Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.

Optimisation of source/drain extension region profile for suppression of short channel effects in sub-50 nm DG SOI MOSFETs with high- k gate dielectrics

Novel technology dependent scaling parameters i.e. spacer to gradient ratio and effective channel length (Leff) are proposed for source/drain engineered DG MOSFET, and their significance in minimizing short channel effects (SCES) in high-k gate dielectrics is discussed in detail. Results show that a high-k dielectric should be associated with a higher spacer to gradient ratio to minimise SCEs The analytical model agrees with simulated data over the entire range of spacer widths, doping gradients, high-k gate dielectrics and effective channel lengths.

Theory of the near K-edge structure in electron energy loss spectroscopy

Arguments are given that lead to a formalism for calculating near K-edge structure in electron energy loss spectroscopy (EELS). This is essentially a one electron picture, while many body effects may be introduced at different levels, such as the local density approximation to density functional theory or the GW approximation to the electron self-energy. Calculations are made within the all electron LMTO scheme in crystals with complex atomic and electronic structures, and these are compared with experiment. (c) 2004 Elsevier B.V. All rights reserved.

Effect of relaxation on the oxygen K-edge electron energy-loss near-edge structure in yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia (YSZ) materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method (NFP-LMTO) as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater's transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr,Y,O, are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

CaII K interstellar observations towards early-type disc and halo stars

We present high-resolution (R = lambda/Deltalambda similar to 40 000) Ca II K interstellar observations (lambda(air) = 3933.66Angstrom) towards 88 mainly B-type stars, of which 74 are taken from the Edinburgh-Cape or Palomar-Green surveys, and 81 have > 25degrees. The majority of the data come from previously existing spectroscopy, although also included are 18 new observations of stars with echelle spectra taken with UVES on the Very Large Telescope UT2 (Kueyen). Some 49 of the sample stars have distance estimates above the Galactic plane (z) greater than or equal to 1 kpc, and are thus good probes of the halo interstellar medium. Of the 362 interstellar Ca K components that we detect, 75 (21 per cent) have absolute values of their LSR velocity values exceeding 40 km s(-1). In terms of the deviation velocity for the sightlines with distance estimates, 46/273 (17 per cent) of components have velocity values exceeding those predicted by standard Galactic rotation by more than 40 km s(-1). Combining this data set with previous observations, we find that the median value of the reduced equivalent width (REW) of stars with z greater than or equal to 1 kpc (EW x sin ) is similar to 115 mAngstrom (n = 80), similar to that observed in extragalactic sightlines by Bowen. Using data of all z distances, the REW at infinity is found to be similar to 130 mAngstrom, with the scaleheight (1) of the Ca II K column density distribution being;z 800 pc (n = 196) and reduced column density at infinity of log[N(Ca II K) cm(-2)] similar to 12.24. This implies that similar to30 per cent of Ca II K absorption occurs at distances exceeding similar to1 kpc. For nine sightlines, with distance exceeding 1 kpc and with a companion object within 5degrees, we find that all but two have values of Ca II reduced equivalent width the same to within similar to20 per cent, when the REW of the nearest object is extrapolated to the distance of the further of the pair, and assuming 1 = 800 pc. For 29 of our sightlines with z greater than or equal to 1 kpc and a H I detection from the Leiden-Dwingeloo survey (beamsize of 0.5degrees), we find log(N(Ca II K)IN(H I)) ranging from -7.4 to - 8.4. Values of the Ca II K abundance relative to neutral hydrogen (log[N(Ca II K) cm(-2)] - log[N(H I) cm(-2)]) are found to be more than similar to0.5 dex higher in stars with distances exceeding approximate to100 pc, when compared with the (log[N(Ca II K) cm(-2)] -log[N(H-tot) cm(-2)]) values found in nearby sightlines such as those in Wakker & Mathis (2000). Finally, stellar Ca II K equivalent widths of the sample are determined for 26 objects.

CaII K interstellar observations towards early-type disc and halo stars - distances to intermediate- and high-velocity clouds

