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Identical twin Steiner triple systems

Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33. In this paper we construct infinite families of identical twin Steiner triple systems

Energetically stable singular vortex cores in an atomic spin-1 Bose-Einstein condensate

We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits energetic hierarchy of length scales resulting from different interaction strengths and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction. We show that in the ferromagnetic phase the resulting stable core structure, despite apparent complexity, can be identified as a single polar core with everywhere nonvanishing axially symmetric density profile. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores.<br/

On the full automorphism group of a Hamiltonian cycle system of odd order

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that this condition is also sufficient except possibly for the class of non-solvable binary groups.Comment: 11 pages, 2 figure

Very Low Energy Supernovae: Light Curves and Spectra of Shock Breakout

The brief transient emitted as a shock wave erupts through the surface of a presupernova star carries information about the stellar radius and explosion energy. Here the CASTRO code, which treats radiation transport using multigroup flux-limited diffusion, is used to simulate the light curves and spectra of shock breakout in very low-energy supernovae (VLE SNe), explosions in giant stars with final kinetic energy much less than 10$^{51}$ erg. VLE SNe light curves, computed here with the KEPLER code, are distinctively faint, red, and long-lived, making them challenging to find with transient surveys. The accompanying shock breakouts are brighter, though briefer, and potentially easier to detect. Previous analytic work provides general guidance, but numerical simulations are challenging due to the range of conditions and lack of equilibration between color and effective temperatures. We consider previous analytic work and extend discussions of color temperature and opacity to the lower energy range explored by these events. Since this is the first application of the CASTRO code to shock breakout, test simulations of normal energy shock breakout of SN1987A are carried out and compared with the literature. A set of breakout light curves and spectra are then calculated for VLE SNe with final kinetic energies in the range $10^{47} - 10^{50}$ ergs for red supergiants with main sequence masses 15 Msun and 25 Msun. The importance of uncertainties in stellar atmosphere model, opacity, and ambient medium is discussed, as are observational prospects with current and forthcoming missions.Comment: 19 pages; submitted to Astrophysical Journa

Solids flow in a polymer extruder

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Nutritional adequacy and content of food bank parcels in Oxfordshire, UK: a comparative analysis of independent and organisational provision

Background: Food bank use has increased significantly in the UK. With the rise in demand, it is imperative that users are receiving food parcels that meet their requirements. The present study aimed to explore whether typical food parcels, supplied by The Trussell Trust and independent food banks, were meeting the daily nutrient and energy requirements of an adult user. Methods: The Trussell Trust (n = 2) and independent food banks (n = 9) were surveyed in Oxfordshire, UK. Data were collected on food bank use, resources, donations and parcel content. The energy and nutrient contents of a representative parcel were compared with the average dietary reference values (DRVs) for an adult. Additional comparisons were made between The Trussell Trust and independent provision. Results: Parcels provided energy, carbohydrate, sugar, protein and fibre contents that significantly exceeded the DRVs. In total, 62.2% of energy was provided as carbohydrate and 569% of the DRV was provided by sugars. The vitamin D and retinol content of the parcels was significantly lower than the DRVs, meeting 25% and 27% of users’ needs respectively; provision of all other micronutrients exceeded the DRVs. The Trussell Trust’s parcels provided significantly less vitamin D and copper than independent parcels. Conclusions: Food bank parcels distributed in Oxfordshire, UK, exceeded energy requirements and provided disproportionately high sugar and carbohydrate and inadequate vitamin A and vitamin D compared to the UK guidelines. Improved links with distributors and access to cold food storage facilities would help to address these issues, via increased fresh food provisio