Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly

We present the results of analytical calculations of the 3-loop contributions to the asymptotic photon vacuum polarization function, in the on shell scheme, and of the 4-loop contributions to the on shell QED beta-function. These are used to evaluate various 4-loop and 5-loop contributions to the muon anomaly. Our analytical contributions to (g-2)_\mu differ significantly from previous numerical results. A very recent numerical re-evaluation of 4-loop muon-anomaly contributions has yielded results much closer to ours.Comment: LaTex, 11 pages, figures available from O.V.T. CERN--TH. 6602/92, OUT--4102--39, BI--TP--92/3

Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

Flotation of coal and sulphur from South African ultrafine colliery wastes

Flotation of coal and sulphur from a typical South African ultrafine colliery waste has been achieved in laboratory-scale batch flotation tests, using dodecane, kerosene, and oleic acid as coal collectors, and xanthates to float the sulphide minerals (with the aid of dextrin as a coal depressant). The use of oleic acid as collector, in conjunction with MIBC frother, produced a coal yield of 56 per cent (much more than was obtained with dodecane or kerosene) at an ash content of 18 per cent, from a feed ash of 34.4 per cent; and a low- sulphur tailings. Sulphide flotation using potassium xanthate (PAX) recovered 26.3 per cent of the total sulphur in the concentrate. Staged addition of xanthate increased the total sulphur recovery to 42.1 per cent and reduced the sulphur content of the tailing further

LensPerfect: Gravitational Lens Massmap Reconstructions Yielding Exact Reproduction of All Multiple Images

We present a new approach to gravitational lens massmap reconstruction. Our massmap solutions perfectly reproduce the positions, fluxes, and shears of all multiple images. And each massmap accurately recovers the underlying mass distribution to a resolution limited by the number of multiple images detected. We demonstrate our technique given a mock galaxy cluster similar to Abell 1689 which gravitationally lenses 19 mock background galaxies to produce 93 multiple images. We also explore cases in which far fewer multiple images are observed, such as four multiple images of a single galaxy. Massmap solutions are never unique, and our method makes it possible to explore an extremely flexible range of physical (and unphysical) solutions, all of which perfectly reproduce the data given. Each reconfiguration of the source galaxies produces a new massmap solution. An optimization routine is provided to find those source positions (and redshifts, within uncertainties) which produce the "most physical" massmap solution, according to a new figure of merit developed here. Our method imposes no assumptions about the slope of the radial profile nor mass following light. But unlike "non-parametric" grid-based methods, the number of free parameters we solve for is only as many as the number of observable constraints (or slightly greater if fluxes are constrained). For each set of source positions and redshifts, massmap solutions are obtained "instantly" via direct matrix inversion by smoothly interpolating the deflection field using a recently developed mathematical technique. Our LensPerfect software is straightforward and easy to use and is made publicly available via our website.Comment: 17 pages, 18 figures, accepted by ApJ. Software and full-color version of paper available at http://www.its.caltech.edu/~coe/LensPerfect

Managing shoulder pain in general practice: The value of academic detailing

Copyright © Royal Australian College of General Practitioners Copyright to Australian Family Physician. Reproduced with permission. Permission to reproduce must be sought from the publisher, The Royal Australian College of General Practitioners.After low back pain and neck pain, shoulder pain is the third musculoskeletal reason for presentation to general practice, with a self reported prevalence of 16-26%. Approximately 1% of the adult population is expected to visit a general practitioner annually for shoulder pain. Shoulder complaints are more common in women and despite the fact that 50% of acute shoulder pain resolves in 8-10 weeks, many patients present with the anticipation of being referred for imaging.Norman A. Broadhurst, Christopher A. Barton, Lisa N. Yelland, David K. Martin and Justin J. Beilb

Young Red Spheroidal Galaxies in the Hubble Deep Fields: Evidence for a Truncated IMF at ~2M_solar and a Constant Space Density to z~2

The optical-IR images of the Northern and Southern Hubble Deep Fields are used to measure the spectral and density evolution of early-type galaxies. The mean optical SED is found to evolve passively towards a mid F-star dominated spectrum by z ~ 2. We demonstrate with realistic simulations that hotter ellipticals would be readily visible if evolution progressed blueward and brightward at z > 2, following a standard IMF. The colour distributions are best fitted by a `red' IMF, deficient above ~2 M_solar and with a spread of formation in the range 1.5 < z_f < 2.5. Traditional age dating is spurious in this context, a distant elliptical can be young but appear red, with an apparent age >3 Gyrs independent of its formation redshift. Regarding density evolution, we demonstrate that the sharp decline in numbers claimed at z > 1 results from a selection bias against distant red galaxies in the optical, where the flux is too weak for morphological classification, but is remedied with relatively modest IR exposures revealing a roughly constant space density to z ~ 2. We point out that the lack of high mass star-formation inferred here and the requirement of metals implicates cooling-flows of pre-enriched gas in the creation of the stellar content of spheroidal galaxies. Deep-field X-ray images will be very helpful to examine this possibility.Comment: 6 pages, 3 figures, submitted to Astrophysical Journal Letters, typographical errors corrected, simulated images with different IMFs illustrated at http://astro.berkeley.edu/~bouwens/ellip.htm