The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients

Consider the Schroeodinger equation: - Du(x) - l(x)u + s(x)u = 0, where D is the Laplacian, l(x) > 0 and s(x) is dominated by l(x). We shall extend the celebrated Kato's result on the asymptotic behavior of the solution to the case where l(x) has unbounded discontinuity. The result will be used to establish the limiting absorption principle for a class of reduced wave operators with discontinuous coefficients.Comment: 29 (twenty-nine) pages; no figures; to appear in Reviews of Mathematical Physic

X-ray Diagnostics of Thermal Conditions of the Hot Plasmas in the Centaurus Cluster

X-ray data of the Centaurus cluster, obtained with {\it XMM-Newton} for 45 ksec, were analyzed. Deprojected EPIC spectra from concentric thin shell regions were reproduced equally well by a single-phase plasma emission model, or by a two-phase model developed by {\it ASCA}, both incorporating cool (1.7--2.0 keV) and hot ($\sim 4$ keV) plasma temperatures. However, EPIC spectra with higher statistics, accumulated over 3-dimentional thick shell regions, were reproduced better by the two-phase model than by the singe-phase one. Therefore, hot and cool plasma phases are inferred to co-exist in the cluster core region within $\sim 70$ kpc. The iron and silicon abundances of the plasma were reconfirmed to increase significantly towards the center, while that of oxygen was consistent with being radially constant. The implied non-solar abundance ratios explains away the previously reported excess X-ray absorption from the central region. Although an additional cool ($\sim 0.7$ keV) emission was detected within $\sim 20$ kpc of the center, the RGS data gave tight upper limits on any emission with a tempeartures below $\sim 0.5$ keV. These results are compiled into a magnetosphere model, which interprets the cool phase as confined within closed magnetic loops anchored to the cD galaxy. When combined with so-called Rosner-Tucker-Vaiana mechanism which applies to solar coronae, this model can potentially explain basic properties of the cool phase, including its temperature and thermal stability.Comment: 53 pages, 11 figures, accepted for publication in Astrophysical Journa

Optical Hall Effect in the Integer Quantum Hall Regime

Optical Hall conductivity $\sigma_{xy}(\omega)$ is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz frequency regime. The Faraday rotation angle ($\sim$ fine structure constant $\sim$ mrad) is found to significantly deviate from the Drude-like behavior to exhibit a plateau-like structure around the Landau-level filling $\nu=2$. The result, which fits with the behavior expected from the carrier localization effect in the ac regime, indicates that the plateau structure, although not quantized, still exists in the terahertz regime.Comment: 4 pages, 4 figure

Highly Frequent Mutations in Negative Regulators of Multiple Virulence Genes in Group A Streptococcal Toxic Shock Syndrome Isolates

Streptococcal toxic shock syndrome (STSS) is a severe invasive infection characterized by the sudden onset of shock and multiorgan failure; it has a high mortality rate. Although a number of studies have attempted to determine the crucial factors behind the onset of STSS, the responsible genes in group A Streptococcus have not been clarified. We previously reported that mutations of csrS/csrR genes, a two-component negative regulator system for multiple virulence genes of Streptococcus pyogenes, are found among the isolates from STSS patients. In the present study, mutations of another negative regulator, rgg, were also found in clinical isolates of STSS patients. The rgg mutants from STSS clinical isolates enhanced lethality and impaired various organs in the mouse models, similar to the csrS mutants, and precluded their being killed by human neutrophils, mainly due to an overproduction of SLO. When we assessed the mutation frequency of csrS, csrR, and rgg genes among S. pyogenes isolates from STSS (164 isolates) and non-invasive infections (59 isolates), 57.3% of the STSS isolates had mutations of one or more genes among three genes, while isolates from patients with non-invasive disease had significantly fewer mutations in these genes (1.7%). The results of the present study suggest that mutations in the negative regulators csrS/csrR and rgg of S. pyogenes are crucial factors in the pathogenesis of STSS, as they lead to the overproduction of multiple virulence factors

Statistics of X-ray observables for the cooling-core and non-cooling core galaxy clusters

