A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Dilthey''s narrative model of human development: Necessary reconsiderations after the philosophical hermeneutics of Heidegger and Gadamer

Paper delivered at theEighth International Human Science Research Conference at Aarhus University (Denmark), 18–22 August 1989.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

Differential effects of identification with family and peers on coping with developmental tasks in adolescence

Adolescents from three Italian cities responded to a questionnaire concerning the particular peer-group with which they were associated and identification with their family, aspects of the process of coping with seven developmental tasks, and demographic characteristics. The participants were 1600 male and female teenagers, with a mean age of 16.28 years, who were approached at schools and various meeting places in three Italian cities. The study shows that effective coping with developmental tasks depends largely on the degree of identification with both family and peer-group. Those who identify with both social groupings show advantages in various critical situations. Adolescents only identifying with either family or peers get emotional and instrumental support from that group but not from the other, thus, they are supported in some critical situations but not in others. Adolescents who are unwilling or unable to identify with their family and/or their peers are less successful in managing the transition to adulthood than others who are close to their parents and peers. Consistent with the findings of previous studies, the type of group adolescents join, be it a formal group or an informal street group, has no significant effect on their coping strategies.     

Does awareness of speech as a sequence of phones arise spontaneously?

It was found that illiterate adults could neither delete nor add a phone at the beginning of a non-word; but these tasks were rather easily performed by people with similar environment and childhood experiences, who learned to read rudimentarily as adults. Awareness of speech as a sequence of phones is thus not attained spontaneously in the course of general cognitive growth, but demands some specific training, which, for most persons, is probably provided by learning to read in the alphabetic system.     

Examining the psychometric properties of the burnout clinical subtype questionnaire (BCSQ-12) in secondary school teachers

Current Psychology - Based on Farber’s burnout proposal, the first aim of this study was to examine the psychometric properties of the short version of the Burnout Clinical Subtype...     

Measuring structural model invariance across internet-recruited and hospital-recruited IBD patients: Experiential avoidance’s effect on psychopathological symptoms

Current Psychology - Research has questioned whether it is feasible to assess psychosocial variables through web-based recruitment methods. Previous literature on IBD focused exclusively on testing...