Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fitting mixtures of Kent distributions to aid in joint set identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planer can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to lit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

HI observations of interacting galaxy pair NGC 4038/9

We present the results of new radio interferometer Hi line observations for the merging galaxy pair NGC 4038/9 ('The Antennae'), obtained using the Australia Telescope Compact Array. The results improve substantially with respect to those of van der Hulst and show in detail the two merging galactic discs and the two tidal tails produced by their interaction. The small edge-on spiral dwarf galaxy ESO 572-G045 is also seen near the tip of the southern tail, but distinct from it. It shows no signs of tidal interaction. The northern tidal tail of the Antennae shows no HI connection to the discs and has an extension towards the west. The southern tidal tail is continuous, with a prominent HI concentration at its tip, roughly at the location of the tidal dwarf galaxy observed optically by Mirabel, Dottori & Lutz. Clear velocity structure is seen along the tidal tails and in the galactic discs. Radio continuum images at 20 and 13 cm are also presented, showing the discs in detail.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.

Analysis of genetic diversity in Cassia brewsteri with randomly amplified DNA fingerprints (RAFS)

Genetic diversity in Cassia brewsteri (F. Muell.) F. Muell. ex Benth. was assessed with Randomly Amplified DNA Fingerprints (RAFs). Thirty accessions of C. brewsteri collected from throughout its natural distribution were analysed with three random decamer primers, along with three accessions of C. tomentella (Benth.) Domin and a single accession of each of C. queenslandica C. T. White and C. marksiana (F. M. Bailey) Domin. The three primers yielded a reproducible amplification profile of 265 scorable polymorphic fragments for the 35 accessions. These molecular markers were used to calculate Nei and Li similarity coefficients between each pair of individuals. A matrix of dissimilarity of each pair of individuals was examined by multidimensional scaling (MDS). The analysis supports the division of C. brewsteri into two subspecies and the suggestion that intergradation of C. brewsteri and C. tomentella can occur where the distributions of these species meet.

Extra-pair paternity and mate-guarding behaviour in the brown thornbill

We used multilocus DNA fingerprinting to assess parentage in the brown thornbill, Acanthiza pusilla, a socially monogamous Australian passerine. Extra-pair paternity was uncommon (6.2% of 178 offspring; 11.9% of 67 broods) and there was no evidence of intra-specific brood parasitism. Extra-pair paternity was limited because pairs spent more time together when females were fertile and males were able to evict intruding males before they could approach the female. Males were responsible for the close proximity of partners during the fertile period. Mate guarding therefore appears to be a male tactic aimed at preventing female infidelity rather than a cooperative behaviour of the pair aimed at preventing extra-pair copulations and/or female harassment. Females did not attempt to escape male guarding and were rarely observed to solicit copulations from intruding males. Nevertheless, females paired to smaller and younger males were more likely to cuckold their mates than females paired to larger and older males. This suggests that females may be more likely to seek or accept extra-pair matings when paired to small, young males or that old, large males are better at preventing their mates from engaging in extra-pair copulations. We found that male age but not male size influences mate-guarding behaviour. Older males tended to respond more aggressively to intruders. We therefore speculate that the relationship between male size/age and extra-pair paternity in brown thornbills may arise because female thornbills prefer large males as mates but are unable to express this preference as easily when paired to older males.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

A review of the genus Ledermuelleriopsis Willmann (Acari : Prostigmata : Stigmaeidae)

The mite family Stigmaeidae (Acari:Prostigmata) is of considerable importance in biological control, but its genera are often poorly defined and have never been subjected to cladistic analysis. Herein, we report the stigmaeid genus Ledermuelleriopsis Willmann from Australia for the first time, present a preliminary phylogenetic analysis that demonstrates that Eustigmaeus Berlese and Ledermuelleriopsis Willman are distinct, review the genus at the world level, and provide diagnostic characters of the adult females for each of the 21 known species. We also catalogue habitats, distributions and localities of holotypes. Four new species from Australia are described and illustrated: L. parvilla, sp. nov. from old dune sand, L. barbellata, sp. nov. from wet-sandy heath litter, and L. pustulosa, sp. nov. and L. claviseta, sp. nov. from dry eucalypt forest litter. A key to adult females of all known Ledermuelleriopsis species is provided. The Australian species and L. incisa Wood from New Zealand can be separated from all other members of the genus by a synapomorphy: the reduction of the number of setae on the aggenital shield to one pair. Results of a preliminary morphological cladistic analysis for those stigmaeid genera in which the larvae and adults of both sexes are known, indicate that Ledermuelleriopsis is basal to a clade containing Cheylostigmaeus Willman and Eustigmaeus.