Uniqueness of the invariant mean on an abelian semigroup

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A note on a result of Mahler's

In a recent paper, Maher [2] proved that for any algebraic number field K of degree n and discriminant d there exists a constant C depending only on n and d such that for any ceiling λP of K there exists a basis α1 ..., αn of the corresponding ideal αλ such that C-(n-1)λ(q) ≤ |αk|q ≤ Cλ(q) for all q; C-n λ(τ) ≤ |αk|τ ≤ λ(τ) for all r; (k = 1, 2, ..., n)

How should we measure psychological resilience in sport performers?

Psychological resilience is important in sport because athletes must constantly withstand a wide range of pressures to attain and sustain high performance. To advance psychologists’ understanding of this area, there exists an urgent need to develop a sport-specific measure of resilience. The purpose of this paper is to review psychometric issues in resilience research and to discuss the implications for sport psychology. Drawing on the wider general psychology literature to inform the discussion, the narrative is divided into three main sections relating to resilience and its assessment: adversity, positive adaptation, and protective factors. The first section reviews the different ways that adversity has been measured and considers the potential problems of using items with varying degrees of controllability and risk. The second section discusses the different approaches to assessing positive adaptation and examines the issue of circularity pervasive in resilience research. The final section explores the various issues related to the assessment of protective factors drawing directly from current measures of resilience in other psychology sub-disciplines. The commentary concludes with key recommendations for sport psychology researchers seeking to develop a measure of psychological resilience in athletes

Zassenhaus conjecture for A<SUB>5</SUB>

We develop a criterion for rational conjugacy of torsion units of the integral group ring ZG of a finite group G, as also a necessary condition for an element of ZG to be a torsion unit, and apply them to verify the Zassenhaus conjecture in case when G=A5

The role of pre-school quality in promoting resilience in the cognitive development of young children

The study reported here investigates the role of pre-school education as a protective factor in the development of children who are at risk due to environmental and individual factors. This investigation builds upon earlier research by examining different kinds of 'quality' in early education and tests the hypothesis that pre-schools of high quality can moderate the impacts of risks upon cognitive development. Cognitive development was measured in 2857 English pre-schoolers at 36 and 58 months of age, together with 22 individual risks to children's development, and assessments were made of the quality of their pre-school provision. Multilevel Structural Equation Modelling revealed that: the global quality of pre-school can moderate the effects of familial risk (such as poverty); the relationships between staff and children can moderate the effects of child level risk (such as low birth weight); and the specific quality of curricular provision can moderate the effects of both. Policy makers need to take quality into account in their efforts to promote resilience in young 'at risk' children through early childhood services

Children with co-occurring anxiety and externalizing disorders: Family risks and implications for competence.

This study used data from 340 mother–child dyads to examine characteristics of children with co-occurring diagnoses of anxiety and externalizing disorders and compared them with children with a sole diagnosis or no diagnosis. Comparisons were made using 4 child-diagnostic groups: anxiety-only, externalizing-only, co-occurrence, and no-problem groups. Most mothers were characterized by low income and histories of psychiatric diagnoses during the child’s lifetime. Analyses using multinomial logistic regressions found the incidence of co-occurring childhood disorders to be significantly linked with maternal affective/anxiety disorders during the child’s lifetime. In exploring implications for developmental competence, we found the co-occurrence group to have the lowest level of adaptive functioning among the 4 groups, faring significantly worse than the no-problem group on both academic achievement and intelligence as assessed by standardized tests. Findings underscore the importance of considering co-occurring behavior problems as a distinct phenomenon when examining children’s developmental outcomes

Capturing Age-group Differences and Developmental Change with the BASC Parent Rating Scales

Estimation of age-group differences and intra-individual change across distinct developmental periods is often challenged by the use of age-appropriate (but non-parallel) measures. We present a short version of the Behavior Assessment System (Reynolds & Kamphaus, 1998), Parent Rating Scales for Children (PRS-C) and Adolescents (PRS-A), which uses only their common-items to derive estimates of the initial constructs optimized for developmental studies. Measurement invariance of a three-factor model (Externalizing, Internalizing, Adaptive Skills) was tested across age-groups (161 mothers using PRS-C; 200 mothers using PRS-A) and over time (115 mothers using PRS-C at baseline and PRS-A five years later) with the original versus short PRS. Results indicated that the short PRS holds a sufficient level of invariance for a robust estimation of age-group differences and intra-individual change, as compared to the original PRS, which held only weak invariance leading to flawed developmental inferences. Importance of test-content parallelism for developmental studies is discussed

A systematic review on health resilience to economic crises

Background The health effects of recent economic crises differ markedly by population group. The objective of this systematic review is to examine evidence from longitudinal studies on factors influencing resilience for any health outcome or health behaviour among the general population living in countries exposed to financial crises. Methods We systematically reviewed studies from six electronic databases (EMBASE, Global Health, MEDLINE, PsycINFO, Scopus, Web of Science) which used quantitative longitudinal study designs and included: (i) exposure to an economic crisis; (ii) changes in health outcomes/behaviours over time; (iii) statistical tests of associations of health risk and/or protective factors with health outcomes/behaviours. The quality of the selected studies was appraised using the Quality Assessment Tool for Quantitative Studies. PRISMA reporting guidelines were followed. Results From 14,584 retrieved records, 22 studies met the eligibility criteria. These studies were conducted across 10 countries in Asia, Europe and North America over the past two decades. Ten socio-demographic factors that increased or protected against health risk were identified: gender, age, education, marital status, household size, employment/occupation, income/ financial constraints, personal beliefs, health status, area of residence, and social relations. These studies addressed physical health, mortality, suicide and suicide attempts, mental health, and health behaviours. Women’s mental health appeared more susceptible to crises than men’s. Lower income levels were associated with greater increases in cardiovascular disease, mortality and worse mental health. Employment status was associated with changes in mental health. Associations with age, marital status, and education were less consistent, although higher education was associated with healthier behaviours. Conclusions Despite widespread rhetoric about the importance of resilience, there was a dearth of studies which operationalised resilience factors. Future conceptual and empirical research is needed to develop the epidemiology of resilience