Regularity of Bound States

We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular Mourre theory which enables us to deal with confined massless Pauli-Fierz models, our primary example, and many-body AC-Stark Hamiltonians. In the simpler context of regular Mourre theory our results boils down to an improvement of results obtained recently in \cite{CGH}.Comment: 70 page

Efficient qubit detection using alkali earth metal ions and a double STIRAP process

We present a scheme for robust and efficient projection measurement of a qubit consisting of the two magnetic sublevels in the electronic ground state of alkali earth metal ions. The scheme is based on two stimulated Raman adiabatic passages (STIRAP) involving four partially coherent laser fields. We show how the efficiency depends on experimentally relevant parameters: Rabi frequencies, pulse widths, laser linewidths, one- and two-photon detunings, residual laser power, laser polarization and ion motion.Comment: 14 pages, 15 figure

Cancer mortality in the United Kingdom: projections to the year 2025

The purpose of this study was to project mortality rates in the United Kingdom for the period 2006–2025 for 21 major cancers on the basis of the observed trends in mortality rates during 1971–2005, and to estimate the implication in terms of expected deaths. Age-period-cohort models were applied to official statistics. The projected decrease in age-standardised mortality rates for all cancers from 2003 to 2023 was 17% in men and 16% in women. Future mortality rates were projected to decline for most cancer sites. In men, there were small projected increases in mortality rates from cancers of the oral cavity, oesophagus and melanoma, with a larger projected increase (14% over 20 years) in mortality of liver cancer. In women, the only projected increase (18%) was for corpus uteri. The numbers of deaths will increase for most cancers, with a 30% increase in all cancers projected for men and a 12% increase projected for women. Mortality rates from cancer as a whole have been falling in the United Kingdom since 1990, and this decline was projected to continue into the future as well as the declining rates in both sexes for most cancers. Actual numbers of deaths will increase for most cancers

Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version is shortened and the arguments streamlined. Minor changes in notation and figures. This version matches the published versio

Influence of gas flow rate on liquid distribution in trickle-beds using perforated plates as liquid distributors

Two wire mesh tomography devices and a liquid collector were used to study the influence of the gas flow rate on liquid distribution when fluids distribution on top of the reactor is ensured by a perforated plate. In opposition to most of the studies realized by other authors, conditions in which the gas has a negative impact in liquid distribution were evidenced. Indeed, the obtained results show that the influence of gas flow rate depends on the quality of the initial distribution, as the gas forces the liquid to "respect" the distribution imposed at the top of the reactor. Finally, a comparison between the two measuring techniques shows the limitations of the liquid collector and the improper conclusions to which its use could lead

On the sizes of z>2 Damped Lyman-alpha Absorbing Galaxies

Recently, the number of detected galaxy counterparts of z > 2 Damped Lyman-alpha Absorbers in QSO spectra has increased substantially so that we today have a sample of 10 detections. M{\o}ller et al. in 2004 made the prediction, based on a hint of a luminosity-metallicity relation for DLAs, that HI size should increase with increasing metallicity. In this paper we investigate the distribution of impact parameter and metallicity that would result from the correlation between galaxy size and metallicity. We compare our observations with simulated data sets given the relation of size and metallicity. The observed sample presented here supports the metallicity-size prediction: The present sample of DLA galaxies is consistent with the model distribution. Our data also show a strong relation between impact parameter and column density of HI. We furthermore compare the observations with several numerical simulations and demonstrate that the observations support a scenario where the relation between size and metallicity is driven by feedback mechanisms controlling the star-formation efficiency and outflow of enriched gas.Comment: Accepted for publishing in MNRAS lette

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit

Serendipitous discovery of a projected pair of QSOs separated by 4.5 arcsec on the sky

We present the serendipitous discovery of a projected pair of quasi-stellar objects (QSOs) with an angular separation of $\Delta\theta =4.50$ arcsec. The redshifts of the two QSOs are widely different: one, our programme target, is a QSO with a spectrum consistent with being a narrow line Seyfert 1 AGN at $z=2.05$. For this target we detect Lyman-$\alpha$, \ion{C}{4}, and \ion{C}{3]}. The other QSO, which by chance was included on the spectroscopic slit, is a Type 1 QSO at a redshift of $z=1.68$, for which we detect \ion{C}{4}, \ion{C}{3]} and \ion{Mg}{2}. We compare this system to previously detected projected QSO pairs and find that only about a dozen previously known pairs have smaller angular separation.Comment: 4 pages, 3 figures. Accepted for publication in A