Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem

Previous research has documented that preservice teachers (PSTs) struggle with under- standing fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs’ understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs’ construction of their own representations for a word problem in developing problem solving skills

Carbon nanotube: a low-loss spin-current waveguide

We demonstrate with a quantum-mechanical approach that carbon nanotubes are excellent spin-current waveguides and are able to carry information stored in a precessing magnetic moment for long distances with very little dispersion and with tunable degrees of attenuation. Pulsed magnetic excitations are predicted to travel with the nanotube Fermi velocity and are able to induce similar excitations in remote locations. Such an efficient way of transporting magnetic information suggests that nanotubes are promising candidates for memory devices with fast magnetization switchings

Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201

Future response of global coastal wetlands to sea-level rise

The response of coastal wetlands to sea-level rise during the twenty-first century remains uncertain. Global-scale projections suggest that between 20 and 90 per cent (for low and high sea-level rise scenarios, respectively) of the present-day coastal wetland area will be lost, which will in turn result in the loss of biodiversity and highly valued ecosystem services(1-3). These projections do not necessarily take into account all essential geomorphological(4-7) and socio-economic system feedbacks(8). Here we present an integrated global modelling approach that considers both the ability of coastal wetlands to build up vertically by sediment accretion, and the accommodation space, namely, the vertical and lateral space available for fine sediments to accumulate and be colonized by wetland vegetation. We use this approach to assess global-scale changes in coastal wetland area in response to global sea-level rise and anthropogenic coastal occupation during the twenty-first century. On the basis of our simulations, we find that, globally, rather than losses, wetland gains of up to 60 per cent of the current area are possible, if more than 37 per cent (our upper estimate for current accommodation space) of coastal wetlands have sufficient accommodation space, and sediment supply remains at present levels. In contrast to previous studies(1-3), we project that until 2100, the loss of global coastal wetland area will range between 0 and 30 per cent, assuming no further accommodation space in addition to current levels. Our simulations suggest that the resilience of global wetlands is primarily driven by the availability of accommodation space, which is strongly influenced by the building of anthropogenic infrastructure in the coastal zone and such infrastructure is expected to change over the twenty-first century. Rather than being an inevitable consequence of global sea-level rise, our findings indicate that large-scale loss of coastal wetlands might be avoidable, if sufficient additional accommodation space can be created through careful nature-based adaptation solutions to coastal management

Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

Fractional Hamiltonian Monodromy is a generalization of the notion of Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A. Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a particular type of non-isolated singularities. In this paper, we analyze the notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin Monodromy of a Riemann surface constructed from the energy-momentum map and associated to a loop in complex space which bypasses the line of singularities. We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n and m:-n resonant systems.Comment: 39 pages, 24 figures. submitted to J. Math. Phy

Death of three Loop Current rings

The life cycle of large anticyclonic rings in the Gulf of Mexico (GOM) is widely described by pinch off from the Loop Current, migration across the Gulf and eventual spin down along the western slope. Extensive observational and modeling efforts provide a relatively consistent picture of rings pinching off from the Loop Current and of complex interaction between anticyclones and cyclones driven by bathymetry along the western and northwestern shelf. The observational record for Loop Current rings (LCRs) during the intermediate period of westward translation is less clear. A number of studies recognize distinct anomalies in LCR characteristics in deep water as the rings enter the western Gulf near 92-94W. These include abrupt changes in the geometry of observed drifter trajectories and derived eddy parameter fits as well as changes in both ring translation speeds and the estimated rate of ring decay. Such observations are consistent with intense interaction and mass exchange between the rings and other coherent mesoscale features known to be present in the western Gulf. We test the hypothesis that interactions with the ambient mesoscale field can lead to rapid loss of coherence of some LCRs well before they reach the \u27eddy graveyard\u27 in the western Gulf. We use the data-assimilating, eddy-resolving numerical GOM model described by Kantha et al. (2005) to assess the fates of readily identified LCRs Fourchon, Juggernaut, and Millenium during the period July 1998 to August 2001. Lagrangian metrics, including relative dispersion of small drifter clusters seeded in the ring cores, analysis of evolving blobs seeded in the ring cores, and finite-scale Lyapunov exponents, are used to track model ring evolution. These metrics clearly show that interactions with existing mesoscale cyclones and anticyclones caused Fourchon and Juggernaut to break up near 92W on advective time scales. In addition, Millenium also experienced an intense deformation, stirring, and mixing episode near 92W. Blob studies showed that the core fluid of Millenium was ultimately dispersed over much of the western basin. Our results show that some LCRs may break up through interactions with existing western Gulf cyclones and anticyclones prior to reaching the western slope

Safety of low dose glucocorticoid treatment in rheumatoid arthritis: published evidence and prospective trial data

Adverse effects of glucocorticoids have been abundantly reported. Published reports on low dose glucocorticoid treatment show that few of the commonly held beliefs about their incidence, prevalence, and impact are supported by clear scientific evidence. Safety data from recent randomised controlled clinical trials of low dose glucocorticoid treatment in RA suggest that adverse effects associated with this drug are modest, and often not statistically different from those of placebo