On the complete integrability of the discrete Nahm equations

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed

Making a wave of difference in water awareness and competence through primary physical education teacher education

Introduction The current study aims to pilot the merit of having PE primary physical education specialists contribute to generalist primary teacher education via the creation and sharing of accessible progression spirals across an environmental progression of space instead of designated activity (Table 1). The final water-based progression blends fundamental movement with core aquatic skills as mediated by respective students across a Kolb reflective learning cycle (1984) and informed by curricular guidelines toward a new PETE national water competence teaching assistant accreditation (DfE, 2013, Swim England, 2021, RLPE-AfPE, 2022). Programme wise, how might primary student teachers benefit from a PE Primary specialist-generalist peer supported teaching and learning addition to the PE PCK experience set? Motorically and competence wise, what are the reported potential and perceived student benefits to this PETE journey? Method Physical education specialist student teachers (12) were taught how to plan and teach using the environmentally coded space set. This they modelled and shared with all other generalists; undergraduate and postgraduate generalist students through our RLPE accessible online padlet series. The progression spiral approach aligns with that of Bruner (1966) and extend from reflective PETE bespoke practices (Graham et al., 2020). Results The full set has been successfully piloted by PE specialists with Year 2, undergraduate and graduate primary student teachers. Table 1. Depicts the Environmentally led and peer supported PETE progression which will be implemented in full this coming aca-demic year. Discussion Aspirationally, we will be better placed to refine and improve the approach, and in so doing, address research questions following this coming academic year. References Bruner, J. (1996). The Process of Education. Cambridge, MA: Harvard University Press. Murray, A., & Howells, K. (in Press). Wheels Up, spiral progression pedagogy towards creative movers using wheels. Journal of Early Childhood Education Research. Stiehl, J., Morris, D. G. S., & Sinclair, C. (2008) Teaching physical activity: Change, challenge and choice. Champaign, IL: Human Kinetics

Suicide substrate reaction-diffusion equations: varying the source

The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of initial and boundary conditions are examined: one modelling an instantaneous point source, akin to an injection of substrate, the other, a continuous point source, akin to a continuing influx, or intravenous drip, of substrate. The quasi-steady-state assumption is applied to obtain analytical solutions for a limited parameter space. Finally, further applications of numerical and analytical experimentation on pharmaceutical mechanisms are described

The Impact of Early Positive Results on a Mathematics and Science Partnership: The Experience of the Institute for Chemistry Literacy Through Computational Science

After one year of implementation, the Institute for Chemistry Literacy through Computational Science, an NSF Mathematics and Science Partnership Institute Project led by the University of Illinois at Urbana-Champaign’s Department of Chemistry, College of Medicine, and National Center for Supercomputing Applications, experienced statistically significant gains in chemistry content knowledge among students of the rural high school teachers participating in its intensive, year-round professional development course, compared to a control group. The project utilizes a two-cohort, delayed-treatment, random control trial, quasi-experimental research design with the second cohort entering treatment one year following the first. The three-year treatment includes intensive two-week summer institutes, occasional school year workshops and year-round, on-line collaborative lesson development, resource sharing, and expert support. The means of student pre-test scores for Cohort I (η=963) and Cohort II (η=862) teachers were not significantly different. The mean gain (difference between pre-test and post-test scores) after seven months in the classroom for Cohort I was 9.8 percentage points, compared to 6.7 percentage points for Cohort II. This statistically significant difference (p\u3c.001) represented an effect size of .25 standard deviation units, and indicated unusually early confirmation of treatment effects. When post-tests were compared, Cohort I students scored significantly higher than Cohort II and supported the gain score differences. The impact of these results on treatment and research plans is discussed. concentrating on the effect of lessening rural teachers’ isolation and increasing access to tools to facilitate learning

On the kinetics of suicide substrates

We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure to obtain accurate, approximate solutions analytically in terms of the rate equation parameters. This systematic technique provides more accurate approximations to the exact (numerical) solutions than other approximate methods which have been proposed based on a pseudo-steady state hypothesis

Circle actions, central extensions and string structures

The caloron correspondence can be understood as an equivalence of categories between $G$-bundles over circle bundles and $LG \rtimes_\rho S^1$-bundles where $LG$ is the group of smooth loops in $G$. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an $LG \rtimes_\rho S^1$-bundle.Comment: 25 page

Twisted K-theory and K-theory of bundle gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on twisted Chern character in non-torsion cas