Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

A small disturbance in the strong vortex flow

A small disturbance in the axisymmetric, bathtub-like flow with strong vorticity is considered and the asymptotic representation of the solution is found. It is shown that if the disturbance is smaller than a certain critical scale, the conventional strong vortex approximation cannot describe the field generated by the disturbance not only in the vicinity of the disturbance but also at the distances much larger than the critical scale. (C) 2001 American Institute of Physics.

Moderately strong vorticity in a bathtub-type flow

Theoretical and numerical analysis is performed for an inviscid axisymmetric vortical bathtub-type flow. The level of vorticity is kept high so that the image of the flow on the radial-axial plane (r-z plane) is not potential. The most significant findings are: (1) the region of validity of the strong vortex approximation is separated from the drain by a buffer region, (2) the power-law asymptote of the stream function, specified by Delta Psi similar to r(4/3) Deltaz, appears near the axis when vorticity in the flow is sufficiently strong and (3) the local Rossby number in the region of the 4/3 power-law the initial vorticity level in the flow and the global Rossby number.

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.

Australia, the United States and a 'China growing strong': managing conflict avoidance

How to deal with a rising China constitutes one of the most seminal challenges facing the ANZUS alliance since its inception a half a century ago. Australia must reconcile its geography and economic interests in Asia with its post-war strategic and historic cultural orientation towards the United States. It must succeed in this policy task without alienating either Beijing or Washington in the process. The extent to which this is achieved will shape Australia's national security posture for decades to come. Three specific components of the 'Sino-American-Australian' triangle are assessed here: the future of Taiwan, the American development of a National Missile Defence (NMD), and the interplay between Sino-American power balancing and multilateral security politics. The policy stakes for Australia and for the continued viability of ANZUS are high in all three policy areas as a new US Administration takes office in early 2001. The article concludes that Australia's best interest is served by applying deliberate modes of decisionmaking in its own relations with both China and the US and by facilitating consistent and systematic dialogue and consultations with both of those great powers on key strategic issues.

Comparative phylogeography of two open forest frogs from eastern Australia

We investigated the phylogeography of two closely related Australian frog species from open forest habitats, Limnodynastes tasmaniensis and L. peronii, using mitochondrial ND4 sequence data. Comparison of our results with previous work on Litoria fallax allowed us to test the generality of phylogeographic patterns among non-rainforest anurans along the east coast of Australia. In general, there was no strong evidence for congruence between overall patterns of genetic structure in the three species. However, phylogenetic breaks congruent with the position of the Burdekin Gap were detected at some level in all species. As previously noted for closed forest taxa, this area of dry habitat appears to have been an important influence on the evolution of several open forest taxa. There were broad geographic similarities in the phylogenetic structuring of southern populations of L. peronii and L. tasmaniensis. Contrarily, although the McPherson Range has previously been noted to coincide geographically with a major mtDNA phylogenetic break in Litoria fallax this pattern is not apparent in L. peronii or L. tasmaniensis. It appears that major phylogeographic splits within L. peronii and L. tasmaniensis may predate the Quaternary. We conclude that phylogeographies of open forest frogs are complex and more difficult to predict than for rainforest taxa, mainly due to an absence of palaeomodels for historical distributions of non-rainforest habitats. (C) 2001 The Linnean Society of London.

Surface diffusion of strong adsorbing vapours on porous carbon

Surface diffusion of strongly adsorbing hydrocarbon vapours on activated carbon was measured by using a constant molar flow method (D.D. Do, Dynamics of a semi-batch adsorber with constant molar supply rate: a method for studying adsorption rate of pure gas, Chem. Eng. Sci. 50 (1995) 549), where pure adsorbate is introduced into a semi-batch adsorber at a constant molar flow rate. The surface diffusivity was determined from the analysis of pressure response versus time, using a linear mathematical model developed earlier. To apply the linear theory over the non-linear range of the adsorption isotherm, we implement a differential increment method on the system which is initially equilibrated with some pre-determined loading. By conducting the experiments at different initial loadings, the surface diffusivity can be extracted as a function of loading. Propane, n-butane, n-hexane, benzene, and ethanol were used as diffusing adsorbate on a commercial activated carbon. It is found that the surface diffusivity of these strongly adsorbing vapours increases rapidly with loading, and the surface diffusion flux contributes significantly to the total flux and cannot be ignored. The surface diffusivity increases with temperature according to the Arrhenius law, and for the paraffins tested it decreases with the molecular weight of the adsorbate. (C) 2002 Elsevier Science Ltd. All rights reserved.

Distribution of two splice variants of the glutamate transporter GLT-1 in the developing rat retina

The distributions of a carboxyl terminal splice variant of the glutamate transporter GLT-1, referred to as GLT-1B, and the carboxyl terminus of the originally described variant of GLT-1, referred to hereafter as GLT-1alpha, were examined using specific antisera. GLT-1B was present in the retina at very early developmental stages. Labelling was demonstrable at embryonic day 14, and strong labelling was evident by embryonic day 18. Such labelling was initially restricted to populations of cone photoreceptors, the processes of which extended through the entire thickness of the retina and appeared to make contact with the retinal ganglion cells. During postnatal development the GLT-1B-positive photoreceptor processes retracted to form the outer plexiform layer, and around postnatal day 7, GLT-1B-immunoreactive bipolar cells appeared. The pattern of labelling of bipolar cell processes within the inner plexiform layer changed during postnatal development. Two strata of strongly immunoreactive terminals were initially evident in the inner plexiform layer, but by adulthood these two bands were no longer evident and labelling was restricted to the somata and processes (but not synaptic terminals) of the bipolar cells, as well as the somata, processes, and terminals of cone photoreceptors. By contrast, GLT-1alpha appeared late in postnatal development and was restricted mainly to a population of amacrine cells, although transient labelling was also associated with punctate elements in the outer plexiform layer, which may represent photoreceptor terminals, (C) 2002 Wiley-Liss, Inc.

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.

Indirect evidence of density-dependent population regulation in Aponomma hydrosauri (Acari : Ixodidae), an ectoparasite of reptiles

The extent to which density-dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density-dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long-term dataset on the distribution of ticks among individual hosts. If density-dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host-parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re-analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density-dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population-scale increase in the aggregation coefficient is indirect evidence of a density-dependent process or processes sufficiently strong to produce a population-wide pattern, and thus also likely to influence population regulation. The direct observation of a density-dependent process is evidence of at least part of the responsible mechanism.