On a semiclassical formula for non-diagonal matrix elements

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.Comment: LaTeX2

Severe Loss of Tritan Color Discrimination in RPE65 Associated Leber Congenital Amaurosis

Purpose: RPE65-associated Leber congenital amaurosis (RPE65-LCA) is a progressive severe retinal dystrophy with early profound dysfunction of rod photoreceptors followed by progressive cone photoreceptor degeneration. We aim to provide detailed information about how cone dysfunction affects color discrimination. Methods: Seven adults (aged 16-21) with RPE65-LCA underwent monocular color discrimination assessment using the Trivector and Ellipse versions of three computerized tests: Cambridge Colour Test (CCT), low vision version of the Cambridge Colour Test (lvvCCT), and the Universal Colour Discrimination Test (UCDT). For comparison, subjects were also tested using the American Optical Hardy Rand Rittler (AO-HRR) plates. Each assessment was repeated three times. Results: The Trivector version of the tests demonstrated that color discrimination along the tritan axis was undetectable in four subjects, and severely reduced in three subjects. These findings were confirmed by the Ellipse version of the tests. Color discrimination along the protan and deutan axes was evident but reduced in six of seven subjects. Four of seven subjects were unable to read any of the HRR plates. Conclusions: The computerized color vision tests adopted in this study provide detailed information about color discrimination in adult RPE65-LCA patients. The condition is associated with severe impairment of color discrimination, particularly along the tritan axis indicating possible early involvement of S-cones, with additional protan and deutan loss to a lesser extent. This psychophysical assessment strategy is likely to be valuable in measuring the impact of therapeutic intervention on cone function

Bismuth vanadate photoanodes for water splitting deposited by radio frequency plasma reactive co-sputtering

Photoactive bismuth vanadate (BiVO4) thin coatings were deposited on fluorine-doped tin oxide glass by plasma reactive sputtering from Bi2O3 and vanadium (V) radio frequency (RF) powered targets. The films were characterized by x-ray diffraction, scanning electron microscopy, energy dispersion spectroscopy, and UV-vis spectroscopy. The effects that the power density supplied to the Bi2O3 target, the post-annealing treatment, and the film thickness have on the structural features and on the photoelectrochemical (PEC) performances of the so obtained BiVO4 film-based photoelectrodes were investigated. Their PEC performance in water splitting was evaluated in a three-electrode cell by both incident photon to current efficiency (IPCE) and linear sweep voltammetry measurements under AM 1.5 G simulated solar light irradiation. A monoclinic phase of BiVO4, which is more photoactive than the tetragonal BiVO4 phase, was obtained by optimizing the power density supplied to the Bi2O3 target, i.e., by tuning the Bi:V:O atomic ratio. The best PEC performance was obtained for a stoichiometric 1:1 Bi:V atomic ratio, attained with 20 W power supplied at the Bi2O3 target and 300 W power supplied at the vanadium target, and an optimal 200 nm thickness of the BiVO4 film, with a 0.65 mA/cm2 photocurrent density attained at 1.23 V vs. standard calomel electrode, under simulated solar light. These results show the suitability of plasma reactive sputtering with two RF powered electrodes for the deposition of BiVO4 photoanodes for water splitting

Low-Mass Relics of Early Star Formation

The earliest stars to form in the Universe were the first sources of light, heat and metals after the Big Bang. The products of their evolution will have had a profound impact on subsequent generations of stars. Recent studies of primordial star formation have shown that, in the absence of metals (elements heavier than helium), the formation of stars with masses 100 times that of the Sun would have been strongly favoured, and that low-mass stars could not have formed before a minimum level of metal enrichment had been reached. The value of this minimum level is very uncertain, but is likely to be between 10^{-6} and 10^{-4} that of the Sun. Here we show that the recent discovery of the most iron-poor star known indicates the presence of dust in extremely low-metallicity gas, and that this dust is crucial for the formation of lower-mass second-generation stars that could survive until today. The dust provides a pathway for cooling the gas that leads to fragmentation of the precursor molecular cloud into smaller clumps, which become the lower-mass stars.Comment: Offprint of Nature 422 (2003), 869-871 (issue 24 April 2003

Dark Stars and Boosted Dark Matter Annihilation Rates

Dark Stars (DS) may constitute the first phase of stellar evolution, powered by dark matter (DM) annihilation. We will investigate here the properties of DS assuming the DM particle has the required properties to explain the excess positron and elec- tron signals in the cosmic rays detected by the PAMELA and FERMI satellites. Any possible DM interpretation of these signals requires exotic DM candidates, with an- nihilation cross sections a few orders of magnitude higher than the canonical value required for correct thermal relic abundance for Weakly Interacting Dark Matter can- didates; additionally in most models the annihilation must be preferentially to lep- tons. Secondly, we study the dependence of DS properties on the concentration pa- rameter of the initial DM density profile of the halos where the first stars are formed. We restrict our study to the DM in the star due to simple (vs. extended) adiabatic contraction and minimal (vs. extended) capture; this simple study is sufficient to illustrate dependence on the cross section and concentration parameter. Our basic results are that the final stellar properties, once the star enters the main sequence, are always roughly the same, regardless of the value of boosted annihilation or concentration parameter in the range between c=2 and c=5: stellar mass ~ 1000M\odot, luminosity ~ 10^7 L\odot, lifetime ~ 10^6 yrs (for the minimal DM models considered here; additional DM would lead to more massive dark stars). However, the lifetime, final mass, and final luminosity of the DS show some dependence on boost factor and concentration parameter as discussed in the paper.Comment: 37 pages, 11 figure

