A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.     

Optimization of global kinetics parameters for heterogeneous propellant combustion using a genetic algorithm

We examine the combustion of heterogeneous propellants for which, necessarily, the chemical kinetics is modelled using simple global schemes. Choosing the parameters for such schemes is a significant challenge, one that, in the past, has usually been met using hand-fitting of experimental data (target data) for global burning properties such as steady burning rates, burn-rate temperature sensitivity, and the like. This is an unsatisfactory strategy in many ways. It is not optimal; and if the target set is large and includes such things as stability criteria, or bounds, difficult to implement. Here we discuss the use of a general optimization strategy which can handle large data sets of a general nature. The key numerical tool is a genetic algorithm that uses MPI on a parallel platform. We use this strategy to determine parameters for HMX/HTPB propellants and AP/HTPB propellants. Only one-dimensional target data are used, corresponding to the burning of pure HMX (AP) or a homogenized blend of fine HMX (AP) and HTPB. The goal is to generate kinetics models that can be used in the numerical simulation of three-dimensional heterogeneous propellant combustion. The results of such simulations will be reported in a sequel.     

A comparison of the reproducibility of the parameters of the 13C-aminopyrine breath test for the assessment of hepatic function

This study determined the within-subject and between-subject variability of different ways of expressing the results of the ¹³C-aminopyrine breath test (¹³C-ABT) and the effect of shortening the test duration. The ¹³C-ABT was conducted on three separate occasions in 10 healthy volunteers and on a single occasion in 22 patients with established liver cirrhosis. The within-subject variability of cumulative percentage dose recovered (cPDR), using measured CO₂ production rate (VCO₂), in the reference group over three trials was 15% over 120 min. Higher within-subject variability in cPDR would have been evident if the test was terminated at either 30 or 60 min. Substitution of predicted VCO₂ to calculate cPDR yielded comparable values at all time points. Significant differences between cirrhotics and reference group were evident after just 10 min using PDR/h, cPDR or enrichment (all P<0.05). The ABT demonstrates clinically acceptable reproducibility. Shortening of the duration may make the test more acceptable clinically, but it is associated with increasing imprecision.     

Substituent effects on the geometry of some trigonal radicals

A simple level of ab initio molecular orbital theory with a split-valence shell basis with d-type polarization functions (6–31G*) is used to predict equilibrium geometries for the ground and some low-lying excited states of AH_n molecules and cations where A is carbon, nitrogen, oxygen or fluorine. The results are shown to be close to the limit for single determinant wave functions in cases where corresponding computations with more extensive bases are available. Comparison with experimental results also shows good agreement although a systematic underestimation of bond lengths up to 3 per cent is evident. For systems where no experimental data are available, the results provide predictions of equilibrium geometry.     

TRINAT: measuring β-decay correlations with laser-trapped atoms

TRIUMF’s neutral atom trap for β decay (TRINAT) has been used to measure the most accurate β-ν correlation. Plans include improving that measurement, and also carrying out a full program of spin-polarized β decay correlation measurements complementary to the decay of the neutron     

Override and update

Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms for the first order theory of the override and update constructions on partial functions, resolving the main unsolved problem in the area.     

Certain hyperbolic regular polygonal tiles are isoperimetric

Geometriae Dedicata - The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular...     

Interstitials in platinum

The defect production rate in platinum irradiated with energetic charged particles is measured as a function of irradiation temperature from below stage I to above the ‘so-called’ stage III. On the basis of these measurements, supplemented by recovery studies, and by other types of irradiations a consistent model of defect production and recovery is platinum on the basis that two distinct interstitial species are present is put forward.     

Distribution of Eigenvalues of Highly Palindromic Toeplitz Matrices

Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d. random variables chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous work (Bryc et al., Ann. Probab. 34(1):1–38, 2006; Hammond and Miller, J. Theor. Probab. 18(3):537–566, 2005) showed that the spectral measures (the density of normalized eigenvalues) converge almost surely to a universal distribution almost that of the Gaussian, independent of p. The deficit from the Gaussian distribution is due to obstructions to solutions of Diophantine equations and can be removed (see Massey et al., J. Theor. Probab. 20(3):637–662, 2007) by making the first row palindromic. In this paper we study the case where there is more than one palindrome in the first row of real symmetric Toeplitz matrices. Using the method of moments and an analysis of the resulting Diophantine equations, we show that the spectral measures converge almost surely to a universal distribution. Assuming a conjecture on the resulting Diophantine sums (which is supported by numerics and some theoretical arguments), we prove that the limiting distribution has a fatter tail than any previously seen limiting spectral measure.