Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

Smoke derived from burnt vegetation stimulates germination of arable weeds

A commercially available smoke-water solution (Seed Starter (R)) stimulated the germination of caryopses and intact florets of Avena fatua L. The solution was most effective when diluted (5-50%) and presented to intact or dehulled grain that had received a short period of dry after-ripening. It was less effective when applied at full strength or to grains that had been freshly harvested. The same stimulatory effect was observed in par-fly after-ripened caryopses of nine different wild oat biotypes obtained from three different cropping regions of the world. When freshly harvested caryopses were re-tested with the commercial solution (100%) for just 7 days prior to placement on to distilled water, a much higher germination percentage was possible than seen with continuous smoke-water incubation. The stimulatory ability of smoke water was more closely matched to that of gibberellic acid than to potassium nitrate, which had little or no effect on freshly harvested caryopses. The smoke-water solution (5-100%) was tested on the germination of 18 other cool temperate arable weed species. All monocotyledonous species tested (viz. Avena sterilis ssp. ludoviciana L., Alopecurus myosuroides, Sorghum halepense, Phalaris paradoxa) responded positively, while those of the dicotyledonous species were either strongly stimulated (greater than or equal to 40% stimulation Malva neglecta), moderately stimulated (greater than or equal to 20% stimulation Galium aparine, Veronica persica), slightly stimulated (Polygonum persicaria, P pennsylvanicum, Fallopia convolvulus), unaffected (P. aviculare, Sinapis arvensis, Heracleum sphondylium, Angelica sylvestris, Mercurialis annua, Veronica hederifolia) or inhibited (Lamium purpureum). The optimal concentrations required to stimulate germination of the monocotyledonous species were similar to those observed for A. fatua (5-10%). However, for the dicotyledonous species slightly stronger solutions were required (10-20%). When the unaffected species were retested using a 10-day pre-chilling treatment, smoke water showed a small promotive response in three (S. arvensis, P. aviculare and V hederifolia) of the six species. When four different smoke-water solutions (Seed Starter (R), Regen 2000 (R), charred-wood solution and wheat-straw solution) were tested on two representative species (A. fatua and M. neglecta), three formulations were effective in promoting the germination of both species, while the fourth (charred-wood solution) was only active on A. fatua. The active concentrations were different for the four solutions. Three solutions were active in the 2-20% dilution range, while the fourth (Regen 2000 (R)) was only active in the 1-2% dilution range and was inhibitory at higher concentrations. These observations are discussed in the context that smoke may play an important ecological role in the management and control of introduced weeds in native and arable communities.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

The management of rice grown on raised beds with continuous furrow irrigation

A field experiment compared two rice (Oryza sativa L.) cropping systems: paddy or raised beds with continuous furrow irrigation; and trialled four cultivars: Starbonnet, Lemont, Amaroo and Ceysvoni, and one test line YRL39; that may vary in adaptation to growth on raised beds. The grain yield of rice ranged from 740 to 1250 g/m(2) and was slightly greater in paddy than on raised beds. Although there were early growth responses to fertilizer nitrogen on raised beds, the crop nitrogen content at maturity mostly exceeded 20 g/m(2) in both systems, so nitrogen was unlikely to have limited yield. Ceysvoni yielded best in both systems, a result of good post-anthesis growth and larger grain size, although its whole-grain mill-out percentage was poor relative to the other cultivars. Starbonnet and Lemont yielded poorly on raised beds, associated with too few tillers and too much leaf area. When grown on raised beds all cultivars experienced a delay in anthesis resulting in more tillers, leaf area and dry weight at anthesis, and probably a greater yield potential. The growth of rice after anthesis, however, was similar on raised beds and in paddy, so reductions in harvest index and grain size on raised beds were recorded. The data indicated that water supply was not a major limitation to rice growth on raised beds, but slower crop development was an issue that would affect the use of raised beds in a cropping system, especially in rice-growing areas where temperatures are too cool for optimal crop development. (C) 2001 Elsevier Science B.V. All rights reserved.

Pediculus humanus capitis infestations in the community: A pilot study into transmission, treatment and factors affecting control

Head lice (Pediculus humanus capitis) infestations affect schoolchildren worldwide, creating social, economic and health consequences for families. Problems with self-detection, chronic infestations and classroom transmission are compounded by increasing resistance of the lice to pediculicides. Public health strategies are based on limited research and little is known about transmission dynamics. Mismanagement and transmission in the general community are blamed for control failure. The purpose of this study was to explore community head-lice experience in Brisbane, Australia, and to identify critical factors underlying control failure. A home-based pilot survey used physical examination to verify transmission and treatment patterns which were self-reported by a group of trace-contact families in addition to other unconnected participants. The survey was enlarged to further compare therapy outcomes and suspected risk factors. The findings reinforce those of previous studies - that children attending school and early childhood centres, and subsequently their families, are most at risk of contracting pediculosis capitis, and some may carry lice for years. First-line (pediculicidal) treatment and even additional physical methods of hand-picking and fine-toothed combing usually fail to eradicate lice quickly and completely (overall cure-rate 39 per cent, n = 84 cases). Failures were linked to hair characteristics. Public education alone may not control pediculosis. Accurate diagnosis requires considerable experience; a strong case exists for returning to institutional surveillance.

