In this paper, we study triple-product-free sets, which are analogous to the widely studied concept of product-free sets. A nonempty subset S of a group G is triple-product-free if $abc \notin S$ for all $a, b, c \in S$. If S is triple-product-free and is not a proper subset of any other triple-product-free set, we say that S is locally maximal. We classify all groups containing a locally maximal triple-product-free set of size 1. We then derive necessary and sufficient conditions for a subset of a group to be locally maximal triple-product-free, and conclude with some observations and comparisons with the situation for standard product-free sets.

Would-be authors with an eagle eye will notice that Animal Welfare has recently revised its comprehensive Instructions for Authors. As well as a number of changes designed to clarify and facilitate the task of making submitted manuscripts suitable for publication without repeated and extensive revision, they may have noticed that there is a more detailed statement on the editorial policy with regard to the use of animals in work described in submitted papers.

No group has exactly one or two nonpower subgroups. We classify groups containing exactly three nonpower subgroups and show that there is a unique finite group with exactly four nonpower subgroups. Finally, we show that given any integer k greater than $4$ , there are infinitely many groups with exactly k nonpower subgroups.

Secondary ion mass spectrometry (SIMS) techniques have been used to study the variation of C isotope ratio and N abundance within selected diamonds in relation to their crystal growth zones. The growth zones are seen in cathodoluminescence (CL), and include both octahedral and cuboid zones within typical diamonds of external octahedral morphology. Compositions were determined by use of a primary 133Cs+ ion beam and measurement of 12C−, 13C, and 12C14N− secondary ions at high mass resolution on a Cameca ims-4f ion microprobe at Edinburgh University.

In each of the diamonds, different growth zones have marked differences in N abundance, which are as great as 0–1400 ppm within one diamond. Changes of several hundred ppm N are common across both octahedral and cuboid growth zones, and appear sharp and abrupt at the boundaries of the growth zones. In general for the common blue CL, luminescence increases with N abundance. The changes in N abundance across fine scale (∼100 µm) growth zones show that the total N contents determined by IR spectroscopy may show great variations of abundance. In contrast, within detection limits, δ13C appears constant across many growth zone boundaries. Thus the factors controlling uptake of N from the fluid/melt reservoir in which natural diamonds grow often do not influence δ13C. No evidence of progressive variation or fractionation of C isotopes during growth was found.

Some original variation in C isotope composition may have been eliminated by diffusion of C atoms subsequent to growth, because of the storage of natural diamonds over millions of years in the Earth's mantle at temperatures of 950–1250°C. Such atomic mobility does not homogenize N distribution because of the proven tendency of N to form aggregates of atoms. A survey of experimental estimates of single atom (C) diffusion parameters, suggests that diffusion distances of ∼100 µm are likely at high temperatures (∼1100°C) over long time periods (∼1.0 Ga). Therefore, with refinement of the diffusion parameters and measurements, the extent of C isotope homogenization in natural diamonds, as well as N aggregation state, might provide quantitative evidence of their time-temperature history under mantle conditions.

Diamonds from George Creek, Colorado, preserve complex intergrowth textures between two major growth generations: homogeneous diamond with yellow-buff cathodoluminescence (CL); and diamond with blue-green CL and local growth zonation. Secondary-ion mass spectrometry (SIMS) has revealed large variations in N concentration and C isotope composition within these diamonds. Even within single stones, N contents and δ13C values can vary from 0 to 750 ppm and 0 to −20‰ respectively. These variations are similar to those recorded elsewhere for entire diamond suites. The CL characteristics correlate directly with N: diamond with yellow-buff CL has uniform N contents, whereas the zoned diamond has bright blue CL bands with high N (50–750 ppm) and dark blue or green CL bands with low N (0–20 ppm). These bands are too narrow (10–5 µm) for analysis by IR spectroscopy. δ13C also varies between the two growth generations in any one diamond plate, and to a lesser extent within these generations, but shows no consistent correlations with either CL or N. The George Creek stones preserve evidence of extreme temporal and/or spatial variations in both δ13C and N concentrations during the period of diamond growth, but the factors controlling N content during diamond growth did not control δ13C.

