The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

Emergence of community-acquired methicillin-resistant Staphylococcus aureus (MRSA) infection in Queensland, Australia

Objectives: To investigate the incidence and epidemiology of non-multiresistant methicillin-resistant Staphylococcus aureus (nmMRSA) infection in south-east Queensland, Australia. Study design: A retrospective survey was done of hospital records of all patients who had non-multiresistant MRSA isolated at Ipswich Hospital (a 250-bed general hospital, 40 km south-west of Brisbane, Queensland, Australia) between March 2000 and June 2001. Laboratory typing of these isolates was done with antibiogram, pulsed-field gel electrophoresis, bacteriophage typing and coagulase gene typing. Results: There were 44 infections caused by nmMRSA. Seventeen infections (39%) occurred in patients from the south-west Pacific Islands (predominantly Samoa, Tonga and New Zealand). Laboratory typing showed that the isolates in Pacific Islanders were Pacific Island strains, and 16/17 of these infections were community acquired. Twenty-three infections (52%) occurred in Caucasians. Eleven of the isolates from Caucasians (48%) were a new predominantly community-acquired strain that we have termed the ‘R’ pulsotype, nine (39%) were Pacific Island strains, and three (13%) were health care institution-associated strains. Four infections occurred in patients who were not Caucasians or Pacific Islanders. Overall, 34 of all 44 infections (77%) were community' acquired. Conclusions: Non-multiresistant MRSA infection, relatively frequently observed in Pacific Islanders in south-east Queensland, is now a risk for Caucasians as well, and is usually community acquired. Clinicians should consider taking microbiological specimens for culture and antimicrobial susceptibility testing in patients with suspected staphylococcal infections who are not responding to empirical therapy with β-lactam antibiotics.

Development time and survival of Verrallina funerea (Theobald) (Diptera : Culicidae) immatures and other brackish water mosquito species in southeast Queensland, Australia

Verrallina funerea (Theobald) is a brackish water mosquito that is recognised as an important pest and vector in southeast Queensland, Australia. Immature development time and survival of Ve. funerea was defined in the laboratory in response to a range of temperatures (17-34 degrees C) and salinities (0-35 parts per thousand (p.p.t)). The expression of autogeny in this species was also assessed. Salinity only had a slight effect on mean development time from hatching to adult emergence (7.0-7.4 d at salinities of 0, 17.5 and 31.5 p.p.t) and survival was uniformly high (97.5-99.0%). Mean development times were shorter at 26, 29 and 32 degrees C (7.0, 6.8 and 6.8 d, respectively) and longest at 17 degrees C (12.2 d). The threshold temperature (t) was 5.8 degrees C and the thermal constant (K) was 142.9 degree-days above t. Survival to adulthood decreased from > 95% (at 17-29 degrees C) to 78% (at 32 degrees C) and 0% (at 34 degrees C). No expression of autogeny was observed. Immature development times of Ve. funerea, Ochlerotatus vigilax (Skuse) and Oc. procax (Skuse) were then determined under field conditions at Maroochy Shire. Following tide and rain inundation, cohorts of newly hatched larvae were monitored daily by dipping, and time until pupation was noted. Tidal inundation triggered hatching of Ve. funerea and Oc. vigilax larvae whereas Oc. procax larvae were found only after rain inundation. Estimates of Ve. funerea and Oc. vigilax field development times were similar (8-9 d) while Oc. procax development time was slightly longer (9-10 d). Based on these survey results, control activities targeting Ve. funerea must be initiated 4 d (if using Bacillus thuringiensis var. israelensis de Barjac) or 5 d (if using s-methoprene) after inundation. However, Casuarina glauca Sieber canopy and branchlets covering breeding habitats may present a problem for the penetration of such treatments.

Structure and thermal stability of Langmuir-Blodgett films of barium arachidate

The structures of multilayer Langmuir-Blodgett films of barium arachidate before and after heat treatment have been investigated using both atomic force microscopy (AFM) and grazing incidence synchrotron X-ray diffraction (GIXD). AFM gave information on surface morphology at molecular resolution while GIXD provided quantitative details of the lattice structures of the films with their crystal symmetries and lattice constants. As-prepared films contained three coexisting structures: two triclinic structures with the molecularchains tilted by about 20degrees from the film normal and with 3 x 1 or 2 x 2 super-lattice features arising from height modulation of the molecules in the films; a rectangular structure with molecules perpendicular to the film surface. Of these, the 3 x 1 structure is dominant with a loose correlation between the bilayers. In the film plane both superstructures are commensurate with the local structures, having different oblique symmetries. The lattice constants for the 3 x 1 structure are a(s) = 3a = 13.86 Angstrom, b(s) = b = 4.31 Angstrom and gamma(s) = gamma = 82.7degrees; for the 2 x 2 structure a(s) = 2a = 16.54 Angstrom, b(s) = 2b = 9.67 Angstrom, gamma(s) = gamma = 88degrees. For the rectangular structure the lattice constants are a = 7.39 Angstrom, b = 4.96 Angstrom and gamma = 90degrees. After annealing, the 2 x 2 and rectangular structures were not observed, while the 3 x 1 structure had developed over the entire film. For the annealed films the correlation length in the film plane is about twice that in the unheated films, and in the out-of-plane direction covers two bilayers. The above lattice parameters, determined by GIXD, differed significantly from the values obtained by AFM, due possibly to distortion of the films by the scanning action of the AFM tip. (C) 2004 Published by Elsevier B.V.