Counting irreducible binomials over finite fields

We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.Comment: 11 page

On Shifted Eisenstein Polynomials

We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials. We determine an upper bound on the maximum shift that is needed given a shifted Eisenstein polynomial and also provide a lower bound on the density of shifted Eisenstein polynomials, which is strictly greater than the density of classical Eisenstein polynomials. We also show that the number of irreducible degree $n$ polynomials that are not shifted Eisenstein polynomials is infinite. We conclude with some numerical results on the densities of shifted Eisenstein polynomials

On the Number of Eisenstein Polynomials of Bounded Height

We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\to \infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$

Effects of Ray Sediment Disturbance on Meiofauna in Tidal and Intertidal Zones

Feeding pits created by rays may directly or indirectly affect the num­bers of meiofauna. We examined the recovery rates of meiofauna inside feeding pits in both intertidal and subtidal areas. Cores were taken inside and immediately outside each pit. Numbers of total meiofauna, nematodes, and other meiofauna found within intertidal pits were significantly reduced following pit formation; the numerically dominant nematodes were reduced by 64%. Recovery to background levels occurred by 48 hours. Numbers of meiofauna in subtidal pits were either unaffected by the feeding activity of rays or differences were undetected due to rapid recovery within 24 h. This is the first study in which comparisons have been made concurrently in adjacent subtidal and intertidal areas

OH rotational lines as a diagnostic of the warm neutral gas in galaxies

We present Infrared Space Observatory (ISO) observations of several OH, CH and H2O rotational lines toward the bright infrared galaxies NGC253 and NGC1068. As found in the Galactic clouds in SgrB2 and Orion, the extragalactic far-IR OH lines change from absorption to emission depending on the physical conditions and distribution of gas and dust along the line of sight. As a result, most of the OH rotational lines that appear in absorption toward NGC253 are observed in emission toward NGC1068. We show that the far-IR spectrum of OH can be used as a powerful diagnostic to derive the physical conditions of extragalactic neutral gas. In particular, we find that a warm (Tk~150 K, n(H2)< 5 10^4 cm^-3) component of molecular gas with an OH abundance of 10^{-7} from the inner <15'' can qualitatively reproduce the OH lines toward NGC253. Similar temperatures but higher densities (5 10^5 cm^-3) are required to explain the OH emission in NGC1068.Comment: 5 pages, 4 figures, accepted in ApJ Part I (2004, October 6

Extragalactic Zeeman Detections in OH Megamasers

We have measured the Zeeman splitting of OH megamaser emission at 1667 MHz from five (ultra)luminous infrared galaxies ([U]LIRGs) using the 305 m Arecibo telescope and the 100 m Green Bank Telescope. Five of eight targeted galaxies show significant Zeeman-splitting detections, with 14 individual masing components detected and line-of-sight magnetic field strengths ranging from ~0.5-18 mG. The detected field strengths are similar to those measured in Galactic OH masers, suggesting that the local process of massive star formation occurs under similar conditions in (U)LIRGs and the Galaxy, in spite of the vastly different large-scale environments. Our measured field strengths are also similar to magnetic field strengths in (U)LIRGs inferred from synchrotron observations, implying that milligauss magnetic fields likely pervade most phases of the interstellar medium in (U)LIRGs. These results provide a promising new tool for probing the astrophysics of distant galaxies.Comment: 32 pages, 14 figures, 8 tables. Accepted for publication in The Astrophysical Journal v680n2, June 20, 2008; corrected 2 typo

Offloading devices for the prevention of heel pressure ulcers: a realist evaluation

Background Heel pressure ulcers can cause pain, reduce mobility, lead to longer hospital stays and in severe cases can lead to sepsis, amputation, and death. Offloading boots are marketed as heel pressure ulcer prevention devices, working by removing pressure to the heel, yet there is little good quality evidence about their clinical effectiveness. Given that evidence is not guiding use of these devices, this study aims to explore, how, when, and why these devices are used in hospital settings. Objective To explore how offloading devices are used to prevent heel pressure ulcers, for whom and in what circumstances. Methods A realist evaluation was undertaken to explore the contexts, mechanisms, and outcomes that might influence how offloading devices are implemented and used in clinical practice for the prevention of heel pressure ulcers in hospitals. Eight Tissue Viability Nurse Specialists from across the UK (England, Wales, and Northern Ireland) were interviewed. Questions sought to elicit whether, and in what ways, initial theories about the use of heel pressure ulcers fitted with interviewee's experiences. Results Thirteen initial theories were refined into three programme theories about how offloading devices are used by nurses ‘proactively’ to prevent heel pressure ulcers, ‘reactively’ to treat and minimise deterioration of early-stage pressure ulcers, and patient factors that influence how these devices are used. Conclusions Offloading devices were used in clinical practice by all the interviewees. It was viewed that they were not suitable to be used by every patient, at every point in their inpatient journey, nor was it financially viable. However, the interviewees thought that identifying suitable ‘at risk’ patient groups that can maintain use of the devices could lead to proactive and cost-effective use of the devices. This understanding of the contexts and mechanisms that influence the effective use of offloading devices has implications for clinical practice and design of clinical trials of offloading devices. Tweetable abstract How, for whom, and in what circumstances do offloading devices work to prevent heel pressure ulcers? Tissue viability nurses' perspectives