Sums of two squares and a power

We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a congruence condition is imposed on $z$. These examples are of interest as there is no congruence obstruction itself for the representation of these $n$. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.Comment: 6 pages, to appear in the memorial volume "From Arithmetic to Zeta-Functions - Number Theory in Memory of Wolfgang Schwarz

A modified Oster-Murray-Harris mechanical model of morphogenesis

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verified through numerical simulations of the full nonlinear model in one and two dimensions. The increased range of boundary conditions that are well-posed, as well as a wider range of parameters that yield bounded steady states, renders the modified model more applicable to, and more robust for, comparisons with experiments

Climate change and the rental sector: Mapping the legislative and policy context: Analysis

The Briefing Paper series of the ‘Rental housing, climate change and adaptive capacity: a case study of Newcastle NSW’ project seeks to provide readers with access to current research on rental sector adaptation to climate change. Briefing Papers produced by the project team are working documents that provide a forum on theoretical, methodological and practical issues related to climate change adaption in rental housing. The project is funded by the National Climate change Adaptation Facility (NCCARF) for 2012. The publication as a ‘Briefing Paper’ does not preclude subsequent publication in scholarly journals, books or reports. Unless otherwise stated, ‘Rental housing, climate change and adaptive capacity’ publications are presented as contributions to debate and discussion and represent our developing thinking about the research. We are hoping that they may facilitate feedback from readers, researchers, renters and housing managers

Climate change and the rental sector: Mapping the legislative and policy context: Local Government

The Briefing Paper series of the ‘Rental housing, climate change and adaptive capacity: a case study of Newcastle NSW’ project seeks to provide readers with access to current research on rental sector adaptation to climate change. Briefing Papers produced by the project team are working documents that provide a forum on theoretical, methodological and practical issues related to climate change adaption in rental housing. The project is funded by the National Climate change Adaptation Facility (NCCARF) for 2012. The publication as a ‘Briefing Paper’ does not preclude subsequent publication in scholarly journals, books or reports. Unless otherwise stated, ‘Rental housing, climate change and adaptive capacity’ publications are presented as contributions to debate and discussion and represent our developing thinking about the research. We are hoping that they may facilitate feedback from readers, researchers, renters and housing managers

The Metropolitan Rhythm of Street Life: A Socio-spatial Analysis of Synagogues and Churches in Nineteenth-century Whitechapel

The German sociologist Georg Simmel wrote in 1903 how the city functions as an alienating environment that is strikingly different from the village or the town: in the city the individual has to adjust to the “metropolitan rhythm of events.” Simmel’s proposition that the nature of the urban setting means that every street crossing creates an intensified tempo “of economic, occupational and social life” is examined here to see the way in which East London functioned – as it has done so now over several centuries – to provide a specifically urban setting for incoming religious minorities to settle and form a community. This chapter focuses on Whitechapel in the year 1899, around a decade later than Charles Booth’s first poverty survey and in the year in which the update to his great map of poverty was drawn up

Variable iron-line emission near the black hole of Markarian 766

We investigate the link between ionised Fe X-ray line emission and continuum emission in the bright nearby AGN, Mrk 766. A new long (433 ks) XMM-Newton observation is analysed, together with archival data from 2000 and 2001. The contribution from ionised line emission is measured and its time variations on short (5-20 ks) timescales are correlated with the continuum emission. The ionised line flux is found to be highly variable and to be strongly correlated with the continuum flux, demonstrating an origin for the ionised line emission that is co-located with the continuum emission. Most likely the emission is ionised reflection from the accretion disc within a few A.U. of the central black hole, and its detection marks the first time that such an origin has been identified other than by fitting to spectral line profiles. Future observations may be able to measure a time lag and hence achieve reverberation mapping of AGN at X-ray energies.Comment: Accepted for publication, Astronomy and Astrophysics letter

Narratives as a Fundamental Component of Consciousness

In this paper, we propose a conceptual architecture that models human (spatially-temporally-modally) cohesive narrative development using a computer representation of quale properties. Qualia are proposed to be the fundamental "cognitive" components humans use to generate cohesive narratives. The engineering approach is based on cognitively inspired technologies and incorporates the novel concept of quale representation for computation of primitive cognitive components of narrative. The ultimate objective of this research is to develop an architecture that emulates the human ability to generate cohesive narratives with incomplete or perturbated information

A Mokken analysis of the literacy in musculoskeletal problems questionnaire.

BACKGROUND: Limited health literacy is known to impact on medication adherence, hospital readmission and potentially poorer health outcomes. The literature on the health literacy of those with musculoskeletal conditions suggests greater functional limitations and increased pain levels. There are a number of measures of health literacy. One that specifically relates to musculoskeletal complaints is the Literacy in Musculoskeletal Problems (LiMP) questionnaire. The LiMP contains 9 multiple choice items that cover anatomy, musculoskeletal conditions and the diagnosis of musculoskeletal complaints. The aim of the study was to evaluate the dimensionality and internal structure of the LiMP in patients attending for osteopathy care at a student-led clinic, as a potential measure of musculoskeletal health literacy. METHOD: Three hundred and sixty-one (n = 361) new patients attending the Victoria University Osteopathy Clinic completed the LiMP and a demographic and health information questionnaire prior to their initial consultation. Mokken scale analysis, a nonparametric item response theory approach, was used to evaluate the dimensionality and structure of the LiMP in this population, to ascertain whether the questionnaire was measuring a single latent construct - musculoskeletal health literacy. McDonald's omega and Cronbach's alpha were calculated as the reliability estimations. The relationship between the LiMP and a single item screen of health literacy was also undertaken. RESULTS: The 9 items on the LiMP did not form a Mokken scale and the reliability estimations were below an acceptable level (alpha and omega <0.45). LiMP items 5 and 8 were more likely to be answered correctly by those with higher health literacy (p < 0.05), however the effect sizes were small (<0.20). CONCLUSION: Calculation of a total score for the LiMP, as advocated by the original authors, is not supported based on data in the present study. Further research is required to explore the relationship of the LiMP items to demographic and clinical data, and to other broader measures of health literacy. Further research may also develop a health literacy measure that is specific to patients seeking manual therapy care for musculoskeletal complaints

Radio Observations of the Supernova Remnant Candidate G312.5-3.0

The radio images from the Parkes-MIT-NRAO (PMN) Southern Sky Survey at 4850 MHz have revealed a number of previously unknown radio sources. One such source, G312.5-3.0 (PMN J1421-6415), has been observed using the multi-frequency capabilities of the Australia Telescope Compact Array (ATCA) at frequencies of 1380 MHz and 2378 MHz. Further observations of the source were made using the Molonglo Observatory Synthesis Telescope (MOST) at a frequency of 843 MHz. The source has an angular size of 18 arcmin and has a distinct shell structure. We present the reduced multi-frequency observations of this source and provide a brief argument for its possible identification as a supernova remnant.Comment: 5 pages, 5 figures, Accepted for publication in MNRA