Mathematics students' conceptions of mathematics

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Anomalous codeposition of cobalt and ruthenium from chloride-sulfate baths

Codeposition of Ru and Co was studied at room temperature and at 50oC with various Ru3+ and Co2+ concentrations in the electrolyte. The codeposition of Co and Ru proved to be anomalous since no pure Ru could be obtained in the presence of Co2+ in the electrolyte, but a significant Co incorporation into the deposit was detected at potentials where the deposition of pure Co was not possible. The composition of the deposits varied monotonously with the change of the concentration ratio of Co2+ and Ru3+. The deposition of Ru was much hindered and the current efficiency was a few percent only when the molar fraction of Co in the deposit was low. Continuous deposits could be obtained only when the molar fraction of Co in the deposit was at least 40 at.%. The deposit morphology was related to the molar fraction of Co in the deposit. The X-ray diffractograms are in conformity with a hexagonal close-packed alloy and indicate the formation of nanocrystalline deposits. Two-pulse plating did not lead to a multilayer but to a Co-rich alloy. Magnetoresistance of the samples decreased with increasing Ru content

The Distances of the Magellanic Clouds

The present status of our knowledge of the distances to the Magellanic Clouds is evaluated from a post-Hipparcos perspective. After a brief summary of the effects of structure, reddening, age and metallicity, the primary distance indicators for the Large Magellanic Cloud are reviewed: The SN 1987A ring, Cepheids, RR Lyraes, Mira variables, and Eclipsing Binaries. Distances derived via these methods are weighted and combined to produce final "best" estimates for the Magellanic Clouds distance moduli.Comment: Invited review article to appear in ``Post Hipparcos Cosmic Candles'', F. Caputo & A. Heck (Eds.), Kluwer Academic Publ., Dordrecht, in pres

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Healthcare expenditure on Indigenous and non-Indigenous Australians at high risk of cardiovascular disease

Background: In spite of bearing a heavier burden of death, disease and disability, there is mixed evidence as to whether Indigenous Australians utilise more or less healthcare services than other Australians given their elevated risk level. This study analyses the Medicare expenditure and its predictors in a cohort of Indigenous and non-Indigenous Australians at high risk of cardiovascular disease. Methods: The healthcare expenditure of participants of the Kanyini Guidelines Adherence with the Polypill (GAP) pragmatic randomised controlled trial was modelled using linear regression methods. 535 adult (48% Indigenous) participants at high risk of cardiovascular disease (CVD) were recruited through 33 primary healthcare services (including 12 Aboriginal Medical Services) across Australia. Results: There was no significant difference in the expenditure of Indigenous and non-Indigenous participants in non-remote areas following adjustment for individual characteristics. Indigenous individuals living in remote areas had lower MBS expenditure ($932 per year P< 0.001) than other individuals. MBS expenditure was found to increase with being aged over 65 years ($128, p=0.013), being female ($472, p=0.003), lower baseline reported quality of life ($102 per 0.1 decrement of utility p=0.004) and a history of diabetes ($324, p=0.001), gout ($631, p=0.022), chronic obstructive pulmonary disease ($469, p=0.019) and established CVD whether receiving guideline-recommended treatment prior to the trial ($452, p=0.005) or not ($483, p=0.04). When controlling for all other characteristics, morbidly obese patients had lower MBS expenditure than other individuals (-$887, p=0.002). Conclusion: The findings suggest that for the majority of participants, once individuals are engaged with a primary care provider, factors other than whether they are Indigenous determine the level of Medicare expenditure for each person. Trial Registration: Australian New Zealand Clinical Trials Registry ACTRN 126080005833347

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

A strong conditional mutualism limits and enhances seed dispersal and germination of a tropical palm

Seed predation and seed dispersal can have strong effects on early life history stages of plants. These processes have often been studied as individual effects, but the degree to which their relative importance co-varies with seed predator abundance and how this influences seed germination rates is poorly understood. Therefore, we used a combination of observations and field experiments to determine the degree to which germination rates of the palm Astrocaryum mexicanum varied with abundance of a small mammal seed predator/disperser, Heteromysdesmarestianus, in a lowland tropical forest. Patterns of abundance of the two species were strongly related; density of H. desmarestianus was low in sites with low density of A. mexicanum and vice versa. Rates of predation and dispersal of A. mexicanum seeds depended on abundance of H. desmarestianus; sites with high densities of H. desmarestianus had the highest rates of seed predation and lowest rates of seed germination, but a greater total number of seeds were dispersed and there was greater density of seedlings, saplings, and adults of A. mexicanum in these sites. When abundance of H. desmarestianus was experimentally reduced, rates of seed predation decreased, but so did dispersal of A. mexicanum seeds. Critically, rates of germination of dispersed seeds were 5 times greater than undispersed seeds. The results suggest that the relationship between A. mexicanum and H. desmarestianus is a conditional mutualism that results in a strong local effect on the abundance of each species. However, the magnitude and direction of these effects are determined by the relative strength of opposing, but related, mechanisms. A. mexicanum nuts provide H. desmarestianus with a critical food resource, and while seed predation on A. mexicanum nuts by H. desmarestianus is very intense, A. mexicanum ultimately benefits because of the relatively high germination rates of its seeds that are dispersed by H. desmarestianus