Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

International Grassland Congress Outlook: An historical review and future expectations

Features of the history of the International Grassland Congress are mentioned. Aspects of a number of failed themes in grassland science are described with respect to molecular biology, intensive systems of ruminant production, carbohydrate use in plant growth, plant succession and range condition, and stocking method. Future expectations are focused on meeting a balance of objectives, maintaining reductionist science, taking new initiatives in plant improvement and in the development of animal production systems, and reducing barriers to international trade. The adoption of grassland science depends upon the growth of new learning, especially through cyclical interaction between scientists and farmers.

Analysis of genetic diversity within Australian lucerne cultivars and implications for future genetic improvement

Lucerne (Medicago sativa L.) is autotetraploid, and predominantly allogamous. This complex breeding structure maximises the genetic diversity within lucerne populations making it difficult to genetically discriminate between populations. The objective of this study was to evaluate the level of random genetic diversity within and between a selection of Australian-grown lucerne cultivars, with tetraploid M. falcata included as a possible divergent control source. This diversity was evaluated using random amplified polymorphic DNA (RAPDs). Nineteen plants from each of 10 cultivars were analysed. Using 11 RAPD primers, 96 polymorphic bands were scored as present or absent across the 190 individuals. Genetic similarity estimates (GSEs) of all pair-wise comparisons were calculated from these data. Mean GSEs within cultivars ranged from 0.43 to 0.51. Cultivar Venus (0.43) had the highest level of intra-population genetic diversity and cultivar Sequel HR (0.51) had the lowest level of intra-population genetic diversity. Mean GSEs between cultivars ranged from 0.31 to 0.49, which overlapped with values obtained for within-cultivar GSE, thus not allowing separation of the cultivars. The high level of intra- and inter-population diversity that was detected is most likely due to the breeding of synthetic cultivars using parents derived from a number of diverse sources. Cultivar-specific polymorphisms were only identified in the M. falcata source, which like M. sativa, is outcrossing and autotetraploid. From a cluster analysis and a principal components analysis, it was clear that M. falcata was distinct from the other cultivars. The results indicate that the M. falcata accession tested has not been widely used in Australian lucerne breeding programs, and offers a means of introducing new genetic diversity into the lucerne gene pool. This provides a means of maximising heterozygosity, which is essential to maximising productivity in lucerne.

Cadmium levels in the lung, liver, kidney cortex, and urine samples from Australians without occupational exposure to metals

The authors undertook this study to assess levels of cadmium exposure in the general population. Samples of lung, liver, and kidney were obtained from 61 cadavers (43 males, 18 females; 2-89 yr of age, mean age = 38.5 yr) who died from accidental causes and who were subject to postmortem examinations at the John Tonge Centre for Forensic Sciences, Queensland Health Scientific Services, Brisbane, Australia, in 1997 and 1998. Samples of bladder urine were also obtained from 22 cadavers. Tissue and urine samples were analyzed for cadmium, zinc, and copper with inductively coupled plasm (ICP) mass spectrometry. The overall mean values for cadmium in the lung, liver, and kidney cortex samples were 0.13, 0.95, and 15.45 mug/gm wet tissue weight. The average renal cadmium level in subjects with high lung-cadmium levels (n = 13) was 6 mug/gm wet tissue weight higher than that of similarly aged subjects who had medium lung-cadmium levels (n = 30). In females, the average level of cadmium in the liver was 74% greater than in males, and the average liver cadmium in females with high lung-cadmium levels was 100% higher than in males in the same age range who had the same high lung-cadmium levels. Renal cadmium accumulation tended to be greater in females than in males who were in the same age range and who had similar lung-cadmium levels, a result that suggested that there was a higher absorption rate of cadmium in females. The mean value for a urinary cadmium excretion of 2.30 mug/gm creatinine was found in a subset of samples that had a mean age of 39 yr and a renal cortex cadmium concentration of 18.6 mug/gm wet tissue weight. Urinary cadmium excretion rates were correlated more strongly with lung and kidney cadmium content than with age or liver cadmium levels. The results suggest that urinary cadmium excretion may be increased in smokers and could provide some estimate of body cadmium burdens in future Australian epidemiological studies.

Ensuring the future of the psychiatrist administrator

Objective: To describe the increasing trend to appoint non-psychiatrist executive managers to Queensland Mental Health Services and report on strategies to safeguard the future of administrative psychiatrists Conclusion: To ensure a future for administrative psychiatrists, we have formed a Queensland Interest group in Administrative Psychiatry and established a Senior Registrar post in Administrative Psychiatry for two years.

Supply chain management as beyond operational efficiency

The orthodoxy of supply chain management (SCM) emphasises competitive advantage through increased operational efficiency and market responsiveness from production and distribution processes into the hands of consumers. It anticipates that future competition will be between chains rather than between firms. While well established in other industry sectors, the SCM concept is newly developed in the Australian agri-food sector. Critical review of the concept has identified key issues of power among channel members, processes of chain initiation and innovation, and the inability of SCM to offer a viable business strategy for some firms. Building on those insights, this paper examines the supply chain concept for horticulture. Horticultural products are characterised by perishability, heterogeneity and lags in production response to market signals. Producers’ profits are vulnerable to quantity, timing of supply and product specification. Many supply chains in smaller industries are loose, fragmented, interwoven, unstable and unique! Firms operating within these environments need an astute understanding of the chains, the hierarchy of channel members and their relative position. Effective business strategies – for individual firms and supply chains - need to be developed and redeveloped to accommodate the dynamic nature of horticulture. Two case studies are discussed as contributions to this early stage of the theoretical development of supply chain management. The SCM concept also has implications for horticultural researchers, involving a wider range of industry stakeholders, technical problems and research skills. As for business management, the usefulness of the concept will depend on its capacity to increase responsiveness to customers’ preferences and customer value.

Review and future directions in the modelling and control of continuous drum granulation

Many granulation plants operate well below design capacity, suffering from high recycle rates and even periodic instabilities. This behaviour cannot be fully predicted using the present models. The main objective of the paper is to provide an overview of the current status of model development for granulation processes and suggest future directions for research and development. The end-use of the models is focused on the optimal design and control of granulation plants using the improved predictions of process dynamics. The development of novel models involving mechanistically based structural switching methods is proposed in the paper. A number of guidelines are proposed for the selection of control relevant model structures. (C) 2002 Published by Elsevier Science B.V.

Future contributions of crop modelling - from heuristics and supporting decision making to understanding genetic regulation and aiding crop improvement

Crop modelling has evolved over the last 30 or so years in concert with advances in crop physiology, crop ecology and computing technology. Having reached a respectable degree of acceptance, it is appropriate to review briefly the course of developments in crop modelling and to project what might be major contributions of crop modelling in the future. Two major opportunities are envisioned for increased modelling activity in the future. One opportunity is in a continuing central, heuristic role to support scientific investigation, to facilitate decision making by crop managers, and to aid in education. Heuristic activities will also extend to the broader system-level issues of environmental and ecological aspects of crop production. The second opportunity is projected as a prime contributor in understanding and advancing the genetic regulation of plant performance and plant improvement. Physiological dissection and modelling of traits provides an avenue by which crop modelling could contribute to enhancing integration of molecular genetic technologies in crop improvement. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.