Background: When measuring young Duchenne Muscular Dystrophy (DMD) patients’ health-related quality of life (HRQoL), parent-proxy reports are heavily relied on. Therefore, it is imperative that the relationship between parent-proxy and child self-report HRQoL is understood. This study examined the level of agreement between children and their parent-proxy rating of the child’s HRQoL. Methods: We used FOR-DMD clinical trial baseline data. HRQoL, measured using the PedsQL inventory, was reported by 178 parent and child (ages 4 to 7 years) dyads. Intracorrelation coefficients (ICC) measured absolute agreement while paired t-tests determined differences in the average HRQoL ratings between groups. Results: The level of agreement between child and parent-proxy ratings of HRQoL was poor for the generic PedsQL scale (ICC: 0.29) and its subscales; and, similarly low for the neuromuscular disease module (ICC:0.16). On average, parents rated their child’s HRQoL as poorer than the children rated themselves in all scales except for psychosocial and school functioning. Conclusions: Child and parent-proxy HRQoL ratings are discordant in this study sample, as occurs in other chronic pediatric diseases. This should be taken into account when interpreting clinical and research HRQoL findings in this population. Future studies should examine reasons for parents’ perception of poorer HRQoL than that reported by their children.

Analytical precision is vital in the interpretation of stable isotope data collected by secondary ion mass spectrometry (SIMS) given the small analysis volumes and the small magnitude of natural isotopic variations. The observed precision of a set of measurements is represented by the standard deviation(precision of an individual measurement) or the standard error of the mean (precision of the mean value). The SIMS data show both systematic variations with time and random Poisson variability, but the former largely cancel out when data for two different isotopes are expressed as a ratio. The precision of a SIMS isotope ratio routinely matches that predicted by Poisson counting statistics and can approach that of conventional bulk analysis techniques for counting times of several hours. All sample analyse must be calibrated for instrumental mass fractionation using SIMS analyses of a standard material. There is often a gradual drift in the mass fractionation with time, but this can be modelled by least-squares regression of the standard isotope ratios. Drift in the sample analyses is eliminated by using the relevant point on this regression line to calibrate each sample. The final precision of a corrected isotope ratio must take into account the scatter in both the sample and the standard data.

Introduction: Ultrasound-guided intravenous (UGIV) insertion performed by nurses has been shown to be more effective than the blind approach for patients with difficult intravenous (IV) access in the emergency department (ED). While both the single-operator (SO) (where a single operator holds the IV and probe) and dual-operator (DO) (where a second operator holds the probe) techniques have been described, the DO is more resource-intensive, requiring a second operator to be present. The objective of this study is to compare the first-attempt cannulation success rates between a SO and DO technique in ED patients with predicted difficult access. Methods: We conducted a randomized controlled non-inferiority trial using a convenience sample of adult ED patients. Participating ED nurses received a one-hour UGIV training session including didactic and practical training on simulated arms. Patients were enrolled if they met any of three criteria for difficult access: (1) history of difficult access, (2) no visible or palpable veins, or (3) two failed blind attempts. Patients requiring active resuscitation, lack of suitable veins on US, or those unable to consent or comply with the procedure were excluded. Eligible patients were randomized to the SO or DO technique and a maximum of two UGIV attempts were allowed. The primary outcome was first-attempt success rate. Additional outcomes included overall success rate, number of attempts, time to successful cannulation, patient pain scores, operator ease of use scores, and complications 30 minutes after insertion. The chi-square test was used to compare success rates between groups and t-tests used for all other secondary outcomes. Results: 42 eligible patients have been approached for our study. 14 were excluded due to lack of visible veins on US or due to ongoing resuscitation. A total of 33 UGIV attempts were performed on 28 patients (17 in SO group, 16 in DO group). There was no statistically significant difference in first attempt success rates between the SO group of 76.5% (95% CI [50.1% to 93.2%]) and the DO group of 68.8% (95% CI [41.3% to 89%]) (p=0.62). There were also no statistically significant differences between the SO and DO groups in time to cannulation (140 vs 165 seconds, p=0.36), patient preference on a 10-point scale (7.0 vs 7.9, p=0.49), patient pain score (6.3 vs 6.6, p=0.87) or nursing ease of use (5.3 vs 6.5 p=0.23) respectively. There were no complications noted in either arm of the study. Conclusion: To date, the SO technique appears to be non-inferior to the DO technique for successful UGIV cannulation. Our results support the use of the SO technique, reducing the need for additional nursing resources when performing this procedure.

