Stochastic comparisons of order statistics,with applications in relibility

This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G^?1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described     

The City: A Social Studies Class

Teaching for economic justice can be challenging for upper elementary and middle school teachers. Many teachers may feel uncomfortable with the subject matter and thus avoid addressing sensitive social issues related to economic/financial inequities. This article describes how selected songs and works of visual art, expressions of social protest and social commentary from past and present, can be used appropriately as starting points for introducing the concept of economic justice. By using principles and strategies of Discipline-Based Arts Education (DBAE) and employing works of art as organizing centers for instruction, potentially sensitive social issues are simultaneously personalized and depersonalized. Music and art provide a relatively safe and comfortable means for teachers to promote student awareness and sensitivity towards economic injustices. Two sample lesson plans, the first for upper elementary students and the second for middle school students, are provided and discussed.     

Student Unit: The Advantages and Disadvantages of Group Placement

Social work supervision has been traditionally seen as central to social work training. Its focus was the emphasis on the one-to-one relationship between student and supervisor. The master-apprentice model prevailed. It is probably because of this that group supervision is a relatively late and still quite rare development, in spite of the fact that field placement resources are strained in practically every School.     

Student units for practice teaching in group care

In this paper, an attempt is made to summarize the British position with regard to the use of student units in social work education. The strengths and limitations associated with student units are evaluated with respect to a practice curriculum for people intending to work in the group care field (institutional care, residential group living and day services). Finally, four different models of student unit are identified in such a way as to show how supervised experience could be organised to improve training for group care practice.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

Mastery, Frequency, and Interaction of Managerial Behaviors Relative to Subunit Effectiveness

The relationships among mastery and frequency ofmanagerial behaviors, and subunit effectiveness havefrequently been confused. This study investigates bothmain and interactive effects. The results show that the interaction effect can often be thestrongest effect and that increasing frequency withoutimproving mastery can sometimes be detrimental.Furthermore, these results offer a possible explanation as to why research of managerial behavior hasbeen so inconclusive. In addition, the results questionpopular advice given often to managers. Finally, somerecommendations are made as to how management development could be made more effective basedon the results of this study.     

Are Individuals’ Desired Family Sizes Stable? Evidence from West German Panel Data

Using West German panel data constructed from the 1988 and 1994/1995 wave of the DJI Familiensurvey, we analyze the stability and determinants of individuals’ total desired fertility. We find considerable variation of total desired fertility across respondents and across interviews. In particular, up to 50% of individuals report a different total desired fertility across survey waves. Multivariate analysis confirms the importance of background factors including growing up with both parents, having more siblings, and being Catholic for preference formation. Consistent with the idea that life course experiences provide new information regarding the expected costs and benefits of different family sizes, the influence of background factors on total desired fertility is strong early in life and weakens as subsequent life course experiences, including childbearing, take effect. Accounting for unobserved individual heterogeneity, we estimate that an additional child may increase the total desired fertility of women with children by 0.14 children, less than what conventional estimates from cross-sectional data would have suggested.     

Entropy as a measure of centrality in networks characterized by path-transfer flow

Recently, Borgatti [Borgatti, S.P., 2005. Centrality and network flow. Social Networks 27, 55–71] proposed a taxonomy of centrality measures based on the way that traffic flows through the network—whether over path, geodesic, trail, or walk, and whether by means of transfer, serial duplication, or parallel duplication. Most of the extant centrality measures assume that traffic propagates via parallel duplication or, alternatively, that it travels over geodesics. Few of the other flow possibilities have centrality measures associated with them. This article proposes an entropy-based measure of centrality appropriate for traffic that propagates by transfer and flows along paths. The proposed measure can be applied to most network types, whether binary or weighted, directed or undirected, connected or disconnected. The measure is illustrated on the gang alliance network of Kennedy et al. [Kennedy, D.M., Braga, A. A., Piehl, A.M., 1998. The (un)known universe: mapping gangs and gang violence in Boston. Crime Prevention Studies 8, 219–262].