Integral closure of rings of integer-valued polynomials on algebras

Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic polynomial of least degree such that $\mu_a(a)=0$. The ring ${\rm Int}_K(A)$ consists of polynomials in $K[X]$ that send elements of $A$ back to $A$ under evaluation. If $D$ has finite residue rings, we show that the integral closure of ${\rm Int}_K(A)$ is the ring of polynomials in $K[X]$ which map the roots in an algebraic closure of $K$ of all the $\mu_a(X)$, $a\in A$, into elements that are integral over $D$. The result is obtained by identifying $A$ with a $D$-subalgebra of the matrix algebra $M_n(K)$ for some $n$ and then considering polynomials which map a matrix to a matrix integral over $D$. We also obtain information about polynomially dense subsets of these rings of polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix, integral closure, pullback, polynomially dense set. accepted for publication in the volume "Commutative rings, integer-valued polynomials and polynomial functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201

Jet-Induced Emission-Line Nebulosity and Star Formation in the High-Redshift Radio Galaxy 4C41.17

The high redshift radio galaxy 4C41.17 consists of a powerful radio source in which previous work has shown that there is strong evidence for jet-induced star formation along the radio axis. We argue that nuclear photoionization is not responsible for the excitation of the emission line clouds and we construct a jet-cloud interaction model to explain the major features revealed by the data. The interaction of a high-powered jet with a dense cloud in the halo of 4C41.17 produces shock-excited emission-line nebulosity through ~1000 km/s shocks and induces star formation. The CIII to CIV line ratio and the CIV luminosity emanating from the shock, imply that the pre-shock density in the line-emitting cloud is high enough (~1-10 cm^-3) that shock initiated star formation could proceed on a timescale of order a few x 10^6 yrs, well within the estimated dynamical age of the radio source. Broad (FWHM ~ 100 - 1400 km/s) emission lines are attributed to the disturbance of the gas cloud by a partial bow--shock and narrow emission lines (FWHM ~ 500 - 650 km/s) (in particular CIV) arise in precursor emission in relatively low metallicity gas. The implied baryonic mass ~ 8 \times 10^{10} solar masses of the cloud is high and implies that Milky Way size condensations existed in the environments of forming radio galaxies at a redshift of 3.8. Our interpretation of the data provides a physical basis for the alignment of the radio, emission-line and UV continuum images in some of the highest redshift radio galaxies and the analysis presented here may form a basis for the calculation of densities and cloud masses in other high redshift radio galaxies.Comment: 18 pages, 5 figures; uses astrobib.sty and aaspp4.sty. Better versions of figures available via anonymous from ftp://mso.anu.edu.au:pub/pub/geoff/4C41.1

Rethinking place and the social work office in the delivery of children's social work services

Limited attention has been given to the concept of place in social work research and practice. This paper draws on the national evaluation of social work practices (SWPs) in England undertaken between 2009 and 2012. SWPs were pilot organisations providing independent social work services for children in out-of-home care in five sites. One factor distinguishing some of these pilots was their attention to place. The evaluation employed a mixed methods approach and we use data from interviews with 121 children and young people in out-of-home care, 19 birth parents and 31 interviews with SWP staff which explored their views and experiences of the SWP offices. Children and young people were alert to the stigma which could attach to social work premises and appreciated offices which were planned and furnished to appear less institutional and more ‘normal’. Daily interactions with staff which conveyed a sense of recognition and value to service users also contributed to a view of some SWP offices as accessible and welcoming places. Both children and parents appreciated offices that provided fun activities that positioned them as active rather than passive. Staff valued opportunities for influencing planning decisions about offices and place was seen to confer a value on them as well as on service users. However, not all the SWPs were able to achieve these aspects of place, and engaging children and families in place was less likely when the service user population was widely dispersed. Recognising the importance of place and how place is constructed through relationships between people as well as through the physical environment appeared to be key to creating offices that combated the stigma attached to out-of-home care. Those leading and managing children’s services should explore ways of involving local communities in planning social work offices and turn attention to making these offices accessible, welcoming, places

