Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Minority Economic Development: The Problem of Business Failures

Inflammatory pseudotumour is a rare condition that can affect various organs. The clinical and histologic appearance of the pseudotumour may mimic haematological, lymphoproliferative, paraneoplastic or malignant processes. A previously healthy 39-year-old man presented with nephrotic syndrome. He had a history of headaches, nausea and swollen ankles. Computed tomography of the abdomen revealed a 6-cm mass in the spleen. Following a renal biopsy, a diagnosis of membranoproliferative glomerulonephritis (MPGN) type I was made. Splenectomy was performed and the examination revealed a mixed population of lymphocytes with predominantly T-cells, B-cells and lymphoplasmacytoid cells. Immunostaining confirmed that the small cells were mostly T-cells positive for all T-cell markers including CD2, CD3, CD4, CD5, CD7 and CD8. A diagnosis of inflammatory pseudotumour was established. The removal of the spleen was followed by remission of glomerulonephritis, but it was complicated by a subphrenic abscess and pneumonia. This association between an inflammatory pseudotumour of the spleen and MPGN has not been previously described. Abnormal immune response due to the inflammation leading to secondary glomerulonephritis might be the main pathogenic mechanism

Lightside Atmospheric Revitalization System

The system was studied as a replacement to the present baseline LiOH system for extended duration shuttle missions. The system consists of three subsystems: a solid amine water desorbed regenerable carbon dioxide removal system, a water vapor electrolysis oxygen generating system, and a Sabatier reactor carbon dioxide reduction system. The system is designed for use on a solar powered shuttle vehicle. The majority of the system's power requirements are utilized on the Sun side of each orbit, when solar power is available

A 10B-based neutron detector with stacked Multiwire Proportional Counters and macrostructured cathodes

We present the results of the measurements of the detection efficiency for a 4.7 \r{A} neutron beam incident upon a detector incorporating a stack of up to five MultiWire Proportional Counters (MWPC) with Boron-coated cathodes. The cathodes were made of Aluminum and had a surface exhibiting millimeter-deep V-shaped grooves of 45{\deg}, upon which the thin Boron film was deposited by DC magnetron sputtering. The incident neutrons interacting with the converter layer deposited on the sidewalls of the grooves have a higher capture probability, owing to the larger effective absorption film thickness. This leads to a higher overall detection efficiency for the grooved cathode when compared to a cathode with a flat surface. Both the experimental results and the predictions of the GEANT4 model suggests that a 5-counter detector stack with coated grooved cathodes has the same efficiency as a 7-counter stack with flat cathodes. The reduction in the number of counters in the stack without altering the detection efficiency will prove highly beneficial for large-area position-sensitive detectors for neutron scattering applications, for which the cost-effective manufacturing of the detector and associated readout electronics is an important objective. The proposed detector concept could be a technological option for one of the new chopper spectrometers and other instruments planned to be built at the future European Spallation Source in Sweden. These results with macrostructured cathodes generally apply not just to MWPCs but to other gaseous detectors as well.Comment: 14 pages, 9 figure

Electronic structure investigation of the cubic inverse perovskite Sc3AlN

The electronic structure and chemical bonding of the recently discovered inverse perovskite Sc3AlN, in comparison to ScN and Sc metal have been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Sc L, N K, Al L1, and Al L2,3 emission spectra are compared with calculated spectra using first principle density-functional theory including dipole transition matrix elements. The main Sc 3d - N 2p and Sc 3d - Al 3p chemical bond regions are identified at -4 eV and -1.4 eV below the Fermi level, respectively. A strongly modified spectral shape of 3s states in the Al L2,3 emission from Sc3AlN in comparison to pure Al metal is found, which reflects the Sc 3d - Al 3p hybridization observed in the Al L1 emission. The differences between the electronic structure of Sc3AlN, ScN, and Sc metal are discussed in relation to the change of the conductivity and elastic properties.Comment: 11 pages, 5 picture

Electronic structure and chemical bonding in Ti4SiC3 investigated by soft x-ray emission spectroscopy and first principle theory

The electronic structure in the new transition metal carbide Ti4SiC3 has been investigated by bulk-sensitive soft x-ray emission spectroscopy and compared to the well-studied Ti3SiC2 and TiC systems. The measured high-resolution Ti L, C K and Si L x-ray emission spectra are discussed with ab initio calculations based on density-functional theory including core-to-valence dipole matrix elements. The detailed investigations of the Ti-C and Ti-Si chemical bonds provide increased understanding of the physical properties of these nanolaminates. A strongly modified spectral shape is detected for the buried Si monolayers due to Si 3p hybridization with the Ti 3d orbitals. As a result of relaxation of the crystal structure and the charge-transfer from Ti (and Si) to C, the strength of the Ti-C covalent bond is increased. The differences between the electronic and crystal structures of Ti4SiC3 and Ti3SiC2 are discussed in relation to the number of Si layers per Ti layer in the two systems and the corresponding change of materials properties.Comment: 12 pages, 7 figures, 1 tabl

