The isodiametric problem with lattice-point constraints

In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the Dirichlet-Voronoi cell of 2L is extremal, i.e., it has minimum diameter among all bodies with the same volume. It is conjectured that these sets are the only extremal bodies, which is proved for all three dimensional and several prominent lattices.Comment: 12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathemati

Professional boundaries: research report

In 2008 the General Social Care Council (GSCC) published Raising standards: Social work conduct in England 2003-2008. This constituted the GSCC’s first report covering the work undertaken to uphold standards and protect people who use social care services. The GSCC’s analysis revealed that a considerable proportion of conduct cases, some 40%, involved allegations of 'inappropriate relations'. In the light of this finding, and the release by the Council for Healthcare Regulatory Excellence (CHRE) of sexual boundaries guidance for healthcare workers at the beginning of this year (Halter et al, 2009), the GSCC committed itself to exploring the possibility of producing professional boundaries guidance for social workers. To begin this exploration, the GSCC commissioned a study in early 2009.This is the report of that study. There were two main purposes. First, to establish what professional boundaries1 guidance currently exists for social workers, or for sections of the workforce that includes social workers in the United Kingdom, and the content of any such guidance. Secondly, to identify and discuss a number of other examples of professional boundaries guidance to act as points of reference for the GSCC’s project. The aim was to identify and discuss examples relevant to the GSCC’s project

Highly erosive glaciers on Mars - the role of water

International audiencePolewards of 30 • in each hemisphere, the surface of Mars hosts a suite of landforms reminiscent of glacial landscapes on Earth. Amongst these landforms are: 1) Viscous Flow Features (VFF), which resemble glaciers on Earth and are thought to contain large volumes of water ice, 2) martian gullies which are km-scale features resembling water-eroded gullies on Earth and 3) arcuate ridges thought to be moraines from previous glaciations. Gullies have been long-associated with a surface unit originally called "pasted-on terrain" and now often called the "latitude dependant mantle". Arcuate ridges are often found at the base of hillslopes with gullies, but are also found on hillslopes with pasted-on terrain and no gullies. We have found a systematic lowering of the slope of the bedrock exposure located topographically above the pasted-on terrain whether that same slope hosts gullies or not. The lowered bedrock exposures display a different surface texture from bedrock exposed on other parts of the crater wall and from fresh crater walls-it appears fragmented and has reduced relief. Using 1-m-digital elevation models from the High Resolution Imaging Science Experiment (HiRISE) we compared the slopes of eight "eroded" craters and seven unmodified craters. We estimated their age using the crater size-frequency distribution of small craters on their ejecta blankets. From this information we calculated bedrock retreat rates for the eroded craters and found they were up to ∼103 m Myr-1-equivalent to erosion rates of wet-based glaciers on Earth. This is several orders of magnitude higher than previous estimates of erosion by VFF (10-2-101 m Myr-1), which themselves are roughly equivalent to cold-based glaciers on Earth. Such erosion rates are sufficient to erase previously existing landforms, such as martian gullies. We hypothesise, therefore, that the pasted-on terrain is a glacial deposit, overturning its previous interpretation as an airfall deposit of ice nucleated on dust. We maintain the interpretation of the arcuate ridges as moraines, but further conclude that they are likely the result of glaciotectonic deformation of sub-marginal and proglacial sediment in the presence of sediment pore-water. We do not support the generation of large quantities of glacial meltwater because it would have broken-up and degraded the arcuate ridges and pasted-on terrain an produced a suite of landforms (e.g., hummocky moraine, lacustrine forms, outwash plains, eskers) which are not observed

Neutron activation analysis traces copper artifacts to geographical point of origin

Impurities remaining in the metallic copper are identified and quantified by spectrographic and neutron activation analysis. Determination of the type of ore used for the copper artifact places the geographic point of origin of the artifact

Bendings of radio jets in BL Lacertae objects I: EVN and MERLIN observations

Several blazars, and BL Lac objects in particular, show a misalignment between the jet orientation on parsec and kiloparsec scales. Some authors (i.e. Conway & Murphy, 1993) have attempted to explain this behaviour invoking helical jets for misalignment angles around 90\degr, showing how in this case there are interesting implications for the understanding of the medium into which the jet is expanding. By comparing sensitive VLA observations (Cassaro et al., 1999) with images available in the literature for the BL Lac objects from the 1-Jy Sample (Stickel et al., 1991), it is clear that there is a wide range of misalignments between the initial jet direction and the kpc-scale jet, when detected. We have carried out VLBI observations of these BL Lac objects, in order to investigate the spatial evolution of the radio jets from few tens to hundreds of mas, and to search for helical jets in this class of sources. We present here the first dataset obtained from EVN+MERLIN observations at 5 GHz for seven objects. From these observations we never have a clear detection of helical jets, we only have a possible signature of their presence in 2 objects. In only one of the sources with a misalignment angle around 90\degr the presence of helical jets can be ruled out. This implies that it is not possible to invoke helical jets to explain the morphology of all the sources showing a misalignment of about 90\degr between the parsec and the kiloparsec scale jets.Comment: 12 pages, 9 figures, latex, accepted by Astronomy & Astrophysic

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

Interventions for the treatment of oral and oropharyngeal cancers: surgical treatment.

