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

Mid-term results after operative treatment of rockwood grade III-V Acromioclavicular joint dislocations with an AC-hook-plate

Acromioclavicular joint dislocations often occur in athletic, young patients after blunt force to the shoulder. Several static and dynamic operative procedures with or without primary ligament replacement have been described. Between February 2003 and March 2009 we treated 313 patients suffering from Rockwood III-V lesions of the AC joint with an AC-hook plate. 225 (72%) of these patients could be followed up. Mean operation time was 42 minutes in the conventional group and 47 minutes in the minimal invasive group. The postoperative pain on a scale from 1 to 10 (VAS-scale) was rated 2.7 in the conventional group and 2.2 in the minimal invasive group. Taft score showed very good and good results in 189 patients (84%). Constant score showed an average of 92.4 of 100 possible points with 89% excellent and good results and 11% satisfying results. All patients had some degree of pain or discomfort with the hookplate in place. These symptoms were relieved after removal of the plate. The overall complication rate was 10.6%. There were 6 superficial soft tissue infections, 1 fracture of the acromion, 7 redislocations after removal of the hook-plate. We observed 4 broken hooks which could be removed at the time of plate removal, 4 seromas and 2 cases of lateral clavicle bone infection, which required early removal of the plate. We can conclude that clavicle hook plate is a convenient device for the surgical treatment of Rockwood Grade III-V dislocations, giving good mid-term results with a low overall complication rate compared to the literature. Early functional therapy is possible and can avoid limitations in postoperative shoulder function

Posttraumatic severe infection of the ankle joint - long term results of the treatment with resection arthrodesis in 133 cases

Although there is a clear trend toward internal fixation for ankle arthrodesis, there is general consensus that external fixation is required for cases of posttraumatic infection. We retrospectively evaluated the technique and clinical long term results of external fixation in a triangular frame for cases of posttraumatic infection of the ankle. From 1993 to 2006 a consecutive series of 155 patients with an infection of the ankle was included in our study. 133 cases of the advanced "Gächter" stage III and IV were treated with arthrodesis. We treated the patients with a two step treatment plan. After radical debridement and sequestrectomy the malleoli and the joint surfaces were resected. An AO fixator was applied with two Steinmann-nails inserted in the tibia and in the calcaneus and the gap was temporary filled with gentamicin beads as the first step. In the second step we performed an autologous bone graft after a period of four weeks. The case notes were evaluated regarding trauma history, medical complaints, further injuries and illnesses, walking and pain status and occupational issues. Mean age at the index procedure was 49.7 years (18-82), 104 patients were male (67,1%). Follow up examination after mean 4.5 years included a standardised questionnaire and a clinical examination including the criteria of the AO-FAS-Score and radiographs. 92,7% of the cases lead to a stable arthrodesis. In 5 patients the arthrodesis was found partly-stable. In six patients (4,5%) the infection was not controllable during the treatment process. These patients had to be treated with a below knee amputation. The mean AOFAS score at follow up was 63,7 (53-92). Overall there is a high degree of remaining disability. The complication rate and the reduced patient comfort reserve this method mainly for infection. Joint salvage is possible in the majority of cases with an earlier stage I and II infection

Decadal timescale shift in the ^14C record of a central equatorial Pacific coral

Coral skeletal radiocarbon records reflect seawater Δ^14C and are useful for reconstructing the history of water mass movement and ventilation in the tropical oceans. Here, we reconstructed the inter-annual variability in central equatorial Pacific surface water Δ^14C from 1922–1956 using near-monthly 14C measurements in a Porites sp. coral skeleton (FI5A) from the windward side of Fanning Island (3°54'32"N, 159°18'88"W). The most pronounced feature in this record is a large, positive shift in the Δ^14C between 1947 and 1956 that coincides with the switch of the Pacific Decadal Oscillation (PDO) from a positive to a negative phase in the mid-1940s. Although the absolute Δ^14C values from 1950–1955 in FI5A differ from the Δ^14C values of another coral core collected from the opposite side of the island, both records show a large, positive shift in their Δ^14C records at that time. The relative increase in the Δ^14C of each record is consistent with the premise that a common mechanism is controlling the Δ^14C records within each coral record. Overall, the Fanning Δ^14C data support the notion that a significant amount of subtropical seawater is arriving at the Equator, but does not allow us to determine the mechanism for its transport