3,5-cycle decompositions

For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n -1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n-2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. (C) 1998 John Wiley & Sons, Inc.

Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

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.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Australian veterinarians who work with horses: views of the future

Objective To give an account of the views held by Australian veterinarians who work with horses on the future of their professional field. Method Questionnaires were mailed to 866 veterinarians who had been identified as working with horses, and 87% were completed and returned. Data were entered onto an Excel spreadsheet, and analysed using the SAS System for Windows. Results Their future prospects were believed to be very good or excellent by >60% of equine veterinarians but by only 30% of mixed practitioners seeing < 10% horses. The main factors believed likely to affect these prospects were the strength of the equine industries and the economic climate affecting horse owners, followed by the encroachment of cities into areas used for horses, competition from other veterinarians including specialist centres and from non-veterinary operators, and their ability to recruit and retain veterinarians with interest, experience and skill with horses. Urban encroachment, competition and recruitment were especially important for those seeing few horses. Concerns were also expressed about the competence and ethical behaviour of other veterinarians, the physical demands and dangers of horse work, the costs of providing equine veterinary services and of being paid for them, the regulatory restrictions imposed by governments and statutory bodies, the potential effects of litigation, and insurance issues. For many veterinarians in mixed practice these factors have reduced and are likely to reduce further the number of horses seen, to the extent that they have scant optimism about the future of horse work in their practices. Conclusion Economic and local factors will result in an increasing proportion of equine veterinary work being done in specialised equine centres, and the future of horse work in many mixed practices is, at best, precarious. A key factor influencing future prospects will be the availability of competent veterinarians committed to working with horses.

Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

The use of 16s rDNA restriction fragment length polymorphism analysis for the identification of non-fermenting gram negative bacilli in a cystic fibrosis microbiology referral service

The utility of 16s rDNA restriction fragment length polymorphism (RFLP) analysis for the partial genomovar differentiation of Burkholderia cepacia complex bacterium is well documented. We compared the 16s rDNA RFLP signatures for a number of non-fermenting gram negative bacilli (NF GNB) LMG control strains and clinical isolates pertaining to the genera Burkholderia, Pseudomonas, Achromobacter (Alcaligenes), Ralstonia, Stenotrophomonas and Pandoraea. A collection of 24 control strain (LMG) and 25 clinical isolates were included in the study. Using conventional PCR, a 1.2 kbp 16s rDNA fragment was generated for each organism. Following restriction digestion and electrophoresis, each clinical isolate RFLP signature was compared to those of the control strain panel. Nineteen different RFLP signatures were detected from the 28 control strains included in the study. TwentyoneyTwenty- five of the clinical isolates could be classified by RFLP analysis into a single genus and species when compared to the patterns produced by the control strain panel. Four clinical B. pseudomallei isolates produced RFLP signatures which were indistinguishable from B. cepacia genomovars I, III and VIII. The identity of these four isolates were confirmed using B. pseudomallei specific PCR. 16s rDNA RFLP analysis can be a useful identification strategy when applied to NF GNB, particularly for those which exhibit colistin sulfate resistance. The use of this molecular based methodology has proved very useful in the setting of a CF referral laboratory particularly when utilised in conjunction with B. cepacia complex and genomovar specific PCR techniques. Species specific PCR or sequence analysis should be considered for selected isolates; especially where discrepancies between epidemiology, phenotypic and genotypic characteristics occur.

Acquisition of negative valence and modified attentional processing by non fear relevant stimuli

The current research examined valence and attentional processing of a priori fear relevant stimuli and investigated the extent to which these characteristics can be acquired by non fear relevant stimuli across an aversive learning episode. The first experiment compared pictures of snakes and spiders with pictures of birds and fish using affective priming, visual search and detection of a dot probe. Snakes and spiders were more negative than birds and fish as indexed by affective priming, and were preferentially attended to in the visual search task. The second experiment exposed the non fear relevant animal pictures, birds and fish, in an aversive learning episode involving an aversive shock US. Skin conductance responding was measured during acquisition. After acquisition, conditioned non fear relevant animal stimuli, CS1, and non conditioned, non fear relevant animal stimuli, CS, were compared across affective priming, visual search and dot probe tasks. During acquisition, skin conductance responses were larger during CS1 than during CS across all three response intervals. After acquisition, CS1 non fear relevant animal pictures were more negative than CS non fear relevant animal pictures as indexed by affective priming, and were preferentially attended to in a dot probe task. These studies provide evidence that negative valence and modified attentional processing can be acquired in a brief aversive learning episode.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

