On the volume of 4-cycle trades

A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v = \V(G)\. This paper determines for which values oft and a there exists a 4-cycle trade of volume t and foundation v.

Cuticular hydrocarbons of Drosophila birchii and D-serrata: Identification and role in mate choice in D-serrata

The cuticular hydrocarbon compositions of two sympatric species of Australian Drosophila in the montium subgroup of the melanogaster group that use cuticular hydrocarbons in mate recognition have been characterized. Drosophila birchii has 34 components in greater than trace amounts, with a carbon number range of C-20 to C-33. Drosophila serrata has 21 components above trace level and a carbon number range of C-24 to C-31. These two species share eight hydrocarbon components, with all but two of them being monoenes. For both species, the (Z)-9-monoenes are the predominant positional isomer. The hydrocarbons of D. birchii are n-alkanes, n-alkenes (Z)-5-, (Z)-7-, (Z)-9-, and (Z)-11-), low to trace levels of homologous (Z,Z)-7,11- and (Z,Z)-9,13-dienes; and trace amounts of (Z,Z)-5,9- C-25:2, a major component of D. serrata. Only one methyl branched hydrocarbon was detected (2-methyl C-28), and it occurred at very low levels. The hydrocarbons of D. serrata are dominated by a homologous series of (Z,Z)-5,9-dienes, and notably, are characterized by the apparent absence of n-alkanes. Homologous series of (Z)-5-, (Z)-7-, and (Z)-9- alkenes are also present in D. serrata as well as 2-methyl alkanes. Drosophila serrata females display strong directional mate choice based on male cuticular hydrocarbons and prefer D. serrata males with higher relative abundances of the 2-methyl alkanes, but lower relative abundances of (Z,Z)-5,9- C-24:2 and (Z)-9-C-25:1.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Black and white and re(a)d all over again: Indigenous minstrelsy in contemporary Canadian and Australian theatre

This essay considers processes by which community identities are challenged by discussing the use of whiteface as an activist strategy in recent indigenous theatre in Canada and Australia. To understand whiteface, I employ Susan Gubar's notion of racechange, processes that test and even transgress racial borders. I also situate whiteface in relation to the history of blackface minstrelsy. Noting the ways these racial performances affirm the hierarchies of color and how power becomes invested in such color codings, the essay highlights indigenous employment of whiteface as a potential form of critical historiography. I then analyze how whiteface functions in two productions, Daniel David Moses's Almighty Voice and His Wife (1991) in Canada and the Queensland Theatre Company's 2000 revival of George Landen Dann's Fountains Beyond in Australia. My analysis posits that such indigenous performances of whiteface can affirm the identity of the marginalized other even as they destabilize the fixity of race and its meanings.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Abnormalities of the PTH-vitamin D axis and bone turnover markers in children, adolescents and adults with cystic fibrosis: comparison with healthy controls

Abnormalities of calcium and vitamin D metabolism in cystic fibrosis (CF) are well documented. We tested the hypothesis that alterations in calcium metabolism are related to vitamin D deficiency, and that bone resorption is increased relative to accretion in patients with CF. Calcitropic hormones, electrolytes, osteocalcin (OC) and bone alkaline phosphatase (BAP), (markers of bone mineralisation), urinary deoxypyridinoline [total (t) Dpd, a marker of bone resorption] and lumbar spine bone mineral density (LS BMD), expressed as a z-score, were measured in 149 (81 M) CF and 141 (61 M) control children aged 5.3-10.99 years, adolescents aged 11-17.99 years and adults aged 18-55.9 years. Data were analysed by multiple regression to adjust for age. In patients, FEV1% predicted and CRP (as disease severity markers), genotype and pancreatic status (PS) were recorded. The distribution of PTH differed between groups (P