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

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

Spacecraft instrument calibration and stability

The following topics are covered: instrument degradation; the Solar Backscatter Ultraviolet (SBUV) Experiment; the Total Ozone Mapping Spectrometer (TOMS); the Stratospheric Aerosol and Gas Experiment 1 (SAGE-1) and SAGE-2 instruments; the Solar Mesosphere Explorer (SME) UV ozone and near infrared airglow instruments; and the Limb Infrared Monitor of the Stratosphere (LIMS)

Using coupled micropillar compression and micro-Laue diffraction to investigate deformation mechanisms in a complex metallic alloy Al13Co4

In this investigation, we have used in-situ micro-Laue diffraction combined with micropillar compression of focused ion beam milled Al13Co4 complex metallic alloy to study the evolution of deformation in Al13Co4. Streaking of the Laue spots showed that the onset of plastic flow occured at stresses as low as 0.8 GPa, although macroscopic yield only becomes apparent at 2 GPa. The measured misorientations, obtained from peak splitting, enabled the geometrically necessary dislocation density to be estimated as 1.1 x 1013 m-2

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

Spectrometry: Report of panel

Spectroscopic measurements are required to define the spectral background and provide the detailed spectral information that is essential for the design of species-specific systems and the analysis of data obtained from them. This function of spectroscopic measurements is expected to be an important part of any tropospheric remote-sensing program, and both emission and absorption spectroscopy are relevant in this context. The data from such observations are of value to tropospheric science in their own right, during the initial phases while species-specific techniques and instruments are under development. In addition, there are a number of unresolved problems in tropospheric radiative transfer and spectroscopy which presently limit the accuracy and reliability of all remote sensing methods. Only through a supporting program of spectroscopic measurements can progress be made in improving the understanding of these aspects of radiative transfer and ultimately reaching the desired confidence in the accuracy to species-specific monitoring techniques

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

Global trends

Measuring trends in ozone, and most other geophysical variables, requires that a small systematic change with time be determined from signals that have large periodic and aperiodic variations. Their time scales range from the day-to-day changes due to atmospheric motions through seasonal and annual variations to 11 year cycles resulting from changes in the sun UV output. Because of the magnitude of all of these variations is not well known and highly variable, it is necessary to measure over more than one period of the variations to remove their effects. This means that at least 2 or more times the 11 year sunspot cycle. Thus, the first requirement is for a long term data record. The second related requirement is that the record be consistent. A third requirement is for reasonable global sampling, to ensure that the effects are representative of the entire Earth. The various observational methods relevant to trend detection are reviewed to characterize their quality and time and space coverage. Available data are then examined for long term trends or recent changes in ozone total content and vertical distribution, as well as related parameters such as stratospheric temperature, source gases and aerosols

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

Cyclotron resonance of the quasi-two-dimensional electron gas at Hg1-xCdxTe grain boundaries

The magnetotransmission of a p-type Hg0.766Cd0.234Te bicrystal containing a single grain boundary with an inversion layer has been investigated in the submillimetre wavelength range. For the first time the cyclotron resonance lines belonging to the various electric subbands of a quasi-two-dimensional carrier system at a grain boundary could be detected. The measured cyclotron masses and the subband densities determined from Shubnikov-de Haas experiments are compared with theoretical predictions and it is found that the data can be explained very well within the framework of a triangular well approximation model which allows for non-parabolic effects