High rate of detection of primary aldosteronism, including surgically treatable forms, after 'non-selective' screening of hypertensive patients

Background Wide testing of the aldosterone: renin ratio among hypertensive individuals has revealed primary aldosteronism to be common, with most patients normokalaemic. Some investigators, however, have reported aldosterone-producing adenoma to be rare among patients so detected. Objective To test the hypothesis that differences among reported studies in the rate of detection of aldosterone-producing adenoma (as opposed to bilateral adrenal hyperplasia) reflect differences in the procedures used for diagnosis of primary aldosteronism, and the methods used to identify aldosterone-producing adenomas. Methods In the newly established Princess Alexandra Hospital Hypertension Unit (PAHHU), we used procedures developed by Greenslopes Hospital Hypertension Unit (which reports that more than 30% of patients with primary aldosteronism have aldosterone-producing adenomas) to diagnose primary aldosteronism and determine the subtype. All patients with an increased aldosterone: renin ratio (measured after correction for hypokalaemia and while the patient was not receiving interfering medications) underwent fludrocortisone suppression testing to confirm or exclude primary aldosteronism; if they were positive, they underwent genetic testing to exclude glucocorticoid-remediable aldosteronism before adrenal venous sampling was used to differentiate lateralizing from bilateral primary aldosteronism. Results This approach allowed PAHHU to diagnose, within 2 years, 54 patients [only seven (13%) hypokalaemic] with primary aldosteronism. All tested negative for glucocorticoid-remediable aldosteronism. Aldosterone production was lateralized to one adrenal in 15 patients (31%; only six hypokalaemic) and was bilateral in 34 (69%; all normokalaemic) of 49 patients who underwent adrenal venous sampling. Among patients with lateralizing adrenal hyperplasia, computed tomography revealed an ipsilateral mass in only six and a contralateral lesion in one. Fourteen patients underwent unilateral adrenalectomy, which cured the hypertension in seven and improved it in the remainder. In patients with bilateral primary aldlosteronism, hypertension responded to spironolactone (112.5-50 mg/ day) or amiloride (2.5-10 mg/day). Conclusion When performed with careful regard to confounding factors, measurement of the aldosterone: renin ratio in all hypertensive individuals, followed by fludrocortisone suppression testing to confirm or exclude primary aldosteronism and adrenal venous sampling to determine the subtype, can result in the detection of significant numbers of patients with specifically treatable or potentially curable hypertension. (C) 2003 Lippincott Williams Wilkins.

Virtual learning communities beyond the classroom: perceptions of tertiary Chinese language and non-language learners

As class contact times are reduced as a result of fiscal restraints in the modern tertiary sector, language instructors are placed in the position of having to find new ways to provide experience and continuity in language learning. Extending 'learning communities'—sites of learner knowledge exchange, exposure to diverse learning styles and strategies, and mutual support—beyond the classroom is one solution to maintaining successful linguistic competencies amongst learners. This, however, can conflict with the diverse extra-curricular commitments faced by tertiary students. The flexibility of web-based learning platforms provides one means of overcoming these obstacles. This study investigates learner perceptions of the use of the WebCT platform's computer medicated communication (CMC) tools as a means of extending the community of learning in tertiary Chinese language and non-language courses. Learner responses to Likert and open-ended questionnaires show that flexibility and reduction of negative affect are seen as significant benefits to 'virtual' interaction and communication, although responses are notably stronger in the non-language compared with the language cohort. While both learner cohorts acknowledge positive learning outcomes, CMC is not seen to consistently further interpersonal rapport beyond that established in the classroom. Maintaining a balance between web-based and classroom learning emerges as a concern, especially amongst language learners. [Author abstract, ed]