A metal rich molecular cloud surrounds GRB 050904 at redshift 6.3

GRB050904 is the gamma-ray burst with the highest measured redshift. We performed time resolved X-ray spectroscopy of the late GRB and early afterglow emission. We find robust evidence for a decrease with time of the soft X-ray absorbing column. We model the evolution of the column density due to the flash ionization of the GRB and early afterglow photons. This allows us to constrain the metallicity and geometry of the absorbing cloud. We conclude that the progenitor of GRB050904 was a massive star embedded in a dense metal enriched molecular cloud with Z~0.03 Z_solar. This is the first local measurement of metallicity in the close environment of a GRB and one of the highest redshift metallicity measurements. We also find that the dust associated with the cloud cannot be similar to that of our Galaxy but must be either sizably depleted or dominated by silicate grains. We discuss the implications of these results for GRB progenitors and high redshift star formation.Comment: 4 pages, 2 figures. Accepted for publication on Astrophysical Journal Letter

Galactic neutron stars I. Space and velocity distributions in the disk and in the halo

Aims. Neutron stars (NSs) produced in the Milky Way are supposedly ten to the eighth - ten to the ninth, of which only $\sim 2 \times 10^{3}$ are observed. Constraining the phase space distribution of NSs may help to characterize the yet undetected population of stellar remnants. Methods. We perform Monte Carlo simulations of NS orbits, under different assumptions concerning the Galactic potential and the distribution of progenitors and birth velocities. We study the resulting phase space distributions, focusing on the statistical properties of the NS populations in the disk and in the solar neighbourhood. Results. It is shown that $\sim 80$ percent of NSs are in bound orbits. The fraction of NSs located in a disk of radius 20 kpc and width 0.4 kpc is $\lesssim 20$ percent. Therefore the majority of NSs populate the halo. Fits for the surface density of the disk, the distribution of heights on the Galactic plane and the velocity distribution of the disk, are given. We also provide sky maps of the projected number density in heliocentric Galactic coordinates (l, b). Our results are compared with previous ones reported in the literature. Conclusions. Obvious applications of our modelling are in the revisiting of accretion luminosities of old isolated NSs, the issue of the observability of the nearest NS and the NS optical depth for microlensing events. These will be the scope of further studies.Comment: 11 pages, 15 figures, accepted for publication in Astronomy and Astrophysic

Prognostic evaluation in patients with advanced cancer in the last months of life:ESMO Clinical Practice Guideline

: • This ESMO Clinical Practice Guideline provides key recommendations for using prognostic estimates in advanced cancer. • The guideline covers recommendations for patients with cancer and an expected survival of months or less. • An algorithm for use of clinical predictions, prognostic factors and multivariable risk prediction models is presented. • The author group encompasses a multidisciplinary group of experts from different institutions in Europe, USA and Asia. • Recommendations are based on available scientific data and the authors’ collective expert opinion

Total hip arthroplasty in an inveterate femoral neck fracture in a patient with congenital insensitivity to pain with anhidrosis

Congenital insensitivity to pain with anhidrosis (CIPA) is an extremely rare disorder characterized by autonomic and sensory nerves malfunction with insensitivity to both deep and superficial painful stimuli, inability to sweat and produce tears, and mild to moderate mental retardation with self-mutilating behavior. Related consequences of inveterate musculoskeletal injuries represent a major issue for these patients, since pain cannot act as a protectionmechanism. For the same reason, the patients are at risk during postoperative rehabilitation, which should be taken into account when selecting an orthopaedic implant. To our knowledge, only one case of total hip arthroplasty has been reported in the literature to date. A 21-year-old Caucasian male patient affected with CIPA arrived at our attention complaining about a functional limitation of the left hip. No history of trauma was reported. The X-rays showed an inveterate femoral neck fracture with a severe necrosis and resorption of the femoral head. We decided to performa total hip arthroplasty with a cemented stem and a cemented dual mobility cup. The postoperative course and rehabilitation were satisfactory, with excellent clinical results, measured with the Harris Hip Score at 1 year

Observational Manifestations of the First Protogalaxies in the 21 cm Line

The absorption properties of the first low-mass protogalaxies (mini-halos) forming at high redshifts in the 21-cm line of atomic hydrogen are considered. The absorption properties of these protogalaxies are shown to depend strongly on both their mass and evolutionary status. The optical depths in the line reach $\sim$0.1-0.2 for small impact parameters of the line of sight. When a protogalaxy being compressed, the influence of gas accretion can be seen manifested in a non-monotonic frequency dependence of the optical depth. The absorption characteristics in the 21-cm line are determined by the thermal and dynamical evolution of the gas in protogalaxies. Since the theoretical line width in the observer's reference frame is 1-6 kHz and the expected separation between lines 8.4 kHz, the lines from low mass protogalaxies can be resolved using ongoing and future low frequency interferometers.Comment: 12 pages, 5 figure