Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

DNA sequence variation in the ITS-1 rDNA subunit and host relationships in sorghum midge, Stenodiplosis sorghicola (Coquillett) (Diptera : Cecidomyiidae), in Australia

Sequence variation in the internal transcribed spacer (ITS-1) ribosomal DNA subunit was examined for sorghum midge obtained from introduced and native hosts in south-eastern and central Queensland. No variation was observed relative to host plant or geographical distance for midges collected from two introduced hosts, grain sorghum (Sorghum bicolor ) and Johnson grass (S. halepense ); however, sequence differences were observed between midges from introduced and native hosts and among midges from a single native host, slender bluegrass (Dichanthium affine ). No evidence was observed of introduced midges on native hosts, or vice versa. These results agree with previously hypothesised host distributions for native and introduced midges in Australia, and expand the sample of introduced hosts to include Johnson grass. They suggest that Stenodiplosis sorghicola , the principal midge infesting grain sorghum, is also the most common species on Johnson grass. This confirms that Johnson grass plays a role in the population dynamics of S. sorghicola and suggests that midges originating from Johnson grass may influence levels of infestation in grain sorghum.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.

Automatic segmentation of the knee bones using 3D active shape models

This paper presents an automated segmentation approach for MR images of the knee bones. The bones are the first stage of a segmentation system for the knee, primarily aimed at the automated segmentation of the cartilages. The segmentation is performed using 3D active shape models (ASM), which are initialized using an affine registration to an atlas. The 3D ASMs of the bones are created automatically using a point distribution model optimization scheme. The accuracy and robustness of the segmentation approach was experimentally validated using an MR database of fat suppressed spoiled gradient recall images.