We consider the functional equation f(xf(x)) = φ(f(x)) where φ : J → J is a given increasing homeomorphism of an open interval J ⊂ (0,∞) and f : (0,∞) → J is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line y = p where p is a fixed point of φ, with a possible exception for p = 1. The range of any non-constant continuous solution is an ...

In this paper, projective representations of generalized chain geometries are investigated, using the concepts and results of [5]. In particular, we study under which conditions such a projective representation maps the chains of a generalized chain geometry Σ(F,R) to reguli; this mainly depends on how the field F is embedded in the ring R. Moreover, we determine all bijective morphisms of a ce...

An extension of classical stability theory to address the stability of perturbations to time-dependent systems is described. Nonnonnality is found to play a central role in determining the stability of systems �ovemed by nonautonomous operators associated with time-dependent systems. This pivotal role of nonnonnahty provIdes a conceptual bridge by which the generalized stability theory develope...

The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formula...

• The distribution of the variables that originates from monitoring the variance when the mean encountered a sustained shift is considered — specifically for the case when measurements from each sample are independent and identically distributed normal random variables. It is shown that the solution to this problem involves a sequence of dependent random variables that are constructed from inde...

Nihill, M. R., Wilson, D. S., and Hugh-Jones, K. (1970). Archives of Disease in Childhood, 45, 122. Generalized glycogenosis type II (Pompe's disease). The characteristic clinical features of 2 cases of Pompe's disease are presented, namely, signs of a cardiomyopathy with skeletal hypotonia and a characteristic ECG with a short PR interval and high voltage QRS complexes. Glycogen storage diseas...

This paper presents the results of two studies on the promotion of personal self-regulation of development, personal control over development and development-related emotions as well as generalized locus of control and psychosomatic well-being in the elderly using autogenic training (AT), a psychophysiological self-control method using self-inductions of physical and mental relaxation. Subjects...

Multi-informant assessments of adult psychopathology often result in discrepancies among informants' reports. Among 157 adults meeting criteria for either the generalized (n = 106) or nongeneralized (n = 51) social anxiety disorder (SAD) subtype, we examined whether discrepancies between patients' and clinicians' reports of patients' symptoms related to variations in both SAD subtype and expres...