The intersection problem for star designs

We determine those triples (m, II, k) of integers for which there are two m-star designs on the same n-set having exactly k stars in common.

Compact stellar systems in the Fornax Cluster: Super-massive star clusters or extremely compact dwarf galaxies?

We describe a population of compact objects in the centre of the Fornax Cluster which were discovered as part of our 2dF Fornax Spectroscopic Survey. These objects have spectra typical of old stellar systems, but are unresolved on photographic sky survey plates. They have absolute magnitudes - 13 < M-B

The evolution and star formation of dwarf galaxies in the Fornax Cluster

We present the results of a spectroscopic survey of 675 bright (16.5 < b(J) < 18) galaxies in a 6 degrees field centred on the Fornax cluster with the FLAIR-II spectrograph on the UK Schmidt Telescope. Three galaxy samples were observed: compact galaxies to search for new blue compact dwarfs, candidate M 32-like compact dwarf ellipticals, and a subset of the brightest known cluster members in order to study the cluster dynamics. We measured redshifts for 516 galaxies, of which 108 were members of the Fornax Cluster. Defining dwarf galaxies to be those with b(J) greater than or equal to 15 (M-B greater than or equal to - 16.5), there are a total of 62 dwarf cluster galaxies in our sample. Nine of these are new cluster members previously misidentified as background galaxies. The cluster dynamics show that the dwarf galaxies are still falling into the cluster whereas the giants are virialized. We classified the observed galaxies as late-type if we detected H alpha emission at an equivalent width greater than 1 Angstrom. The spectra were obtained through fixed apertures, so they reflect activity in the galaxy cores, but this does not significantly bias the classifications of the compact dwarfs in our sample. The new classifications reveal a higher rate of star formation among the dwarf galaxies than suggested by morphological classification: 35 per cent have significant H alpha emission indicative of star formations but only 19 per cent were morphologically classified as late-types. The star-forming dwarf galaxies span the full range of physical sizes and we find no evidence in our data for a distinct class of star-forming blue compact dwarf (BCD) galaxy. The distribution of scale sizes is consistent with evolutionary processes which transform late-type dwarfs to early-type dwarfs. The fraction of dwarfs with active star formation drops rapidly towards the cluster centre: this is the usual density-morphology relation confirmed here for dwarf galaxies. The star-forming dwarfs are concentrated in the outer regions of the cluster, the most extreme in an infalling subcluster. We estimate gas depletion time-scales for five dwarfs with detected Hi emission: these are long (of order 10(10) yr), indicating that an active gas removal process must be involved if they are transformed into gas-poor dwarfs as they fall further into the cluster. Finally, in agreement with our previous results, we find no compact dwarf elliptical (M 32-like) galaxies in the Fornax Cluster.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Behaviour rating scales for older people with dementia: which is the best for use by nurses?

There is increasing awareness of the importance of disruptive behaviour in people with dementia and the need for rating scales to accurately and reliably measure this behaviour. When rating scales are to be administered by nurses, scale characteristics must take into account the limitations of the nursing role and the nature of the environment in which nurses work. This paper reviews thirty-one rating scales that have been used to measure behaviour in dementia. From this analysis, five scales were identified as suitable for use by nurses when measuring disruptive behaviour in older people with dementia.

Clinical evaluation of the WOMAC 3.0 OA Index in numeric rating scale format using a computerized touch screen version

Background: The Western Ontario and McMaster Universities (WOMAC) Osteoarthritis Index is a previously described self-administered questionnaire covering three domains: pain, stiffness and function. It has been validated in patients with osteoarthritis (OA) of the hip or knee in a paper-based format. Aim: To validate the WOMAC 3.0 using a numerical rating scale in a computerized touch screen format allowing immediate evaluation of the questionnaire. In the computed version cartoons, written and audio instruments were included in order facilitate application. Methods: Fifty patients, demographically balanced, with radiographically proven primary hip or knee OA completed the classical paper and the new computerized WOMAC version. Subjects were randomized either to paper format or computerized format first to balance possible order effects, Results: The intra-class correlation coefficients for pain, stiffness and function values were 0.915, 0.745 and 0.940, respectively. The Spearman correlation coefficients for pain, stiffness and function were 0.88, 0.77 and 0.87, respectively. Conclusion: These data indicate that the computerized WOMAC OA index 3.0 is comparable to the paper WOMAC in all three dimensions. The computerized version would allow physicians to get an immediate result and if present a direct comparison with a previous exam. (C) 2002 OsteoArthritis Research Society International. Published by Elsevier Science Ltd. All rights reserved.

