On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

Ni(II)-doped CsCdBrCl2: Variation of spectral and structural properties via mixed-halide coordination

A new addition to the family of single-molecule magnets is reported: an Fete cage stabilized with benzoate and pyridonate ligands. Monte Carlo methods have been used to derive exchange parameters within the cage, and hence model susceptibility behavior.

Irrational schematic beliefs and psychological distress in caregivers of people with traumatic brain injury

Objective: To investigate the relation between irrational schematic beliefs and psychological distress in caregivers of persons with traumatic brain injury (TBI). Design: Cross-sectional mail survey. Participants: One hundred sixteen caregivers of persons with TBI living in the Australian states of Victoria and Queensland who were members of community support groups and brain injury associations. Measures: The Irrational Beliefs Inventory, Brief Symptom Inventory, income satisfaction, degree of personality and behavior change in the TBI individual, and injury severity. Results: Hierarchical regression analyses showed that after controlling for the effects of characteristics of the caregiving situation and the individual with TBI, greater adherence to irrational beliefs was related to higher levels of global psychological distress. Specifically, irrational beliefs related to Worrying were associated with all areas of psychological distress. Conclusion: Results support the cognitive theory proposal that irrational beliefs play an important role in the adaptation to TBI caregiving. Findings suggest the inclusion of cognitive therapy strategies in interventions for caregivers.

The role of illness, resources, appraisal, and coping strategies in adjustment to HIV/AIDS: The direct and buffering effects

This study examined the utility of a stress and coping model of adjustment to HIV/AIDS. A total of 114 HN-infected gay or bisexual men were interviewed and they completed self-administered scales. Predictors included illness variables (disease stage and number of symptoms), coping resources (optimism and social support), appraisal (threat, challenge, and controllability), and coping strategies (problem-and emotion-focused). Adjustment outcomes were depression, global distress, social adjustment, and subjective health status. Results from hierarchical regression analyses indicated that better adjustment was related to an asymptomatic illness stage, fewer HN-related symptoms, greater social support, challenge and controllability appraisals, problem-focused coping, and lower threat appraisals and reliance on emotion focused coping. There was limited support for the stress-buffering effects of optimism. Findings support the utility of a stress and coping model of adjustment to HIV/AIDS.

Mindreading and moral awareness in popular and rejected preschoolers

This study sought to examine links among young children's peer relations, their moral understanding in terms of the ability to distinguish lies from mistakes, and their theory-of-mind development. Based on sociometric measures, 109 children with a mean age of 4.8 years were divided into groups of popular and rejected preschoolers. Rejected children who had a stable mutual friend scored higher on measures of moral understanding and theory of mind than did rejected children without such friendships. Similarly, popular children who had a stable mutual friendship outperformed other popular children on mindreading, although their moral understanding was no better than that of the popular group who lacked mutual friends. Hierarchical multiple regression analyses revealed that peer popularity was a significant independent predictor of children's moral understanding after any effects of verbal maturity, age and theory-of-mind were statistically controlled. Moreover, having a reciprocal stable friendship made a significant independent contribution to the explanation of individual differences in mindreading, over and above age and verbal maturity, which also contributed significantly. These results are discussed in terms of conversational, cognitive, and emotional processes in the development of social cognition.

The mechanisms of combustion and continuous reactions during mechanical alloying

Some materials exhibit a combustion event during mechanical alloying, which results in the rapid transformation of reactants into products, while others show a slow transformation of reactants into products, In this paper, the continuous W + C --> WC reaction is compared to the Ti + C --> TiC combustion reaction. Rietveld refinement of X-ray diffraction patterns is used to show that these particular reactions proceed through different pathways, determined by crystallographic factors of the reactants. When a crystallographic relationship exists between the reactants and the products, such as that between W and WC, the product forms slowly over a period of time. In contrast, insertion of C into the Ti structure is associated with atomic rearrangements within the crowded lattice planes and the subsequent catastrophic failure of the reactant lattices results in combustion to form TiC. (C) 2001 Academic Press.

A typology of community opportunity and vulnerability in metropolitan Australia

A multivariate model using hierarchical clustering and discriminant analysis is used to identify clusters of community opportunity and community vulnerability across Australia's mega metropolitan regions, Variables used in the model measure aspects of structural economic change, occupational change, human capital, income, unemployment, family/household disadvantage, and housing stress. A nine-cluster solution is used to categorise communities across metropolitan space. Significant between-city variations in the incidence of these clusters of opportunity and vulnerability are apparent, suggesting the emergence of marked differentiation between Australia's mega metropolitan regions in their adjustments to changing economic and social conditions. JEL classification: C49, R11, R12.

The Alcohol Helplessness Scale and its prediction of depression among problem drinkers

Event-specific scales commonly have greater power than generalized scales in prediction of specific disorders and in testing mediator models for predicting such disorders. Therefore, in a preliminary study, a 6-item Alcohol Helplessness Scale was constructed and found to be reliable for a sample of 98 problem drinkers. Hierarchical multiple regression and its derivative path analysis were used to test whether helplessness and self-efficacy moderate or mediate the link between alcohol dependence and depression, A test of a moderation model was not supported, whereas a test of a mediation model was supported. Helplessness and self-efficacy both significantly and independently mediated between alcohol dependence and depression. Nevertheless, a significant direct effect of alcohol dependence on depression also remained, (C) 2001 John Wiley & Sons, Inc.