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.

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.