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Magic squares have long been popular in recreational mathematics. Their potential for introducing students to ideas in linear algebra was recognised over forty years ago in  and later in . More recently they have proved to be a fascinating topic for undergraduate exploration, especially when students have access to a computer algebra package . Some results on powers of magic square matrices can be found in ,  and . (Readers who google the title ‘Odd magic powers’ of Thompson’s paper  will be treated to a wide variety of non-mathematical exotica!)
The Glasgow area has a combination of highly variable superficial deposits and a legacy of heavy industry, quarrying and mining. These factors create complex foundation and hydrological conditions, influencing the movement of contaminants through the subsurface and giving rise locally to unstable ground conditions. Digital geological three-dimensional models developed by the British Geological Survey are helping to resolve the complex geology underlying Glasgow, providing a key tool for planning and environmental management. The models, covering an area of 3200km2 to a depth of 1.2km, include glacial and post-glacial deposits and the underlying, faulted Carboniferous igneous and sedimentary rocks. Control data, including 95,000 boreholes, digital mine plans and published geological maps, were used in model development. Digital outputs from the models include maps of depth to key horizons, such as rockhead or depth to mine workings. The models have formed the basis for the development of site-scale high-resolution geological models and provide input data for a wide range of other applications from groundwater modelling to stochastic lithological modelling.
Recently a friend kindly made me a birthday card whose background consisted of rows and rows of digits, some 3000 in all. There appeared to be no discernible pattern in the digits. Perhaps they had been taken from a table of random numbers. They were certainly not the opening digits of the decimal parts of π or , although they might, so far as I knew, have been consecutive digits of either number in some section remote from the decimal point.
On thinking about this, I realised that they must be the opening digits of the decimal part of the square root of some whole number. Indeed, they must be the opening digits of the decimal parts of the square roots of infinitely many positive integers. It is remarkably easy to prove this and the argument is simple enough to be appreciated and understood in school classrooms at GCSE level.
A new approach is proposed to analyze Bremsstrahlung X-rays that are emitted from laser-produced plasmas (LPP) and are measured by a stack type spectrometer. This new method is based on a spectral tomographic reconstruction concept with the variational principle for optimization, without referring to the electron energy distribution of a plasma. This approach is applied to the analysis of some experimental data obtained at a few major laser facilities to demonstrate the applicability of the method. Slope temperatures of X-rays from LPP are determined with a two-temperature model, showing different spectral characteristics of X-rays depending on laser properties used in the experiments.
Nutritional impact of the Tick front-of-pack labelling programme was evaluated by investigating nutrient changes to the purchased food supply and the nutritional quality of Tick v. non-Tick products. Factors influencing manufacturers’ decisions to develop and license Tick products were also explored.
Observational, cross-sectional and change over time data.
New Zealand food supply, 2011–2013.
Forty-five newly licensed Tick products from five food categories were analysed: Edible Oil Spreads, Yoghurt & Dairy Desserts, Frozen Desserts, Ready Meals and Processed Poultry. Four manufacturers of these products were interviewed.
Eligible products (31 % of all Tick products in these categories) removed 4·1 million megajoules of energy, 156·0 tonnes of saturated fat, 15·4 tonnes of trans-fat and 4·0 tonnes of sodium from food products sold in New Zealand over three years. In each food category, these Tick products were, on average, 14–76 % lower in energy, saturated fat, trans-fat and sodium than non-Tick products, indicating healthier options. Participating manufacturers reported that international market trends and consumer demand for tasty, healthy foods primarily influenced Tick product development and sales. Tick was used as part of their marketing strategy as it was perceived as a credible, well-recognised logo for New Zealand consumers. Tick was cited as the primary initiative encouraging saturated fat reduction.
The Tick Programme is continuing to encourage manufacturers to make meaningful improvements to the nutritional quality of the New Zealand food supply. Over time, these changes are likely to influence population nutrient intakes and reduce CVD risk factors.
During the Skylab period from June 1973 to January 1974 approximately 1500 type III metre-wave radio bursts or burst groups were reported (Solar Geophysical Data Prompt Reports). The longitudinal distribution of these type III bursts closely resembles that of sunspots and of the coronal transients observed above 2 R⊙ by the white-light coronagraph on Skylab. White light ejection transients appear as large loop or blob-like structures which carry material outward from the Sun and rearrange the corona. In front of the main, bright structures there are weak enhancements of brightness, termed forerunners (Jackson and Hildner 1978; Jackson 1978). In this paper we enquire into whether or not type III bursts are in any way related to the onset of solar mass ejections indicated by coronal transients.