PKS2250-41: a case study for triggering

We present the results of a multiwavelength study of the z = 0.31 radio source PKS2250-41. Integral field unit and long-slit spectroscopy obtained using VIMOS and FORS1 on the VLT, and archival HST optical imaging observations are used to study the morphology, kinematics and ionisation state of the extended emission line region (EELR) surrounding this source, and also a companion galaxy at a similar redshift. Near-infrared imaging observations obtained using the NTT are used to analyse the underlying galaxy morphologies. The EELR displays a complex variety of different gas kinematics and ionization states, consistent with a mixture of radio source shocks and AGN photoionization. The radio galaxy is likely to lie within a group environment, and is plausibly undergoing interactions with one or more other objects. The disk-like galaxy to the northeast of the radio source lies at a similar redshift to the radio galaxy itself, and has its major axis position angle aligned with the filamentary continuum and line emission extending outwards from the radio galaxy. This filamentary structure is most plausibly interpreted as a tidal structure associated with an interaction involving the radio source host galaxy and the aligned companion galaxy to the north-east; this encounter may have potentially triggered the current epoch of radio source activity. Overall, PKS2250-41 displays some of the best evidence that radio source activity can be triggered in this manner. [abridged]Comment: 16 pages, 13 figures (some colour). Accepted for publication in MNRAS. Abstract abridge

Consistent Quantum Counterfactuals

An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum reasoning together with the ``one framework'' rule prevents a logical contradiction, and there is no evidence for any mysterious nonlocal influences. Counterfactual reasoning can support a realistic interpretation of standard quantum theory (measurements reveal what is actually there) under appropriate circumstances.Comment: Minor modifications to make it agree with published version. Latex 8 pages, 2 figure

Terrorism Preparedness in State Health Departments --- United States, 2001--2003

The anthrax attacks in fall 2001 highlighted the role of infectious disease (ID) epidemiologists in terrorism preparedness and response. Beginning in 2002, state health departments (SHDs) received approximately $1 billion in new federal funding to prepare for and respond to terrorism, infectious disease outbreaks, and other public health threats and emergencies (1). This funding is being used in part to improve epidemiologic and surveillance capabilities. To determine how states have used a portion of their new funding to increase ID epidemiology capacity, the Iowa Department of Public Health\u27s Center for Acute Disease Epidemiology and the Iowa State University Department of Microbiology conducted two surveys of U.S. state epidemiologists during September 2000--August 2001 and October 2002--June 2003. This report summarizes the results of these surveys, which determined that although the number of SHD epidemiology workers assigned to ID and terrorism preparedness increased by 132%, concerns remained regarding the ability of SHDs to hire qualified personnel. These findings underscore the need to develop additional and more diverse training venues for current and future ID epidemiologists

Fast outflows in compact radio sources: evidence for AGN-induced feedback in the early stages of radio source evolution

We present intermediate resolution, wide wavelength coverage spectra for a complete sample of 14 compact radio sources taken with the aim of investigating the impact of the nuclear activity on the circumnuclear (ISM) in the early stages of radio source evolution. We observe spatially extended line emission (up to 20 kpc) in the majority of sources which is consistent with a quiescent halo. In the nuclear apertures we observe broad, highly complex emission line profiles. Multiple Gaussian modelling of the [O III]5007 line reveals 2-4 components which can have FWHM and blueshifts relative to the halo of up to 2000 km/s. We interpret these broad, blueshifted components as material in outflow and discuss the kinematical evidence for jet-driven outflows. Comparisons with samples in the literature show that compact radio sources harbour more extreme nuclear kinematics than their extended counterparts, a trend seen within our sample with larger velocities in the smaller sources. The observed velocities are also likely to be influenced by source orientation with respect to the observer's line of sight. Nine sources have associated HI absorption. In common with the optical emission line gas, the HI profiles are often highly complex with the majority of the detected components significantly blueshifted, tracing outflows in the neutral gas. The sample has been tested for stratification in the ISM (FWHM/ionisation potential/critical density) as suggested by Holt et al. (2003) for PKS1345+12 but we find no significant trends within the sample using a Spearman Rank analysis. This study supports the idea that compact radio sources are young radio loud AGN observed during the early stages of their evolution and currently shedding their natal cocoons through extreme circumnuclear outflows.Comment: Accepted for publication in MNRAS, 24 pages, 7 figure

Attracting, trapping and killing disease-transmitting mosquitoes using odor-baited stations - The Ifakara Odor-Baited Stations

