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.

Relationships between nutrition screening checklists and the health and well-being of older Australian women

Objectives: To examine associations between nutrition screening checklists and the health of older women. Design: Cross-sectional postal survey including measures of health and health service utilisation, as well as the Australian Nutrition Screening Initiative (ANSI), adapted from the Nutrition Screening Initiative (NSI). Setting: Australia, 1996. Subjects: In total, 12 939 women aged 70-75 years randomly selected as part of the Australian Longitudinal Study on Women's Health. Results: Responses to individual items in the ANSI checklist, and ANSI and NSI scores, were associated with measures of health and health service utilisation. Women with high ANSI and NSI scores had poorer physical and mental health, higher health care utilisation and were less likely to be in the acceptable weight range. The performance of an unweighted score (TSI) was also examined and showed similar results. Whereas ANSI classified 30% of the women as 'high-risk', only 13% and 12% were classified as 'high-risk' by the NSI and TSI, respectively. However, for identifying women with body mass index outside the acceptable range, sensitivity, specificity and positive predictive values for all of these checklists were less than 60%. Conclusions: Higher scores on both the ANSI and NSI are associated with poorer health. The simpler unweighted method of scoring the ANSI (TSI) showed better discrimination for the identification of 'at risk' women than the weighted ANSI method. The predictive value of individual items and the checklist scores need to be examined longitudinally.

A probabilistic analysis of Clostridium perfringens growth during food service operations

The purpose of this study was threefold: first, the study was designed to illustrate the use of data and information collected in food safety surveys in a quantitative risk assessment. In this case, the focus was on the food service industry; however, similar data from other parts of the food chain could be similarly incorporated. The second objective was to quantitatively describe and better understand the role that the food service industry plays in the safety of food. The third objective was to illustrate the additional decision-making information that is available when uncertainty and variability are incorporated into the modelling of systems. (C) 2002 Elsevier Science B.V. All rights reserved.

Point source inoculation of Mesocyclops (Copepoda : Cyclopidae) gives widespread control of Ochlerotatus and Aedes (Diptera : Culicidae) immatures in service manholes and pits in North Queensland, Australia

This study details the novel application of predacious copepods, genus Mesocyclops, for control of Ochlerotatus tremulus (Theobald) group and Aedes aegypti (L.) mosquito larvae in subterranean habitats in north Queensland, Australia. During June 1997, 50 Mesocyclops sp. I were inoculated into one service manhole in South Townsville. Wet season rainfall and flooding in both 1998 and 2000 was responsible for the dispersal of copepods via the underground pipe system to 29 of 35 manholes over an area of 1.33 km(2). Significant reductions in Aedes and Ochlerotatus larvae ensued. In these habitats, Mesocyclops and Metacyclops were able to survive dry periods, when substrate moisture content ranged from 13.8 to 79.9%. At the semiarid inland towns of Hughenden and Richmond, cracking clay soil prevents drainage of water from shallow service pits where Oc. tremulus immatures numbered from 292-18,460 per pit. Introduction of Mesocyclops copepods into these sites during May 1999 resulted in 100% control of Oc. tremulus for 18 mo. One uninoculated pit subsequently became positive for Mesocyclops with resultant control of mosquito larvae.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Application of fairness theory to service failures and service recovery

This article presents a fairness theory-based conceptual framework for studying and managing consumers’ emotions during service recovery attempts. The conceptual framework highlights the central role played by counterfactual thinking and accountability. Findings from five focus groups are also presented to lend further support to the conceptual framework. Essentially, the article argues that a service failure event triggers an emotional response in the consumer, and from here the consumer commences an assessment of the situation, considering procedural justice, interactional justice, and distributive justice elements, while engaging in counterfactual thinking and apportioning accountability. More specifically, the customer assesses whether the service provider could and should have done something more to remedy the problem and how the customer would have felt had these actions been taken. The authors argue that during this process situational effort is taken into account when assessing accountability. When service providers do not appear to exhibit an appropriate level of effort, consumers attribute this to the service provider not caring. This in turn leads to the customer feeling more negative emotions, such as anger and frustration. Managerial implications of the study are discussed.

The role of gender in reactions to service failure and recovery

Male and female consumers place different emphasis on elements of the service recovery process. Perceptions were influenced by gender of the service provider and by a match of customer and service provider gender. The study, an experimental design with 712 respondents, found that when service providers, irrespective of gender, display concern and give customers voice and a sizable compensation, both men and women reported more positive attitudes compared with when this was not so. Combinations of high voice with high outcome and high voice with high concern were especially important in positively influencing perceptions of effort, regardless of gender. However, the authors also found that there were significant differences between male and female respondents regarding their perceptions of how service recovery should be handled. Women want their views heard during service recovery attempts and to be allowed to provide input. Men, in contrast, do not view voice as important.