BACKGROUND: Surgery is an important part of the management of oral cavity cancer with regard to both the removal of the primary tumour and removal of lymph nodes in the neck. Surgery is less frequently used in oropharyngeal cancer. Surgery alone may be treatment for early stage disease or surgery may be used in combination with radiotherapy, chemotherapy and immunotherapy/biotherapy. There is variation in the recommended timing and extent of surgery in the overall treatment regimens of people with these cancers. OBJECTIVES: To determine which surgical treatment modalities for oral cavity and oropharyngeal cancers result in increased overall survival, disease free survival, progression free survival and reduced recurrence. SEARCH STRATEGY: The following electronic databases were searched: the Cochrane Oral Health Group Trials Register (to 17 February 2011), the Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2011, Issue 1), MEDLINE via OVID (1950 to 17 February 2011) and EMBASE via OVID (1980 to 17 February 2011). There were no restrictions regarding language or date of publication. SELECTION CRITERIA: Randomised controlled trials where more than 50% of participants had primary tumours of the oral cavity or oropharynx, and which compared two or more surgical treatment modalities or surgery versus other treatment modalities. DATA COLLECTION AND ANALYSIS: Data extraction and assessment of risk of bias was undertaken independently by two or more review authors. Study authors were contacted for additional information as required. Adverse events data were collected from published trials. MAIN RESULTS: Seven trials (n = 669; 667 with cancers of the oral cavity) satisfied the inclusion criteria, but none were assessed as low risk of bias. Trials were grouped into three main comparisons. Four trials compared elective neck dissection (ND) with therapeutic neck dissection in patients with oral cavity cancer and clinically negative neck nodes, but differences in type of surgery and duration of follow-up made meta-analysis inappropriate. Three of these trials reported overall and disease free survival. One trial showed a benefit for elective supraomohyoid neck dissection compared to therapeutic ND in overall and disease free survival. Two trials found no difference between elective radical ND and therapeutic ND for the outcomes of overall survival and disease free survival. All four trials found reduced locoregional recurrence following elective ND.A further two trials compared elective radical ND with elective selective ND and found no difference in overall survival, disease free survival or recurrence. The final trial compared surgery plus radiotherapy to radiotherapy alone but data were unreliable because the trial stopped early and there were multiple protocol violations.None of the trials reported quality of life as an outcome. Two trials, evaluating different comparisons reported adverse effects of treatment. AUTHORS' CONCLUSIONS: Seven included trials evaluated neck dissection surgery in patients with oral cavity cancers. The review found weak evidence that elective neck dissection of clinically negative neck nodes at the time of removal of the primary tumour results in reduced locoregional recurrence, but there is insufficient evidence to conclude that elective neck dissection increases overall survival or disease free survival compared to therapeutic neck dissection. There is very weak evidence from one trial that elective supraomohyoid neck dissection may be associated with increased overall and disease free survival. There is no evidence that radical neck dissection increases overall survival compared to conservative neck dissection surgery. Reporting of adverse events in all trials was poor and it was not possible to compare the quality of life of patients undergoing different surgeries

Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil

The population of SNe/SNRs in the starburst galaxy Arp 220. A self-consistent analysis of 20 years of VLBI monitoring

The nearby ultra-luminous infrared galaxy (ULIRG) Arp 220 is an excellent laboratory for studies of extreme astrophysical environments. For 20 years, Very Long Baseline Interferometry (VLBI) has been used to monitor a population of compact sources thought to be supernovae (SNe), supernova remnants (SNRs) and possibly active galactic nuclei (AGNs). Using new and archival VLBI data spanning 20 years, we obtain 23 high-resolution radio images of Arp 220 at wavelengths from 18 cm to 2 cm. From model-fitting to the images we obtain estimates of flux densities and sizes of all detected sources. We detect radio continuum emission from 97 compact sources and present flux densities and sizes for all analysed observation epochs. We find evidence for a LD-relation within Arp 220, with larger sources being less luminous. We find a compact source LF $n(L)\propto L^\beta$ with $\beta=-2.19\pm0.15$, similar to SNRs in normal galaxies. Based on simulations we argue that there are many relatively large and weak sources below our detection threshold. The observations can be explained by a mixed population of SNe and SNRs, where the former expand in a dense circumstellar medium (CSM) and the latter interact with the surrounding interstellar medium (ISM). Nine sources are likely luminous, type IIn SNe. This number of luminous SNe correspond to few percent of the total number of SNe in Arp 220 which is consistent with a total SN-rate of 4 yr$^{-1}$ as inferred from the total radio emission given a normal stellar initial mass function (IMF). Based on the fitted luminosity function, we argue that emission from all compact sources, also below our detection threshold, make up at most 20\% of the total radio emission at GHz frequencies.Comment: Accepted for publication in Astronomy and Astrophysic