On some algebras associated to genus one curves

Haile, Han and Kuo have studied certain non-commutative algebras associated to a binary quartic or ternary cubic form. We extend their construction to pairs of quadratic forms in four variables, and conjecture a further generalisation to genus one curves of arbitrary degree. These constructions give an explicit realisation of an isomorphism relating the Weil-Châtelet and Brauer groups of an elliptic curve

Vegetation Type Dominates the Spatial Variability in CH<inf>4</inf> Emissions Across Multiple Arctic Tundra Landscapes

Methane (CH4) emissions from Arctic tundra are an important feedback to global climate. Currently, modelling and predicting CH4 fluxes at broader scales are limited by the challenge of upscaling plot-scale measurements in spatially heterogeneous landscapes, and by uncertainties regarding key controls of CH4 emissions. In this study, CH4 and CO2 fluxes were measured together with a range of environmental variables and detailed vegetation analysis at four sites spanning 300 km latitude from Barrow to Ivotuk (Alaska). We used multiple regression modelling to identify drivers of CH4 flux, and to examine relationships between gross primary productivity (GPP), dissolved organic carbon (DOC) and CH4 fluxes. We found that a highly simplified vegetation classification consisting of just three vegetation types (wet sedge, tussock sedge and other) explained 54% of the variation in CH4 fluxes across the entire transect, performing almost as well as a more complex model including water table, sedge height and soil moisture (explaining 58% of the variation in CH4 fluxes). Substantial CH4 emissions were recorded from tussock sedges in locations even when the water table was lower than 40 cm below the surface, demonstrating the importance of plant-mediated transport. We also found no relationship between instantaneous GPP and CH4 fluxes, suggesting that models should be cautious in assuming a direct relationship between primary production and CH4 emissions. Our findings demonstrate the importance of vegetation as an integrator of processes controlling CH4 emissions in Arctic ecosystems, and provide a simplified framework for upscaling plot scale CH4 flux measurements from Arctic ecosystems

Environmental and vegetation controls on the spatial variability of CH4 emission from wet-sedge and tussock tundra ecosystems in the Arctic

Aims Despite multiple studies investigating the environmental controls on CH4 fluxes from arctic tundra ecosystems, the high spatial variability of CH4 emissions is not fully understood. This makes the upscaling of CH4 fluxes from plot to regional scale, particularly challenging. The goal of this study is to refine our knowledge of the spatial variability and controls on CH4 emission from tundra ecosystems. Methods CH4 fluxes were measured in four sites across a variety of wet-sedge and tussock tundra ecosystems in Alaska using chambers and a Los Gatos CO2 and CH4 gas analyser. Results All sites were found to be sources of CH4, with northern sites (in Barrow) showing similar CH4 emission rates to the southernmost site (ca. 300 km south, Ivotuk). Gross primary productivity (GPP), water level and soil temperature were the most important environmental controls on CH4 emission. Greater vascular plant cover was linked with higher CH4 emission, but this increased emission with increased vascular plant cover was much higher (86 %) in the drier sites, than the wettest sites (30 %), suggesting that transport and/or substrate availability were crucial limiting factors for CH4 emission in these tundra ecosystems. Conclusions Overall, this study provides an increased understanding of the fine scale spatial controls on CH4 flux, in particular the key role that plant cover and GPP play in enhancing CH4 emissions from tundra soils