This paper describes a preliminary series of observations of the Sun made at a frequency of 80 MHz with the 3 km radioheliograph of the Culgoora Observatory. The instrument records, at one-second intervals, pictures of the solar image in the form of 60 (E-W) × 48 (N-S) points, each separated in angle by half the Rayleigh limit (2’ arc in the zenith). At the time of the present observations the instrument was incomplete in three main respects : (a) the facilities for recording opposite senses of circular polarization were not available; (b) the automatic image compensation for zenith-angle foreshortening was not available—hence the optical disk of the Sun appears elliptical; and (c) the phase and amplitude calibration procedures had not been fully established, resulting in a higher sidelobe level than that specified in the design—the effects are sometimes evident in the pictures as spoke-like brightenings.
Studies of coronal transients observed in white-light (Gosling et al., 1976) have shown that fast-moving events (≤ 400 km s-1) are closely associated with flares and with type II and IV radio bursts while slow-moving events are not. We now report the first detection of the radio counterpart of a slow-moving transient. The event of 1974 January 21 is shown to be visible on maps of the quiet Sun made at a frequency of 80 MHz.
On 17 June 1968 we observed a flare event with the 80 MHz Culgoora radioheliograph consisting of a sequence of two type II bursts followed by enhanced emission possibly of type IV. In this paper we shall attempt to summarize some ofthe profuse data collected by the radioheliograph during this event and relate it to data from the radiospectrograph and Hα films of the associated flare (the Hα films were kindly made available by the Division of Physics, CSIRO).
A randomized controlled trial of three school-based programs and a no-intervention control group was conducted to evaluate their efficacy in reducing eating disorder and obesity risk factors.
A total of 1316 grade 7 and 8 girls and boys (mean age = 13.21 years) across three Australian states were randomly allocated to: Media Smart; Life Smart; the Helping, Encouraging, Listening and Protecting Peers (HELPP) initiative; or control (usual school class). Risk factors were measured at baseline, post-program (5 weeks later), and at the 6- and 12-month follow-ups.
Media Smart girls had half the rate of onset of clinically significant concerns about shape and weight than control girls at the 12-month follow-up. Media Smart and HELPP girls reported significantly lower weight and shape concern than Life Smart girls at the 12-month follow-up. Media Smart and control girls scored significantly lower than HELPP girls on eating concerns and perceived pressure at the 6-month follow-up. Media Smart and HELPP boys experienced significant benefit on media internalization compared with control boys and these were sustained at the 12-month follow-up in Media Smart boys. A group × time effect found that Media Smart participants reported more physical activity than control and HELPP participants at the 6-month follow-up, while a main effect for group found Media Smart participants reported less screen time than controls.
Media Smart was the only program to show benefit on both disordered eating and obesity risk factors. Whilst further investigations are indicated, this study suggests that this program is a promising approach to reducing risk factors for both problems.
Theorem 1: Infinitely many ellipses pass through the four vertices of a given convex quadrilateral.
Much of the geometry that I studied as an undergraduate in the 1950s concerned complex projective space, in which convexity plays no part. So I found Theorem 1 especially piquant and sought to understand it better. This article is the result. After examining the convexity of quadrilaterals in general, especially those inscribed in conics, I consider the following problem. Let P be a variable point in the plane, distinct from the vertices of a given convex quadrilateral ABCD. It is well known that there is a unique conic, S (P), through the five points A, B, C, D and P. How does the nature of this conic depend on the position of P? As a spin-off, we get a very short proof of Theorem 1. Finally I look at what happens when the quadrilateral ABCD is not convex. In this case, S (P) is always a hyperbola, but the distribution of A, B, C and D on its branches is still of interest.
A synthesis of the upper Moscovian sedimentological and palaeontological record of terrestrial habitats across the Variscan foreland and adjacent intramontane basins (an area which is referred to here as Variscan Euramerica) suggests a contraction and progressive westward shift of the coal swamps. These changes can be correlated with pulses of tectonic activity (tectonic phases) resulting from the northwards migration of the Variscan Front. This tectonic activity caused disruption to the landscapes and drainage patterns where the coal swamps were growing, which became less suitable to growth of the dominant plants of the swamps, the arborescent lycopsids. They were progressively replaced by vegetation dominated by marattialean ferns, which through a combination of slower growth and larger canopies resulted in less evapo-transpiration. This in turn caused localised reductions in rainfall, which further affected the ability of the lycopsids to dominate the swamp vegetation. These changes were initially localised and where the coal swamps were able to survive the lycopsids and pteridosperms show little change in either species diversity or biogeography, indicating that at this time there was minimal regional-scale climate change taking place. By Asturian times, however, the process had accelerated and the swamps in Variscan Euramerica became progressively replaced by predominantly conifer and cordaite vegetation that favoured much drier substrates. Except in localised pockets in intramontane basins of the Variscan Mountains, the last development of coal swamps in Variscan Euramerica was of early Cantabrian age. Further west, lycopsid-dominated coal swamps persisted for a little longer. The last remnants of the lycopsid-dominated coal swamps in the Illinois Basin disappeared probably by middle-late Cantabrian times, as the cycle of contracting wetlands and regional reductions in rainfall generated its own momentum, and no longer needed the impetus of tectonic instability. This tectonically-driven decline in the Euramerican coal swamps was probably responsible for an annual increase in atmospheric CO2 of c. 0.37 ppm, and may have been implicated in the marked increase in global temperatures near the Moscovian – Kasimovian boundary, and the onset of the Late Pennsylvanian interglacial.
