GHP: a maple package for performing calculations in the Geroch-Held-Penrose formalism

We present a new symbolic algebra package, written for Maple, for performing computations in the Geroch-Held-Penrose formalism. We demonstrate the essential features and capabilities of our package by investigating Petrov-D vacuum solutions of Einstein's field equations.

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.

Algebraically special coplanar shear-free perfect fluids in general relativity

We investigate all algebraically special, not conformally flat, shear-free, isentropic (p(w), w + p ≠ 0), perfect fluid solutions of Einstein's field equations. We show, using the GHP formalism, that if the repeated principle null direction of the Weyl tensor is coplanar with the fluid's 4-velocity and vorticity vector (assumed nonzero), then the fluid's expansion must vanish.

Similarity solutions of partial differential equations using DESOLV

We present and describe new reduction routines included in DESOLV which, in many cases, may allow the complete automation of the determination of similarity solutions of partial differential equations.

Fractional polynomials and model selection in generalized estimating equations analysis, with an application to a longitudinal epidemiologic study in Australia

In epidemiologic studies, researchers often need to establish a nonlinear exposure-response relation between a continuous risk factor and a health outcome. Furthermore, periodic interviews are often conducted to take repeated measurements from an individual. The authors proposed to use fractional polynomial models to jointly analyze the effects of 2 continuous risk factors on a health outcome. This method was applied to an analysis of the effects of age and cumulative fluoride exposure on forced vital capacity in a longitudinal study of lung function carried out among aluminum workers in Australia (1995-2003). Generalized estimating equations and the quasi-likelihood under the independence model criterion were used. The authors found that the second-degree fractional polynomial models for age and fluoride fitted the data best. The best model for age was robust across different models for fluoride, and the best model for fluoride was also robust. No evidence was found to suggest that the effects of smoking and cumulative fluoride exposure on change in forced vital capacity over time were significant. The trend 1 model, which included the unexposed persons in the analysis of trend in forced vital capacity over tertiles of fluoride exposure, did not fit the data well, and caution should be exercised when this method is used.

Application of the Hottel-Whillier equations to the analysis of a building integrated photovoltaic/thermal solar collector

The idea of combining photovoltaic and solar thermal collectors (PVT collectors) to provide electrical and heat energy is not new, however it is an area that has received only limited attention. With concern growing over energy sources and their usage, PVTs have become an area receiving more attention. Although PVTs are not as prevalent as solar thermal systems, the integration of photovoltaic and solar thermal collectors into the walls or roofing structure of a building could provide greater opportunity for the use of renewable solar energy technologies in domestic, commercial and industrial applications. As such, the design of a novel building integrated photovoltaic/thermal (BIPVT) solar collector is theoretically analysed through the use of a modified Hottel-Whillier model. The thermal and electrical efficiency under a range of conditions are subsequently determined and results showing how key design parameters influence the performance of the BIPVT system are presented.

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.

What can student-generated diagrams tell us about their understanding of chemical equations?

Chemical equations are representations that use symbols to summarise the net changes occurring in a reaction whereas depictions such as drawings of the submicroscopic level provide representations of the chemical transformations. While the ability to balance and interpret chemical equations is key to understanding many concepts in chemistry, many undergraduate chemistry students struggle to master these skills. The equations contain a great deal of implicit information and novices may not be able to make the connection between the equation and the actual chemical transformations that are occurring. This paper reports on a study which used submicroscopic diagrams to probe students' understanding of chemical equations. Assessment tasks required students to interpret diagrams, construct diagrams and to relate diagrams to symbolic representations. The analysis showed that some students have misconceptions about the molecular nature and chemical formulae and could not distinguish between coefficients and subscripts when representing chemical formulae. While students were generally able to balance a chemical equation presented as a set of diagrams, a significant number could not generate the balanced equation based on a diagram of the progress of a reaction, The study has demonstrated the use of student-generated diagrams to provide insight into students' understandings of chemical equations.

Purely magnetic spacetimes in general relativity

Given the deep links between Maxwell's equations and General Relativity, it is natural to ask whether there exist solutions of the field equations which are purely magnetic, like Dirac's magnetic monopole. The thesis succeeds in producing two entirely new families of purely magnetic solutions.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Towards an understanding of knowledge sharing behavior of CCOs in Bangladesh : a proposed structural equations model

This paper explores the question or whether Call Center Operators (CCO) share information or knowledge with their clients and if their knowledge sharing behavior has any impact on the sustainability of their relationships with their clients.

Student-generated submicro diagrams : a useful tool for teaching and learning chemical equations and stoichiometry

This paper reports on a pedagogical approach to the teaching of chemical equations introduced to first year university students with little previous chemical knowledge. During the instruction period students had to interpret and construct diagrams of reactions at the submicro level, and relate them to chemical equations at the symbolic level with the aim of improving their conceptual understanding of chemical equations and stoichiometry. Students received instruction in symbol conventions, practice through graded tutorial tasks, and feedback on their efforts over the semester. Analysis of the student responses to formative test and summative exam items over consecutive years indicates that there was a consistent improvement in the abilities of the various cohorts to answer stoichiometry questions correctly. The responses provide evidence for diagrams of the submicro level being used as tools for reasoning in solving chemical problems, to recognise misconceptions of chemical formulae and to recognise the value of using various multiple representations of chemical reactions connecting the submicro and symbolic levels of representation. The student-generated submicro diagrams serve as a visualisation tool for teaching and learning abstract concepts in solving stoichiometric problems. We argue that the use of diagrams of the submicro level provides a more complete picture of the reaction, rather than a net summary of a chemical equation, leading to a deeper conceptual understanding.

Computational modeling aspects of photon transport equations in biological media

This paper presents an overview of modeling light propagation through biological media by solving the photon transport equation. Different variants of the photon transport equation (PTE) are discussed. Several methods for modeling static distributions and the transient response are presented. A discussion on how to mix and match electromagnetic problems with the PTE is also provided.