BACKGROUND: To accelerate efforts towards control and possibly elimination of mosquito-borne diseases such as malaria and lymphatic filariasis, optimally located outdoor interventions could be used to complement existing intradomicilliary vector control methods such as house spraying with insecticides and insecticidal bednets. METHODS: We describe a new odor-baited station for trapping, contaminating and killing disease-transmitting mosquitoes. This device, named the 'Ifakara Odor-baited Station' (Ifakara OBS), is a 4 m3 hut-shaped canvas box with seven openings, two of which may be fitted with interception traps to catch exiting mosquitoes. It is baited with synthetic human odors and may be augmented with contaminants including toxic insecticides or biological agents. RESULTS: In field trials where panels of fabric were soaked in 1% pirimiphos-methyl solution and suspended inside the Ifakara OBS, at least 73.6% of Anopheles arabiensis, 78.7% of Culex and 60% of Mansonia mosquitoes sampled while exiting the OBS, died within 24 hours. When used simply as a trap and evaluated against two existing outdoor traps, Ifakara Tent trap and Mosquito Magnet-X(R), the OBS proved more efficacious than the Ifakara Tent trap in catching all mosquito species found (P < 0.001). Compared to the Mosquito Magnet-X(R), it was equally efficacious in catching An. arabiensis (P = 0.969), but was less efficacious against Culex (P < 0.001) or Mansonia species (P < 0.001). CONCLUSION: The Ifakara OBS is efficacious against disease-carrying mosquitoes including the malaria vector, An. arabiensis and Culicine vectors of filarial worms and arboviruses. It can be used simultaneously as a trap and as a contamination or killing station, meaning most mosquitoes which escape trapping would leave when already contaminated and die shortly afterwards. This technique has potential to complement current vector control methods, by targeting mosquitoes in places other than human dwellings, but its effectiveness in the field will require cheap, long-lasting and easy-to-use mosquito lures

Dominant Nuclear Outflow Driving Mechanisms in Powerful Radio Galaxies

In order to identify the dominant nuclear outflow mechanisms in Active Galactic Nuclei, we have undertaken deep, high resolution observations of two compact radio sources (PKS 1549-79 and PKS 1345+12) with the Advanced Camera for Surveys (ACS) aboard the Hubble Space Telescope. Not only are these targets known to have powerful emission line outflows, but they also contain all the potential drivers for the outflows: relativistic jets, quasar nuclei and starbursts. ACS allows the compact nature (<0.15") of these radio sources to be optically resolved for the first time. Through comparison with existing radio maps we have seen consistency in the nuclear position angles of both the optical emission line and radio data. There is no evidence for bi-conical emission line features on the large-scale and there is a divergance in the relative position angles of the optical and radio structure. This enables us to exclude starburst driven outflows. However, we are unable to clearly distinguish between radiative AGN wind driven outflows and outflows powered by relativistic radio jets. The small scale bi-conical features, indicative of such mechanisms could be below the resolution limit of ACS, especially if aligned close to the line of sight. In addition, there may be offsets between the radio and optical nuclei induced by heavy dust obscuration, nebular continuum or scattered light from the AGN.Comment: 9 pages, 8 figures, emulateapj, ApJ Accepte

Massive Ellipticals at High Redshift: NICMOS Imaging of Z~1 Radio Galaxies

We present deep, continuum images of eleven high-redshift (0.811 < z < 1.875) 3CR radio galaxies observed with NICMOS. Our images probe the rest-frame optical light where stars are expected to dominate the galaxy luminosity. The rest-frame UV light of eight of these galaxies demonstrates the well-known ``alignment effect''. Most of the radio galaxies have rounder, more symmetric morphologies at rest-frame optical wavelengths. Here we show the most direct evidence that in most cases the stellar hosts are normal elliptical galaxies with de Vaucouleurs law light profiles. For a few galaxies very faint traces of the UV-bright aligned component are also visible in the infrared images. We derive both the effective radius and surface-brightness for nine of eleven sample galaxies by fitting surface-brightness models to them. We find their sizes are similar to those of local FRII radio source hosts and are in general larger than other local galaxies. The derived host galaxy luminosities are very high and lie at the bright end of luminosity functions constructed at similar redshifts. The galaxies in our sample are also brighter than the rest-frame size--surface-brightness locus defined by the low-redshift sources. Passive evolution roughly aligns the z ~ 1 galaxies with the low-redshift samples. The optical host is sometimes centered on a local minimum in the rest-frame UV emission, suggesting the presence of substantial dust obscuration. We also see good evidence of nuclear point sources in three galaxies. Overall, our results are consistent with the hypothesis that these galaxies have already formed the bulk of their stars at redshifts greater than z >~ 2, and that the AGN phenomenon takes place within otherwise normal, perhaps passively evolving, galaxies. (abridged)Comment: 28 pages, 14 figures, accepted to ApJ. Uses AASTEX and emulateapj