Links between different analytic descriptions of constant mean curvature surfaces

Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system $$\begin{split} &\partial \psi_{1} = (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{2} \\ &\bar{\partial} \psi_{2} =- (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{1} \end{split}$$ descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out, that the instanton solutions correspond to different Weierstrass parametrizations of the standard sphere $S^{2} \subset E^{3}$

Patterns of Lorentz symmetry breaking in QED by CPT-odd interaction

A tiny Lorentz symmetry breaking can be mediated in Electrodynamics by means of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its presence makes the vacuum optically active that has been recently estimated from astrophysical data. We examine two possibilities for the CS vector to be time-like or space-like, under the assumption that it originates from v.e.v. of some pseudoscalar matter. It is shown that: a) a time-like CS vector makes the vacuum unstable under pairs creation of tachyonic photon modes with the finite vacuum decay rate, i.e. it is unlikely realized at macroscopic time scales; b) on the contrary, the space-like CS vector does not yield any tachyonic modes and, moreover, if its dynamical counterpart is substantially described by a scale invariant interaction, then the QED radiation effects induce the dynamical breaking of Lorentz symmetry, i.e. the occurrence of space-like CS vector appears to be rather natural.Comment: 9 pages, LaTeX, version to appear in Phys.Lett.

The use of systematic reviews in the planning, design and conduct of randomised trials: a retrospective cohort of NIHR HTA funded trials

BACKGROUND: A systematic review, with or without a meta-analysis, should be undertaken to determine if the research question of interest has already been answered before a new trial begins. There has been limited research on how systematic reviews are used within the design of new trials, the aims of this study were to investigate how systematic reviews of earlier trials are used in the planning and design of new randomised trials. METHODS: Documentation from the application process for all randomised trials funded by the National Institute for Health Research Health Technology Assessment (NIHR HTA) between 2006 and 2008 were obtained. This included the: commissioning brief (if appropriate), outline application, minutes of the Board meeting in which the outline application was discussed, full application, detailed project description, referee comments, investigator response to referee comments, Board minutes on the full application and the trial protocol. Data were extracted on references to systematic reviews and how any such reviews had been used in the planning and design of the trial. RESULTS: 50 randomised trials were funded by NIHR HTA during this period and documentation was available for 48 of these. The cohort was predominately individually randomised parallel trials aiming to detect superiority between two treatments for a single primary outcome. 37 trials (77.1%) referenced a systematic review within the application and 20 of these (i.e. 41.7% of the total) used information contained in the systematic review in the design or planning of the new trial. The main areas in which systematic reviews were used were in the selection or definition of an outcome to be measured in the trial (7 of 37, 18.9%), the sample size calculation (7, 18.9%), the duration of follow up (8, 21.6%) and the approach to describing adverse events (9, 24.3%). Boards did not comment on the presence/absence or use of systematic reviews in any application. CONCLUSIONS: Systematic reviews were referenced in most funded applications but just over half of these used the review to inform the design. There is an expectation from funders that applicants will use a systematic review to justify the need for a new trial but no expectation regarding further use of a systematic review to aid planning and design of the trial. Guidelines for applicants and funders should be developed to promote the use of systematic reviews in the design and planning of randomised trials, to optimise delivery of new studies informed by the most up-to-date evidence base and to minimise waste in research

Phemeranthus rugospermus (Holz.) Kiger

https://thekeep.eiu.edu/herbarium_specimens_byname/20844/thumbnail.jp

Metric of a tidally perturbed spinning black hole

We explicitly construct the metric of a Kerr black hole that is tidally perturbed by the external universe in the slow-motion approximation. This approximation assumes that the external universe changes slowly relative to the rotation rate of the hole, thus allowing the parameterization of the Newman-Penrose scalar $\psi_0$ by time-dependent electric and magnetic tidal tensors. This approximation, however, does not constrain how big the spin of the background hole can be and, in principle, the perturbed metric can model rapidly spinning holes. We first generate a potential by acting with a differential operator on $\psi_0$. From this potential we arrive at the metric perturbation by use of the Chrzanowski procedure in the ingoing radiation gauge. We provide explicit analytic formulae for this metric perturbation in spherical Kerr-Schild coordinates, where the perturbation is finite at the horizon. This perturbation is parametrized by the mass and Kerr spin parameter of the background hole together with the electric and magnetic tidal tensors that describe the time evolution of the perturbation produced by the external universe. In order to take the metric accurate far away from the hole, these tidal tensors should be determined by asymptotically matching this metric to another one valid far from the hole. The tidally perturbed metric constructed here could be useful in initial data constructions to describe the metric near the horizons of a binary system of spinning holes. This perturbed metric could also be used to construct waveforms and study the absorption of mass and angular momentum by a Kerr black hole when external processes generate gravitational radiation.Comment: 17 pages, 3 figures. Final PRD version, minor typos, etc corrected. v3: corrected typo in Eq. (35) and (57

Effective Values of Komar Conserved Quantities and Their Applications

We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effcetive values of mass and angular momentum are then used to derive an identity ($K_{\chi^{\mu}}=2ST$) which relates the Komar conserved charge ($K_{\chi^{\mu}}$) corresponding to the null Killing vector ($\chi^{\mu}$) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.Comment: v3, minor modifications over v2; LaTex, 9 pages, no figures, to appear in Int. Jour. Theo. Phy

The optical system of the H.E.S.S. imaging atmospheric Cherenkov telescopes, Part II: mirror alignment and point spread function

Mirror facets of the H.E.S.S. imaging atmospheric Cherenkov telescopes are aligned using stars imaged onto the closed lid of the PMT camera, viewed by a CCD camera. The alignment procedure works reliably and includes the automatic analysis of CCD images and control of the facet alignment actuators. On-axis, 80% of the reflected light is contained in a circle of less than 1 mrad diameter. The spot widens with increasing angle to the telescope axis. In accordance with simulations, the spot size has roughly doubled at an angle of 1.4 degr. from the axis. The expected variation of spot size with elevation due to deformations of the support structure is visible, but is completely non-critical over the usual working range. Overall, the optical quality of the telescope exceeds the specifications.Comment: 23 pages, 13 figure

Testing Non-commutative QED, Constructing Non-commutative MHD

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.Comment: 14 pages, LaTeX; minor corrections, references adde