Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

Investigating the role of customers’ perceptions of employee effort and justice in service recovery

Purpose: The purpose of this paper is, first, to identify the relationship, if any, between customers’ perceptions of justice (functional element) and employee effort (symbolic element) and their effects on satisfaction and loyalty in the context of service recovery and, second, to determine the impact of cross-cultural differences on these relationships. Design/methodology/approach: Survey data from actual customers were gathered in three countries (n = 414) and analyzed using structural equation modeling to test the proposed hypotheses. Findings: The results demonstrate the role of the constructs of perceived employee effort and perceived justice in influencing post-recovery satisfaction and loyalty across cultures. While perceived justice is valued across cultures, customers from feminine (masculine) cultures require more (less) employee effort to influence post-recovery satisfaction positively. Customers from low (high) uncertainty cultures are more (less) willing to give the provider another chance after a service recovery. Research limitations/implications: The study shows that both functional and symbolic elements of service recovery are important determinants of customer satisfaction and loyalty and that their influence can be significant in a cross-cultural context. Practical implications: International service managers must consider the nature of cultural differences in their markets to develop and implement tailored recovery strategies that can result in satisfied customers. Originality/value: This study is the first to integrate the functional and symbolic elements of service recovery, their impact on customers’ behavioral responses and the influence of cultural variations

A Model for the Study of Development Processes in Dental Research

In studying developmental processes in dental research, variables other than chronological age must often be taken into account if we are to characterize di$erences in the developmental patterns of the groups under consideration. In particular, in addition to age, appropriate developmental models may have to incorporate cohort, time-of-measurement, and learning effects. One such model is described in this article and applied to caries development and gingival condition in the Nymegen Growth Study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66854/2/10.1177_00220345760550031201.pd

Determinants of (non-)recognition of depression by general practitioners: Results of the Netherlands study of depression and anxiety

Background: Although most depressed patients are treated in primary care, not all are recognized as such. This study explores the determinants of (non-)recognition of depression by general practitioners (GPs), with a focus on specific depression symptoms as possible determinants. Methods: Recognition of depression by GPs was investigated in 484 primary care participants of the Netherlands Study of Depression and Anxiety, with a DSM-IV diagnosis of depression in the past year. Recognition (yes/no) by GPs was based on medical file extractions (GP diagnosis of depressive symptoms/depressive disorder and/or use of antidepressants/referral to mental health care). Potential determinants of (non-)recognition (patient, depression, patient-GP interaction, and GP characteristics) were bivariately tested and variables with a p-value <= 0.2 entered into a multilevel multivariate model. Subgroup analysis was performed on 361 respondents with more reliable GP diagnosis data. Results: 60.5% of patients were recognized by their GP. Patients who did not consult their GP for mental problems, and without comorbid anxiety disorder(s) were less often recognized. In the subgroup, where 68.7% was recognized, in addition to these, decreasing number of symptoms of depression and increased appetite were associated with decreased recognition. No GP characteristics were retained in the final model. Limitations: Some data on recognition were collected retrospectively. Conclusions: In addition to patients without a comorbid anxiety disorder or who did not consult their GP for mental problems, GPs less often recognized patients with fewer depression symptoms or with increased appetite. Recognition may be improved by informing/teaching GPs that also increased appetite can be a symptom of depression. (C) 2012 Elsevier B.V. All rights reserved