Psychometric evaluation of the Early/Late Preferences Scale

This paper examines the psychometric quality of the Early/Late Preferences Scale (PS) relative to that of the Composite Morningness Scale (CS). Questionnaires were completed by 670 undergraduate students aged 16-37 years (mean 22.5), of whom 64% were female. Both scales displayed satisfactory inter-item correlations and similar total mean scores to those reported previously, although the CS had higher variability. Principal axis factor analysis produced single-factor solutions for both scales, although loadings for Items 7 and 9 on the PS were low. Internal consistencies for both scales were good (PS=0.86, CS=0.90) with only a small improvement achieved by deleting Items 7 and 9 from the PS. Test-retest reliability over 11 weeks was good for both scales (PS=0.92, CS=0.89). Differences between morning, evening and intermediate groups in self-rated alertness at different times of day, and significant correlations with other indices of morning-evening orientation, provided evidence of validity for both scales. These results indicate that PS is psychometrically comparable with CS. In view of its simpler format and lower cultural specificity, PS may be considered a preferable measure for most applications.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

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.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

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.

How reliably do rheumatologists measure shoulder movement?

Objective: To assess the intrarater and interrater reliability among rheumatologists of a standardised protocol for measurement of shoulder movements using a gravity inclinometer. Methods: After instruction, six rheurnatologists independently assessed eight movements of the shoulder, including total and glenohumeral flexion, total and glenohumeral abduction, external rotation in neutral and in abduction, internal rotation in abduction and hand behind back, in random order in six patients with shoulder pain and stiffness according to a 6x6 Latin square design using a standardised protocol. These assessments were then repeated. Analysis of variance was used to partition total variability into components of variance in order to calculate intraclass correlation coefficients (ICCs). Results: The intrarater and interrater reliability of different shoulder movements varied widely. The movement of hand behind back and total shoulder flexion yielded the highest ICC scores for both intrarater reliability (0.91 and 0.83, respectively) and interrater reliability (0.80 and 0.72, respectively). Low ICC scores were found for the movements of glenohumeral abduction, external rotation in abduction, and internal rotation in abduction (intrarater ICCs 0.35, 0.43, and 0.32, respectively), and external rotation in neutral, external rotation in abduction, and internal rotation in abduction (interrater ICCs 0.29, 0.11, and 0.06, respectively). Conclusions: The measurement of shoulder movements using a standardised protocol by rheumatologists produced variable intrarater and interrater reliability. Reasonable reliability was obtained only for the movement of hand behind back and total shoulder flexion.

Development of a measure of coping with multiple sclerosis caregiving

Development of a self-report measure of coping specific to multiple sclerosis (MS) caregiving is needed to advance our understanding of the role of coping in adaptation to caring for a person with MS and to contribute to a lack of empirical data on MS caregiving. A total of 213 MS caregivers and their care recipients completed a Coping with MS Caregiving Inventory (CMSCI) and measures of adjustment (psychological distress), appraisal and illness. A subsample (n = 64) also completed the Ways of Coping Checklist (WCC) and additional adjustment measures (depression, caregiving impact. dyadic adjustment, and relationship conflict and reciprocity). Factor analyses revealed 5 factors: Supportive Engagement, Criticism and Coercion, Practical Assistance, Avoidance, and Positive Reframing. Subscales had internal reliabilities comparable to similar scales and were empirically distinct. Preliminary construct validation data are consistent with recent MS caregiving research that links passive avoidant emotion-focused coping with poorer adjustment, and relationship-focused coping caregiving research that links greater reliance on positive relationship-focused coping and less reliance on criticism with better adjustment. Results extend this research by revealing new relations between coping and adaptation to MS caregiving. Convergent validation data suggest that although the inventory differs from the WCC, it does share certain conceptual similarities with this scale.

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.