Bonding mechanism in the nitrides Ti2AlN and TiN: an experimental and theoretical investigation

The electronic structure of nanolaminate Ti2AlN and TiN thin films has been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Ti L, N K, Al L1 and Al L2,3 emission spectra are compared with calculated spectra using ab initio density-functional theory including dipole transition matrix elements. Three different types of bond regions are identified; a relatively weak Ti 3d - Al 3p bonding between -1 and -2 eV below the Fermi level, and Ti 3d - N 2p and Ti 3d - N 2s bonding which are deeper in energy observed at -4.8 eV and -15 eV below the Fermi level, respectively. A strongly modified spectral shape of 3s states of Al L2,3 emission from Ti2AlN in comparison to pure Al metal is found, which reflects the Ti 3d - Al 3p hybridization observed in the Al L1 emission. The differences between the electronic and crystal structures of Ti2AlN and TiN are discussed in relation to the intercalated Al layers of the former compound and the change of the materials properties in comparison to the isostructural carbides.Comment: 18 pages, 7 figures; http://link.aps.org/doi/10.1103/PhysRevB.76.19512

Electronic structure investigation of Ti3AlC2, Ti3SiC2, and Ti3GeC2 by soft-X-ray emission spectroscopy

The electronic structures of epitaxially grown films of Ti3AlC2, Ti3SiC2 and Ti3GeC2 have been investigated by bulk-sensitive soft X-ray emission spectroscopy. The measured high-resolution Ti L, C K, Al L, Si L and Ge M emission spectra are compared with ab initio density-functional theory including core-to-valence dipole matrix elements. A qualitative agreement between experiment and theory is obtained. A weak covalent Ti-Al bond is manifested by a pronounced shoulder in the Ti L-emission of Ti3AlC2. As Al is replaced with Si or Ge, the shoulder disappears. For the buried Al and Si-layers, strongly hybridized spectral shapes are detected in Ti3AlC2 and Ti3SiC2, respectively. As a result of relaxation of the crystal structure and the increased charge-transfer from Ti to C, the Ti-C bonding is strengthened. The differences between the electronic structures are discussed in relation to the bonding in the nanolaminates and the corresponding change of materials properties.Comment: 15 pages, 8 figure

Molecular Hydrogen and Global Star Formation Relations in Galaxies

(ABRIDGED) We use hydrodynamical simulations of disk galaxies to study relations between star formation and properties of the molecular interstellar medium (ISM). We implement a model for the ISM that includes low-temperature (T<10^4K) cooling, directly ties the star formation rate to the molecular gas density, and accounts for the destruction of H2 by an interstellar radiation field from young stars. We demonstrate that the ISM and star formation model simultaneously produces a spatially-resolved molecular-gas surface density Schmidt-Kennicutt relation of the form Sigma_SFR \propto Sigma_Hmol^n_mol with n_mol~1.4 independent of galaxy mass, and a total gas surface density -- star formation rate relation Sigma_SFR \propto Sigma_gas^n_tot with a power-law index that steepens from n_tot~2 for large galaxies to n_tot>~4 for small dwarf galaxies. We show that deviations from the disk-averaged Sigma_SFR \propto Sigma_gas^1.4 correlation determined by Kennicutt (1998) owe primarily to spatial trends in the molecular fraction f_H2 and may explain observed deviations from the global Schmidt-Kennicutt relation.Comment: Version accepted by ApJ, high-res version available at http://kicp.uchicago.edu/~brant/astro-ph/molecular_ism/rk2007.pd

Some Restrictions Abroad Affecting Corporations

A neutron detector concept based on solid layers of boron carbide enriched in 1 B has been in development for the last few years as an alternative for He-3 by collaboration between the ILL, ESS and Linkoping University. This Multi-Grid detector uses layers of aluminum substrates coated with (B4C)-B-10 on both sides that are traversed by the incoming neutrons. Detection is achieved using a gas counter readout principle. By segmenting the substrate and using multiple anode wires, the detector is made inherently position sensitive. This development is aimed primarily at neutron scattering instruments with large detector areas, such as time-of-flight chopper spectrometers. The most recent prototype has been built to be interchangeable with the He-3 detectors of IN6 at ILL. The 1 B detector has an active area of 32 x 48 cm(2). It was installed at the IN6 instrument and operated for several weeks, collecting data in parallel with the regularly scheduled experiments, thus providing the first side-by-side comparison with the conventional He-3 detectors. Results include an efficiency comparison, assessment of the in-detector scattering contribution, sensitivity to gamma-rays and the signal-to-noise ratio in time-of-flight spectra. The good expected performance has been confirmed with the exception of an unexpected background count rate. This has been identified as natural alpha activity in aluminum. New convertor substrates are under study to eliminate this source of background