In 1990, two selection lines of Merino sheep were established for low and high behavioural reactivity (calm and nervous temperament) at the University of Western Australia. Breeding records consistently showed that calm ewes weaned 10% to 19% more lambs than the nervous ewes. We hypothesise that calm ewes could have a higher ovulation rate than nervous ewes and/or calm ewes could have a lower rate of embryo mortality than nervous ewes. We tested these hypotheses by comparing the ovulation rate and the rate of embryo mortality between the calm and nervous lines before and after synchronisation and artificial insemination. Merino ewes from the temperament selection lines (calm, n=100; nervous, n=100) were synchronised (early breeding season) for artificial insemination (day 0) (intravaginal sponges containing fluogestone acetate and eCG immediately after sponge withdrawal). On day-17 and 11 ovarian cyclicity and corpora lutea, and on days 30 and 74 pregnancies and embryos/foetuses were determined by ultrasound. Progesterone, insulin and leptin concentrations were determined in blood plasma samples from days 5, 12 and 17. Ovarian cyclicity before and after oestrus synchronisation did not differ between the lines, but ovulation rate did (day-17: calm 1.63; nervous 1.26; P<0.01; day 11: calm 1.83; nervous 1.57; P<0.05). Ovulation rate on day 11 in nervous ewes was higher than on day-17. Loss of embryos by day 30 was high (calm: 71/150; nervous: 68/130); but nervous ewes had a lower proportion (15/47) of multiple pregnancies compared with calm ewes (30/46; P<0.01). Reproductive loss between days 30 and 74 represented 7.3% of the overall loss. Temperament did not affect concentrations of progesterone, but nervous ewes had higher insulin (32.0 pmol/l±1.17 SEM; P=0.013) and lower leptin (1.18 μg/l±0.04 SEM; P=0.002) concentrations than calm ewes (insulin: 27.8 pmol/l±1.17 SEM; leptin: 1.35 μg/l±0.04 SEM). The differences in reproductive outcomes between the calm and nervous ewes were mainly due to a higher ovulation rate in calm ewes. We suggest that reproduction in nervous ewes is compromised by factors leading up to ovulation and conception, or the uterine environment during early pregnancy, that reflect differences in energy utilisation.

Site-specific weed management can increase crop production efficiency by minimizing herbicide input costs without compromising crop yields. A reduction in herbicide inputs resulting from site-specific weed management may also decrease the probability level of nonpoint pollution compared with conventional herbicide applications. A 4.5-ha field was selected to compare site-specific and conventional weed management techniques in 1997 and 1998 at Knoxville, TN. Variable rate applications (VRAs) of atrazine preemergence (PRE) followed by dicamba postemergence (POST) were investigated for the reduction of herbicide inputs and their resulting impact on weed control and corn yield. VRAs of atrazine were on the basis of weed density data collected in 1996. VRAs of dicamba were according to common cocklebur density evaluations within the field. Compared with conventional applications, atrazine usage was decreased by 43 and 32% in the site-specific application treatments in 1997 and 1998, respectively. VRAs of dicamba reduced herbicide inputs by greater than 45% for 1997 and 1998. Corn yields were similar for the conventional and site-specific treatments in both years. On the basis of these data, site-specific herbicide applications have the greatest potential and least risk for managing weeds when POST or PRE + POST variable rate herbicide applications are used.