Conjugacy theorems for loop reductive group schemes and Lie algebras

The conjugacy of split Cartan subalgebras in the finite dimensional simple case (Chevalley) and in the symmetrizable Kac-Moody case (Peterson-Kac) are fundamental results of the theory of Lie algebras. Among the Kac-Moody Lie algebras the affine algebras stand out. This paper deals with the problem of conjugacy for a class of algebras --extended affine Lie algebras-- that are in a precise sense higher nullity analogues of the affine algebras. Unlike the methods used by Peterson-Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of reductive group schemes developed by Demazure and Grothendieck, and on the work of J. Tits on buildingsComment: Publi\'e dans Bulletin of Mathematical Sciences 4 (2014), 281-32

Physical Drivers of Phytoplankton Bloom Initiation in the Southern Ocean's Scotia Sea

Abstract: The Scotia Sea is the site of one of the largest spring phytoplankton blooms in the Southern Ocean. Past studies suggest that shelf‐iron inputs are responsible for the high productivity in this region, but the physical mechanisms that initiate and sustain the bloom are not well understood. Analysis of profiling float data from 2002 to 2017 shows that the Scotia Sea has an unusually shallow mixed‐layer depth during the transition from winter to spring, allowing the region to support a bloom earlier in the season than elsewhere in the Antarctic Circumpolar Current. We compare these results to the mixed‐layer depth in the 1/6° data‐assimilating Southern Ocean State Estimate and then use the model output to assess the physical balances governing mixed‐layer variability in the region. Results indicate the importance of lateral advection of Weddell Sea surface waters in setting the stratification. A Lagrangian particle release experiment run backward in time suggests that Weddell outflow constitutes 10% of the waters in the upper 200 m of the water column in the bloom region. This dense Weddell water subducts below the surface waters in the Scotia Sea, establishing a sharp subsurface density contrast that cannot be overcome by wintertime convection. Profiling float trajectories are consistent with the formation of Taylor columns over the region's complex bathymetry, which may also contribute to the unique stratification. Furthermore, biogeochemical measurements from 2016 and 2017 bloom events suggest that vertical exchange associated with this Taylor column enhances productivity by delivering nutrients to the euphotic zone

The synthesis of 15 mu infrared horizon radiance profiles from meteorological data inputs

Computational computer program for modeling infrared horizon radiance profile using pressure and temperature profile input

Quaternion algebras with the same subfields

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F /K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields

Intercomparisons of HIRDLS, COSMIC and SABER for the detection of stratospheric gravity waves

Colocated temperature profiles from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC), High Resolution Dynamics Limb Sounder (HIRDLS) and the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) mission are compared over the years 2006–2007 to assess their relative performances for the detection of stratospheric gravity waves. Two methods are used, one based on a simple comparison of the standard deviations and correlation coefficients of high-pass filtered profiles from each instrument, and the other based on Stockwell transform analyses of the profiles for vertical wavelength and temperature perturbation scales. It is concluded, when allowing for their different vertical resolution capabilites, that the three instruments reproduce each other's results for magnitude and vertical scale of perturbations to within their resolution limits in approximately 50 % of cases, but with a positive frequency and temperature bias in the case of COSMIC. This is possibly indicative of a slightly higher vertical resolution being available to the constellation than estimated

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3: Minor corrections, section numbering changed to match published version. v4: Sign errors in Proposition 6.8(d) corrected. This version incorporates an erratum to the published versio

The precautions of clinical waste: disposable medical sharps in the United Kingdom

This article deals with recent changes in UK guidance on clinical waste, in particular a shift to disposable, single-use instruments and sharps. I use interviews conducted with nurses from a GP practice and two clinical waste managers at alternative treatment and incineration sites as a springboard for reflection on the relationship between the legislation on clinical waste management and its implementation. Scrutinizing the UK guidance, European legislation and World Health Organization principles, I draw out interviewees’ concerns that the changed practices lead to an expansion of the hazardous waste category, with an increased volume going to incineration. This raises questions regarding the regulations’ environmental and health effects, and regarding the precautionary approach embedded in the regulations. Tracing the diverse reverberations of the term ‘waste’ in different points along the journeys made by sharps in particular, and locating these questions in relation to existing literature on waste, I emphasize that public health rationales for the new practices are not made clear in the guidance. I suggest that this relative silence on the subject conceals both the uncertainties regarding the necessity for these means of managing the risks of infectious waste, and the tensions between policies of precautionary public health and environmental sustainability

Caloric dose-responsive genes in blood cells differentiate the metabolic status of obese men.

We have investigated the postprandial transcriptional response of blood cells to increasing caloric doses of a meal challenge to test whether the dynamic response of the human organism to the ingestion of food is dependent on metabolic health. The randomized crossover study included seven normal weight and seven obese men consuming three doses (500/1000/1500 kcal) of a high-fat meal. The blood cell transcriptome was measured before and 2, 4, and 6 h after meal ingestion (168 samples). We applied univariate and multivariate statistics to investigate differentially expressed genes in both study groups. We identified 624 probe sets that were up- or down-regulated after the caloric challenge in a dose-dependent manner. These transcripts were most responsive to the 1500 kcal challenge in the obese group and were associated with postprandial insulin and oxidative phosphorylation. Furthermore, the data revealed a separation of the obese group into individuals whose response was close to the normal weight group and individuals with a transcriptional response indicative of a loss of metabolic flexibility. The molecular signature provided by the postprandial transcriptomic response of blood cells to increasing caloric doses of a high-fat meal challenge may represent a sensitive way to evaluate the qualitative impact of food on human health