A phylogeny for the genus Isoodon and a range extension for I-obesulus peninsulae based on mtDNA control region and morphology

Short-nosed bandicoots, Isoodon, have undergone marked range contractions since European colonisation of Australia and are currently divided into many subspecies, the validity of which is debated. Discriminant function analysis of morphology and a phylogeny of Isoodon based on mtDNA control region sequences indicate a clear split between two of the three recognised species, I. macrourus and I. obesulus/auratus. However, while all previously recognised taxa within the I. obesulus/auratus group are morphologically distinct, I. auratus and I. obesulus are not phylogenetically distinct for mtDNA. The genetic divergence between I. obesulus and I. auratus (2.6%) is similar to that found among geographic isolates of the former (I. o. obesulus and I. o. peninsulae: 2.7%). Further, the divergence between geographically close populations of two different species (I. o. obesulus from Western Australia and I. a. barrowensis: 1.2%) is smaller than that among subspecies within I. auratus (I. a. barrowensis and I. auratus from northern Western Australia: 1.7%). A newly discovered population of Isoodon in the Lamb Range, far north Queensland, sympatric with a population of I. m. torosus, is shown to represent a range extension of I. o. peninsulae (350 km). It seems plausible that what is currently considered as two species, I. obesulus and I. auratus, was once one continuous species now represented by isolated populations that have diverged morphologically as a consequence of adaptation to the diverse environments that occur throughout their range. The taxonomy of these populations is discussed in relation to their morphological distinctiveness and genetic similarity.

The application of statistical process control charts to the detection and monitoring of hospital-acquired infections

The monitoring of infection control indicators including hospital-acquired infections is an established part of quality maintenance programmes in many health-care facilities. However, surveillance data use can be frustrated by the infrequent nature of many infections. Traditional methods of analysis often provide delayed identification of increasing infection occurrence, placing patients at preventable risk. The application of Shewhart, Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) statistical process control charts to the monitoring of indicator infections allows continuous real-time assessment. The Shewhart chart will detect large changes, while CUSUM and EWMA methods are more suited to recognition of small to moderate sustained change. When used together, Shewhart and EWMA methods are ideal for monitoring bacteraemia and multiresistant organism rates. Shewhart and CUSUM charts are suitable for surgical infection surveillance.

Quality Assurance Through a Continuous Curriculum Review (CCR) Strategy: Reflections on a Pilot Project

Institutional research can be defined as "the activity in which the research effort of an academic institution is directed at the solution of its own problems and to the enhancement of its own performance" (Woodward, 1993, p. 113). This paper describes and reflects on an attempt at the University of Queensland to address the need for course quality appraisal for improvement. The strategy, Continuous Curriculum Review (CCR) is simply an attempt to trial and promote regular comprehensive data collection for developing 'snapshot' views of whole curricula so that decisions about what to change and what to change first can be made in an empirically defensible and timely manner. The strategy and reporting protocols that were developed are described, and the costs and benefits of engaging in this kind of data gathering exercise for quality assurance and quality enhancement purposes are discussed.

Transient mesenteric ischaemic episodes tracked by continuous jejunal PCO2 monitoring during liquid feeding

Objective: To test the effect of liquid feeds on the responses to splanchnic ischaemia of a continuous rapid response PCO2 sensor inserted in the jejunum. Design: Prospective experimental animal study in a university research laboratory. Subjects: Adult male Wistar rats. Interventions: Adult male Wistar rats (285-425 g) were anaethetised with sodium pentobarbitone 60 mg/ kg i.p. and ventilated with 100 % oxygen and isoflurane via tracheostomy to a PaCO2 of 30-40 mmHg. A sensor was inserted into the mid-jejunum to record PCO2 every second. Distal aortic pressure was transduced. Four control rats received no feeds whilst in another four rats liquid feed was infused into the proximal jejunum at 3 ml/h. In each rat five episodes of splanchnic ischaemia were induced by 2-min elevations of an aortic sling to a mean distal aortic pressure of 30 mmHg. Measurements and main results: PCO2 elevations were always detectable, usually less than a minute from the onset of splanchnic ischaemia in both fed and unfed rats, with no difference in mean times to detectable response. In the fed rats there was a small but significant increase in the time to peak sensor response (196 +/- 16 vs. 180 +/- 12 s) and a trend towards an elevated mean baseline luminal PCO2 (67 +/- 9 vs. 55 +/- 4 mmHg). Conclusions: Brief episodes of splanchnic ischaemia were tracked successfully by a rapid response jejunal continuous PCO2 sensor during the infusion of a proprietary liquid feed preparation despite minor changes in PCO2 response characteristics and a possible elevation in baseline luminal PCO2.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.