We compare existing high spectral resolution (R = lambda/Deltalambda similar to 40 000) Ca II Kobservations (lambda(air) = 3933.66 Angstrom) towards 88 mainly B-type stars, and new observations taken using the Intermediate dispersion Spectrograph and Imaging System (ISIS) on the William Herschel Telescope at R similar to 10 000 towards three stars taken from the Palomar-Green Survey, with 21-cm HI emission-line profiles, in order to search for optical absorption towards known intermediate- and high-velocity cloud complexes. Given certain assumptions, limits to the gas phase abundance of Ca II are estimated for the cloud components. We use the data to derive the following distances from the Galactic plane (z). (i) Tentative lower z-height limits of 2800 and 4100 pc towards complex C using lack of absorption in the spectra of HD341617 and PG 0855 + 294, respectively. (ii) A weak lower z-height of 1400 pc towards complex WA-WB using lack of absorption in EC 09470-1433 and a weak lower limit of 2470 pc using lack of absorption in EC 09452-1403. (iii) An upper z- height of 2470 pc towards a southern intermediate- velocity cloud (IVC) with v(LSR) = -55 km s(-1) using PG 2351 + 198. (iv) Detection of a possible IVC in Ca II absorption at v(LSR) = +52 km s(-1) using EC 20104-2944. No associated HI in emission is detected. At this position, normal Galactic rotation predicts velocities of up to similar to+ 25 km s(-1). The detection puts an upper z-height of 1860 pc to the cloud. (v) Tentative HI and Ca II K detections towards an IVC at similar to+70 km s(-1) in the direction of high-velocity cloud (HVC) complex WE, sightline EC 06387-8045, indicating that the IVC may be at a z-height lower than 1770 pc. (vi) Detection of Ca II K absorption in the spectrum of PG 0855 + 294 in the direction of IV20, indicating that this IVC has a z-height smaller than 4100 pc. (vii) A weak lower z-height of 4300 pc towards a small HVC with v(LSR) = +115 km s(-1) at l, b = 200degrees, + 52degrees, using lack of absorption in the Ca II K spectrum of PG 0955 + 291.

Oscillator strengths for transitions in C-like ions between K XIV and Mn XX

Energy levels and oscillator strengths (transition probabilities) have been calculated for transitions among 46 fine-structure levels of the (1s(2)) 2s(2) 2p(2), 2s2p(3),2p(4), 2s(2)2p3s, 2s(2) 2p3p and 2s(2)2p3d configurations of C-like K XIV, Sc XVI, Ti XVII, V XVIII, Cr XIX and Mn XX using the GRASP code. Configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels agree within 3% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.

Identification in the Ca II K spectral region of sharp-lined B- type stars

Previous Call K observations of the B-type star HD 83206 have revealed putative high-velocity interstellar clouds (HVCs) at Local Standard of Rest (LSR) velocities of -80 and -110 km s(- 1). Similar results were also found for the sightline towards HD135485. In this article, we show that these absorption lines are in fact due tr, stellar SII features. As the Call K absorption line in B-type stars is often used to assess the presence and distance of HVCs. we also present a very high quality spectrum of HD 83206 in the Ca II K region (similar to+/-4 Angstrom or +/-300 km s(-1)), so that in the future confusion between stellar lines and HVC features may be avoided.

Ca II K observations of QSOs in the line-of-sight to the Magellanic Bridge

We describe medium-resolution spectroscopic observations taken with the ESO Multi-Mode Instrument (EMMI) in the CaII K line (lambda air = 3933.661 angstrom) towards 7 QSOs located in the line-of-sight to the Magellanic Bridge. At a spectral resolution R =lambda/Delta lambda = 6000, five of the sightlines have a signal-to-noise ( S/N) ratio of similar to 20 or higher. Definite Ca absorption due to Bridge material is detected towards 3 objects, with probable detection towards two other sightlines. Gas-phase CaII K Bridge and Milky Way abundances or lower limits for the all sightlines are estimated by the use of Parkes 21-cm H. emission line data. These data only have a spatial resolution of 14 arcmin compared with the optical observations which have milli-arcsecond resolution. With this caveat, for the three objects with sound CaII K detections, we find that the ionic abundance of CaII K relative to HI, A = log( N( CaK)/ N( HI)) for low- velocity Galactic gas ranges from - 8.3 to - 8.8 dex, with HI column densities varying from 3- 6 x 10(20) cm(-2). For Magellanic Bridge gas, the values of A are similar to 0.5 dex higher, ranging from similar to- 7.8 to - 8.2 dex, with N( HI) = 1- 5 x 1020 cm(-2). Higher values of A correspond to lower values of N( HI), although numbers are small. For the sightline towards B 0251 - 675, the Bridge gas has two different velocities, and in only one of these is CaII tentatively detected, perhaps indicating gas of a different origin or present-day characteristics ( such as dust content), although this conclusion is uncertain and there is the possibility that one of the components could be related to the Magellanic Stream. Higher signal-to-noise CaII K data and higher resolution H. data are required to determine whether A changes with N( HI) over the Bridge and if the implied difference in the metalicity of the two Bridge components towards B 0251-675 is real.

Single- and multiphoton detachment of K

Single- and multiphoton detachment rates have been calculated for K- using the R-matrix Floquet approach. Single-photon detachment rates, obtained at a laser field peak intensity of 10(9) W cm(-2), are discussed and compared with other theoretical work. Two-photon detachment rates at the same intensity have also been obtained, and similarities with results from earlier calculations for Li- and Na- are discussed. Three-photon rates are also presented at this laser intensity, and are compared and contrasted with those arising in the single-photon case, since both involve resonance structure with P-1(o) symmetry. The influence of resonances such as the 5s(2) S-1(e) doubly excited state and excitations of the residual atom are also considered.