A foliar rating system for comparing the resistance of banana cultivars grown as tissue-cultured plantlets in the laboratory to Fusarium wilt

A foliar rating system was developed to assess the progress of Fusarium wilt ( Panama disease) caused by Fusarium oxysporum f. sp. cubense in seven banana cultivars differing in their resistance to race 1 of the pathogen. Plantlets were transplanted into unamended soil naturally infested with the pathogen, soil amended with urea and soil amended with aged chicken manure. A corm invasion score was also developed to assess the accuracy of the foliar symptom score as an indicator of cultivar resistance. On the basis of foliar symptom scores alone, the response of five of the seven cultivars in the chicken manure treatment corresponded to their known field response. However, the response of the other two cultivars, both susceptible to the pathogen in the field, fell into two categories. One had a high foliar symptom score and a correspondingly high corm invasion score, whereas the other had a low foliar symptom score and a high corm invasion score. Breeders need to be aware of the two categories of susceptible response, if inferior breeding material is to be rejected early on in a breeding program.

Lifetime Subsidies in Australian Private Health Insurance Markets with Community Rating

This paper considers the problem of inducing low-risk individuals of all ages to buy private health insurance in Australia. Our proposed subsidy scheme improves upon the age-based penalty scheme under the current "Australian Lifetime Cover" (LTC) scheme. We generate an alternative subsidy profile that obviates adverse selection in private health insurance markets with mandated, age-based, community rating. Our proposal is novel in that we generate subsidies that are both risk- and age-specific, based upon actual risk probabilities. The approach we take may prove useful in other jurisdictions where the extant law mandates community rating in private health insurance markets. Furthermore, our approach is useful in jurisdictions that seek to maintain private insurance to complement existing universal public systems.

Phase behavior, crystallization, and nanostructures in thermoset blends of epoxy resin and amphiphilic star-shaped block copolymers

This article reports thermoset blends of bisphenol A-type epoxy resin (ER) and two amphiphilic four-arm star-shaped diblock copolymers based on hydrophilic poly(ethylene oxide) (PEO) and hydrophobic poly(propylene oxide) (PPO). 4,4'-Methylenedianiline (MDA) was used as a curing agent. The first star-shaped diblock copolymer with 70 wt% ethylene oxide (EO), denoted as (PPO-PEO)(4), consists of four PPO-PEO diblock arms with PPO blocks attached on an ethylenediamine core; the second one with 40 wt% EO, denoted as (PEO-PPO)(4), contains four PEO-PPO diblock arms with PEO blocks attached on an ethylenediamine core. The phase behavior, crystallization, and nanoscale structures were investigated by differential scanning calorimetry, transmission electron microscopy, and small-angle X-ray scattering. It was found that the MDA-cured ER/(PPO-PEO)(4) blends are not macroscopically phase-separated over the entire blend composition range. There exist, however, two microphases in the ER/(PPO-PEO)(4) blends. The PPO blocks form a separated microphase, whereas the ER and the PEO blocks, which are miscible, form another microphase. The ER/(PPO-PEO)(4) blends show composition-dependent nanostructures on the order of 10-30 nm. The 80/20 ER/(PPO-PEO)(4) blend displays spherical PPO micelles uniformly dispersed in a continuous ER-rich matrix. The 60/40 ER/(PPO-PEO)(4) blend displays a combined morphology of worm-like micelles and spherical micelles with characteristic of a bicontinuous microphase structure. Macroscopic phase separation took place in the MDA-cured ER/(PEO-PPO)(4) blends. The MDA-cured ER/(PEO-PPO)(4) blends with (PEO-PPO)(4) content up to 50 wt% exhibit phase-separated structures on the order of 0.5-1 mu m. This can be considered to be due to the different EO content and block sequence of the (PEO-PPO)(4) copolymer. (c) 2006 Wiley Periodicals, Inc.