Continual low-level exposure of sheep to the helminth Teladorsagia circumcincta elicits a temporary protective immunity, where factors in the immune abomasal mucosa prevent penetration of infective larvae, but which is essentially lost within 6 weeks of cessation of parasite challenge. Here, a proteomic approach was used to identify proteins that are differentially regulated in immune compared to naïve sheep, as potential key mediators of immunity. Six naïve sheep and 12 sheep trickle-infected with T. circumcincta were treated with anthelmintic, and the naïve (control) and 6 immune sheep were killed 7 days later. The remaining 6 sheep (immune waning) were killed 42 days after anthelmintic treatment. Abomasal tissue samples were subjected to 2D-gel electrophoresis and densitometric analysis. Selected spots (n=73) were identified by peptide mass fingerprinting and confirmatory Western blotting was carried out for 10 proteins. Spots selectively up-regulated in immune versus control, but not immune waning versus control sheep, included galectin-15 and thioredoxin, which were confirmed by Western blotting. In immune sheep, serum albumin was significantly down-regulated and albumin proteolytic cleavage fragments were increased compared to controls. Unexpectedly, albumin mRNA was relatively highly expressed in control mucosa, down-regulated in immune, and was immunolocalized to mucus-producing epithelial cells. Thus we have identified differential expression of a number of proteins following T. circumcincta trickle infection that may play a role in host protection and inhibition of parasite establishment.
Strains of California encephalitis virus (snowshoe hare subtype) were isolated from 8 of 475 pools comprising 23747 unengorged female mosquitoes of five species collected at three of six locations throughout the Mackenzie Valley of the Northwest Territories, Canada, from latitudes 60 to 69° N between 10 and 24 July 1976. Minimum field infection rates included 1:2734 for Aedes communis, 1:256 to 1:3662 for A. hexodontus and 1:911 to 1:1611 for A. punctor. Northway virus was also isolated from 1 of 3662 A. hexodontus mosquitoes collected at Inuvik (69° N, 135° W). Transmission of CE virus by A. communis infected by feeding on virus in defibrinated blood and incubation at 0, 13 and 23 °C for 13–20 days clearly demonstrates the importance of this species as a natural vector, and transmission of CE virus by Culiseta inornata after incubation at 0 and 13 °C following intrathoracic injection strengthens evidence of its role as a natural vector. Immunofiuorescence was less reliable than imunoperoxidase for detection of CE viral antigen in mosquito salivary glands.
Texel muscling quantitative trait locus (TM-QTL) is a QTL on chromosome 18, originally identified in purebred UK Texel sheep, which was reported to increase ultrasonically measured muscle depth at the third lumbar vertebra by around 4% to 7%. The objective of the present study was to comprehensively evaluate the TM-QTL and to determine whether it could provide benefits to the UK sheep industry through increased carcass meat yield in crossbred slaughter lambs. Effects of this QTL on a range of carcass traits, including those measured in vivo and by dissection, were evaluated in heterozygous carrier and non-carrier lambs produced by crossing heterozygous carrier Texel rams with non-carrier Mule (Bluefaced Leicester × Scottish Blackface) ewes from a lowland flock. The TM-QTL was found to increase loin muscling in crossbred lambs at a given live weight or carcass weight, as measured by ultrasound, X-ray computed tomography (CT) and carcass dissection. Depth of M. longissimus lumborum (MLL) was greater in TM-QTL carrier lambs compared to non-carriers as measured by both ultrasound at the third lumbar vertebra (+4.5%; P = 0.033) and CT scanning at the fifth lumbar vertebra (+6.7%; P = 0.004). Width and area of MLL measured using CT were also greater in TM-QTL carrier lambs compared to non-carriers (+3.0%; P = 0.013 and +5.1%; P = 0.047, respectively). Loin muscle volume measured using CT was greater in TM-QTL carriers than in non-carriers (+5.9%; P = 0.005) and the dissected weight of the MLL was +7.1% greater in TM-QTL carriers compared to non-carriers (P < 0.001). The proportion of the total carcass lean meat yield (LMY) that was contained within the loin region was slightly higher in TM-QTL carriers than in non-carriers (0.154 v. 0.145; P = 0.006). However, TM-QTL was found to have no significant effect on the total weight or proportion of LMY or of saleable meat yield in the carcass measured by dissection, or on muscling in the hind leg measured by CT or dissection. This work has verified that the inheritance of TM-QTL is associated with increased loin muscling in crossbred lambs, as has previously been reported for purebred Texel lambs.