We present a statistical study of the occurrence and effects of the cooling cores in the clusters of galaxies in a flux-limited sample, HIFLUGCS, based on ROSAT and ASCA observations. About 49% of the clusters in this sample have a significant, classically-calculated cooling-flow, mass-deposition rate. The upper envelope of the derived mass-deposition rate is roughly proportional to the cluster mass, and the fraction of cooling core clusters is found to decrease with it. The cooling core clusters are found to have smaller core radii than non-cooling core clusters, while some non-cooling core clusters have high $\beta$ values (> 0.8). In the relation of the X-ray luminosity vs. the temperature and the mass, the cooling core clusters show a significantly higher normalization. A systematic correlation analysis, also involving relations of the gas mass and the total infrared luminosity, indicates that this bias is shown to be mostly due to an enhanced X-ray luminosity for cooling core clusters, while the other parameters, like temperature, mass, and gas mass may be less affected by the occurrence of a cooling core. These results may be explained by at least some of the non-cooling core clusters being in dynamically young states compared with cooling core clusters, and they may turn into cooling core clusters in a later evolutionary stage

Detection of an X-Ray Hot Region in the Virgo Cluster of Galaxies with ASCA

Based on mapping observations with ASCA, an unusual hot region with a spatial extent of 1 square degree was discovered between M87 and M49 at a center coordinate of R. A. = 12h 27m 36s and Dec. = $9^\circ18'$ (J2000). The X-ray emission from the region has a 2-10 keV flux of $1 \times 10^{-11}$ ergs s$^{-1}$ cm$^{-2}$ and a temperature of $kT \gtrsim 4$ keV, which is significantly higher than that in the surrounding medium of $\sim 2$ keV. The internal thermal energy in the hot region is estimated to be $V n k T \sim 10^{60}$ ergs with a gas density of $\sim 10^{-4}$ cm$^{-3}$. A power-law spectrum with a photon index $1.7-2.3$ is also allowed by the data. The hot region suggests there is an energy input due to a shock which is probably caused by the motion of the gas associated with M49, infalling toward the M87 cluster with a velocity $\gtrsim 1000$ km s$^{-1}$.Comment: 12 pages, 3 figures, accepted to ApJ

The galaxy cluster X-ray luminosity--gravitational mass relation in the light of the WMAP 3rd year data

The 3rd year WMAP results mark a shift in best fit values of cosmological parameters compared to the 1st year data and the concordance cosmological model. We test the consistency of the new results with previous constraints on cosmological parameters from the HIFLUGCS galaxy cluster sample and the impact of this shift on the X-ray luminosity-gravitational mass relation. The measured X-ray luminosity function combined with the observed luminosity-mass relation are compared to mass functions predicted for given cosmological parameter values. The luminosity function and luminosity-mass relation derived previously from HIFLUGCS are in perfect agreement with mass functions predicted using the best fit parameter values from the 3rd year WMAP data (OmegaM=0.238, sigma8=0.74) and inconsistent with the concordance cosmological model (OmegaM=0.3, sigma8=0.9), assuming a flat Universe. Trying to force consistency with the concordance model requires artificially decreasing the normalization of the luminosity-mass relation by a factor of 2. The shift in best fit values for OmegaM and sigma8 has a significant impact on predictions of cluster abundances. The new WMAP results are now in perfect agreement with previous results on the OmegaM-sigma8 relation determined from the mass function of HIFLUGCS clusters and other X-ray cluster samples (the ``low cluster normalization''). We conclude that - unless the true values of OmegaM and sigma8 differ significantly from the 3rd year WMAP results - the luminosity-mass relation is well described by their previous determination from X-ray observations of clusters, with a conservative upper limit on the bias factor of 1.5. These conclusions are currently being tested in a complete follow-up program of all HIFLUGCS clusters with Chandra and XMM-Newton.Comment: 4 pages; A&A Letters, in press; replaced to match accepted version; also available at http://www.reiprich.ne

UV observations of the galaxy cluster Abell 1795 with the optical monitor on XMM-Newton

We present the results of an analysis of broad band UV observations of the central regions of Abell 1795 observed with the optical monitor on XMM-Newton. As have been found with other UV observations of the central regions of clusters of galaxies, we find evidence for star formation. However, we also find evidence for absorption in the cD galaxy on a more extended scale than has been seen with optical imaging. We also report the first UV observation of part of the filamentary structure seen in H$\alpha$, X-rays and very deep U band imaging. The part of the filament we see is very blue with UV colours consistent with a very early (O/B) stellar population. This is the first direct evidence of a dominant population of early type stars at the centre of Abell 1795 and implies very recent star formation at the centre of this clusterComment: 6 pages, 3 figures accepted by A&A Letter