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.

The measurement of actual acidity in acid sulfate soils and the determination of sulfidic acidity in suspension after peroxide oxidation

Improvements to the routine methods for the determination of actual acidity in suspension for acid sulfate soils (ASS) are introduced. The titratable sulfidic acidity (TSA) results using an improved peroxide-based method were compared with the theoretical acidity predicted by the chromium reducible sulfur method for 9 acid sulfate soils. The regression between these 2 measures of sulfidic acidity was highly significant, the slope of the regression line not significantly different from unity (P = 0.05) and the intercept not significantly different from zero. This contrasts with results of other workers using earlier peroxide oxidation methods, where TSA substantially underestimated the theoretical acidity predicted by reduced inorganic sulfur analysis. Comparison was made between the 2 principal measurements from the improved peroxide method (TSA and S-POS), with S-POS converted to theoretical sulfidic acidity to allow comparison. The relationship between these 2 measurements was highly significant. The effects of titration in suspension, as well as raising titration end points to pH 6.5, were investigated, principally with respect to the titratable actual acidity (TAA) result. TAA results obtained by KCl extraction were compared with those obtained using BaCl2, MgCl2, and water extraction. TAA in 1 M KCl suspensions titrated to pH 6.5 agreed well with titratable actual acidity measured using the 25-h extraction approach of the Lin et al. (2000a) BaCl2 method. Both BaCl2 and KCl solutions were ineffective at fully recovering acidity from synthetic jarosite without repeated extraction and titration. The application of correction factors for the estimation of total actual acidity in ASS is not supported by the results of this investigation. Acid sulfate soils that contain substantial quantities of jarosite or other acid-producing but relatively insoluble sulfate minerals continue to prove problematic to chemically analyse; however, an approach for estimating this component is discussed.

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.

Well-formedness judgment: A comparison of offline and online performance in Broca's aphasics

0na eg rcarmitimcaal tfieca tcuorem opfr ethhee nospieornat iodneafli cdietf i(nAitiCoDn )o ft hthaet frequently co-occurs with Broca’s aphasia is above-chance performance on well-formedness judgment tasks for many syntactic constructions, but impaired performance where syntactic binding of traces to their antecedents occurs. However, the methodologies used to establish this aspect of the performance profile of the ACD have been predominantly offline. Offline well-formedness tasks entail extralinguistic processing (e.g. perception, attention, short-term memory, conscious reflection) in varying amounts and the influence of such processes on parsing mechanisms is yet to be fully established. In order to (a) further understand the role of extra-linguistic processing on parsing, and (b) gain a more direct insight into the online nature of parsing in Broca’s aphasia, 8 subjects underwent a series of wellformedness judgment investigations using both offline and online test batteries. The sentence types and error types used were motivated by three current theories about the nature of the ACD, namely, the Trace-Based Account (Grodzinsky, 2000), the Mapping Hypothesis (Linebarger et al., 1983) and Capacity proposals (e.g. Frazier & Friederici, 1991). The results from the present investigation speak directly to the three aforementioned theories and also demonstrate the important role that extralinguistic processing plays during offline assessment. The clinical implications of the different outcomes from the offline vs. online tasks are also discussed.

ANZUS - Alive and well after fifty years

Marking its fiftieth anniversary in late 2001, the ANZUS alliance remains Australia's primary security relationship and one of the United States' most important defence arrangements in the Asia-Pacific region. It is argued here that ANZUS has defied many common suppositions advanced by international relations theorists on how alliances work. It thus represents an important refutation of arguments that they are short-term instruments of mere policy expediency and are largely interest-dependent. Cultural and normative factors are powerful, if often underrated, determinants for ANZUS's perpetuation. ANZUS may thus constitute an important test case for expanding our understanding of alliance politics beyond the usual preconditions and prerogatives normally associated with such a relationship.

Effects of the solute ionization on the adsorption of aromatic compounds from dilute aqueous solutions by activated carbon

Adsorption of four dissociating aromatic compounds and one nondissociating compound on a commercial activated carbon is investigated systematically. All adsorption experiments were carried out in pH-controlled aqueous solutions. The adsorption isotherms are fitted to the binary homogeneous Langmuir model, where the concentrations of the molecular and the ionic species in the liquid phase are expressed in terms of the sum of the two and the degree of solute ionization. Examination of the relationships between the solution pH, the degree of ionization of the solutes, and the model parameters is found to give new insights into the adsorption process. Furthermore, this is used to correlate the variation of the monolayer capacity with the solution pH.

