscrutable, reason why we (or others) are permitted to suffer? In this paper I examine John Hick's influential response to this question, a response predicated on the notion of 'epistemic distance': God must remain epistemically distant and hence hidden from us so as to preserve our free will. Commentators of Hick's work, however, disagree as to whether the kind of free will that is thought to be made possible by epistemic distance is the freedom to believe that God exists, or the freedom to choose between good and evil, or the freedom to enter into a personal relationship with God. I argue that it is only the last of these three varieties of free will that Hick has in mind. But this kind of freedom, I go on to argue, does not necessitate an epistemically distant God, and so the problem of divine hiddenness remains unsolved.

Born of fire, possessed by darkness : mysticism and Australian poetry

This dissertation is structured around five Australian mystical poets: Ada Cambridge, John Shaw Neilson, Francis Webb, Judith Wright and Kevin Hart. It examines the varieties of Western Christian mysticism upon which these poets draw, or with which they exhibit affinities. A short prelude section to each chapter considers the thematic parallels of their contemporaries, while the final chapter critically investigates constructions of Indigeneity in Australian mystical poetry and the renegotiated mystical poetics of Indigenous poets and theologians. The central argument of this dissertation is that an understanding of Western Christian mysticism is essential to the study of Australian poetry. There are three sub-arguments: firstly, that Australian literary criticism regarding the mystical largely avoids the concept of mysticism as a shifting notion both historically and in the present; secondly, that what passes for mysticism is recurringly subject to poorly defined constructions of mysticism as well as individual poets’ use of the mystical for personal, creative or ideological purposes; thirdly, that in avoiding the concept of a shifting notion critics have ignored the increasing contribution of Australian poets to national and international discourses of mysticism.

Thermodynamics and kinetics of the formation of Al2 O3/ MgAl2O4/MgO in Al-Silica metal matrix composite

The formation of Al₂O₃, MgAl₂O₄, and MgO has been widely studied in different Al base metal matrix composites, but the studies on thermodynamic aspects of the Al₂O₃/ MgAl₂O₄/MgO phase equilibria have been limited to few systems such as Al/Al₂O₃ and Al/SiC. The present study analyzes the Al₂O₃/MgAl₂O₄ and MgAl₂O₄/MgO equilibria with respect to the temperature and the Mg content in Al/SiO2 system using an extended Miedema model. There is a linear and parabolic variation in Mg with respect to the temperature for MgAl₂O₄/MgO and Al₂O₃/MgAl₂O₄ equilibria, respectively, and the influence of Si and Cu in the two equilibria is not appreciable. The experimental verification has been limited to MgAl₂O₄/MgO equilibria due to the high Mg content (≥0.5 wt pct) required for composite processing. The study has been carried out on two varieties of Al/SiO₂ composites, i.e., Al/Silica gel and Al/Micro silica processed by liquid metallurgy route (stir casting route). MgO is found to be more stable compared to MgAl₂O₄ at Mg levels ≥5 and 1 wt pct in Al/Silica gel and Al/Micro silica composites, respectively, at 1073 K. MgO is also found to be more stable at lower Mg content (3 wt pct) in Al/Silica gel composite with decreasing particle size of silica gel from 180 micron to submicron and nanolevels. The MgO to MgAl₂O₄ transformation has taken place through a series of transition phases influenced by the different thermodynamic and kinetic parameters such as holding temperature, Mg concentration in the alloy, holding time, and silica particle size.

Transcriptional regulation of the yghJ-pppA-yghG-gspCDEFGHIJKLM cluster, encoding the type II secretion pathway in Enterotoxigenic Escherichia coli

The gene cluster gspCDEFGHIJKLM codes for various structural components of the type II secretion pathway which is responsible for the secretion of heat-labile enterotoxin by enterotoxigenic Escherichia coli (ETEC). In this work, we used a variety of molecular approaches to elucidate the transcriptional organization of the ETEC type II secretion system and to unravel the mechanisms by which the expression of these genes is controlled. We showed that the gspCDEFGHIJKLM cluster and three other upstream genes, yghJ, pppA, and yghG, are cotranscribed and that a promoter located in the upstream region of yghJ plays a major role in the expression of this 14-gene transcriptional unit. Transcription of the yghJ promoter was repressed 168-fold upon a temperature downshift from 37°C to 22°C. This temperature-induced repression was mediated by the global regulatory proteins H-NS and StpA. Deletion mutagenesis showed that the promoter region encompassing positions −321 to +301 relative to the start site of transcription of yghJ was required for full repression. The yghJ promoter region is predicted to be highly curved and bound H-NS or StpA directly. The binding of H-NS or StpA blocked transcription initiation by inhibiting promoter open complex formation. Unraveling the mechanisms of regulation of type II secretion by ETEC enhances our understanding of the pathogenesis of ETEC and other pathogenic varieties of E. coli.

Seven heavens? The character and importance of afterlife belief among contemporary Australians

This article draws on in-depth qualitative interviews with 52 people to examine the meaning and character of afterlife belief among contemporary Australians. It explores the varieties of afterlife belief and considers the impact such beliefs have, particularly in relation to death and dying. The analysis reveals that afterlife belief is varied, individualistic and mainly arrived at with little to no reference to orthodox religious teaching. People variously believe in heaven, reincarnation, life on another planet or something more abstract. Those who follow faithfully a religious tradition are largely ignorant of detailed theological doctrines about life after death and like other kinds of believers, exercise their own authority and judgment over matters of belief.

Analytical assessment of optimum magnet pole-arc for PMSM under influence of different magnetization patterns

Permanent magnet synchronous machines (PMSMs) are popular in both industrial and domestic applications because of its high efficiency, power density, and reliability as compared with the conventional types of electrical machines. Generally, the analytical models and their field solutions are preferable to provide an accurate insight of the PMSM performances, instead of using the finite element models, because the former takes a considerably shorter computational time. PMSM design could have different properties of either slotted or slotless, or varieties of magnet placement on the rotor. By focusing on semi-closed surface-mounted PMSMs, the 2D analytical subdomain model in [1] demonstrates an accurate prediction of the magnetic fields that can facilitate the evaluation of the global quantities of PMSMs, such as cogging torque (Tcog), back-EMF, and total harmonic distortion (THDv). Previously, researchers investigated the influences of the machine performance by a single factor, e.g., the variation of Tcog during changes of magnet pole-arc (αP) [2, 3], or slot-opening [2, 3]. These investigations normally considered two types of magnetization patterns, i.e., parallel (PaM) and radial magnetization (RM). Therefore, the motivation of our work hinges on predicting the optimum value of αP in designing a surface-mounted PMSM under influence of four different magnetization patterns, using the analytical subdomain model.