Comparison of adsorption capacity of p-Cresol & p-Nitrophenol by activated carbon in single and double solute

Adsorption of p-Cresol and p-Nitrophenol by untreated activated carbon in single and multisolute solutions was carried out at 301 K and at controlled pH conditions. In acidic conditions, well below the pK(a) of both solutes, it was observed that the adsorbate solubility and the electron density of aromatic rings influenced the extent of adsorption by affecting the extent of London dispersion forces. The fitted parameters obtained from single-solute Langmuir equation show that Q(max) and the adsorption affinity of carbon for the compound with low pK(a) decrease more significantly. In higher solution pH conditions, on the other hand, it was found that electrostatic forces played a significant role on the extent of adsorption. The presence of another compound decreases Q(max) and the adsorption affinity of carbon for the principal compound. The effect of pH, on the carbon surface and on the solute molecules, must be considered. Adsorption of the solute at higher pH values was found to be dependent on the concentration of anionic form of the solute. The isotherm data were fitted to the Langmuir isotherm equation for both single and double solute solutions.

The strength of concentrated Mg-Zn solid solutions

Solid solution effects on the hardness and flow stress have been studied for zinc contents between 0.2 and 2.4 at% (0.5 and 6.9 wt%) in Mg. The alloys were grain refined with 0.6 wt% zirconium to ensure a similar grain size at all compositions. The hardness increases with the zinc content as Hv(10) (kg mm(-2)) = 9 Zn (at%) + 33. At low solute concentrations the (0.2%) proof strength does not change significantly with concentration. At concentrations above 0.7 at%, within the supersaturated solid solution region, the rate of solid solution hardening is high, following a c(2) rule, where c is the atom fraction of Zn. It is suggested that short-range order may account for most of the observed strengthening in concentrated Mg-Zn alloys.

The impact of participation in activities while on vacation on senior's psychological well-being: A path model application

This article extends earlier research regarding the relationships between senior travelers’ participation in activities while on vacation, their overall satisfaction with their travel experiences, and their psychological well-being. A path model was developed to depict the direct and indirect relationships between these variables by using a sample of senior tourists traveling on North American escorted tour itineraries. Whereas the direct effect accounted for 98% of the relationships between the senior tourists’ levels of participation in activities and their psychological well-being, the indirect effect was negligible. The study concluded that senior tourists’activity levels were significantly related to their psychological well-being, but their satisfaction with the tours was not.

Mental health: How well are occupational therapists equipped for a changed practice environment?

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How well do general practitioners deliver palliative care? A systematic review

General practitioners (GPs) deliver the majority of palliative care to patients in the last year of life. This article seeks to examine the nature of GP care, perceptions of the GPs themselves and others of that care, the adequacy of palliative care training, issues relating to accessibility of GPs to palliative care patients, and strategies that may be of use in encouraging more effective delivery of palliative care by GPs. Medline and PubMed databases from 1966 to 2000 were searched, and 135 references identified. Sixty-six of these described studies relevant to GP palliative care. GPs value this part of their work. Most of the time, patients appreciate the contribution the GP makes to palliative care particularly if the GP is accessible, takes time to listen, allows patient and carer to ventilate their feelings, and is seen to be making efforts made regarding symptom relief. However, reports from bereaved relatives suggest that palliative care is performed less well in the community than in other settings. GPs express discomfort about their competence to perform palliative care adequately. They tend to miss symptoms which are not treatable by them, or which are less common. However, with appropriate specialist support and facilities, GPs have been shown to deliver sound and effective care. GP comfort working with specialist teams increases with exposure to this form of patient management, as does the understanding of the potential other team members have in contributing to the care of the patient. Formal arrangements engaging GPs to work with specialist teams have been shown to improve functional outcomes, patient satisfaction, improve effective use of resources and improve effective physician behaviour in other areas of medicine. Efforts by specialist services to develop formal involvement of GPs in the care of individual patients, may be an effective method of improving GP palliative care skills and appreciation of the roles specialist services can play.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Effects of surface chemistry on aromatic compound adsorption from dilute aqueous solutions by activated carbon

Adsorption of one nondissociating and four dissociating aromatic compounds onto three untreated activated carbons from dilute aqueous solutions were investigated. All adsorption experiments were preformed in pH-controlled solutions. The experimental isotherms were analyzed using the homogeneous Langmuir model. The surface chemical properties of the activated carbons were characterized using a combination of water adsorption, X-ray photoemission spectroscopy, and mass titration. These data give rise to a new insight into the adsorption mechanism of aromatic solutes, in their molecular and ionic forms, onto untreated activated carbons. It was found that, for the hydrophilic activated carbons, the dominant adsorption forces were observed to be dipolar interactions when the solutes were in their molecular form whereas dispersive forces, such as pi-pi interactions, were most likely dominant in the case of the basic hydrophobic carbons. However, when the solutes were in their ionic form adsorption occurs in all cases through dispersive forces.