The 12-Item General Health Questionnaire (GHQ-12): Reliability,external validity and factor structure in the Spanish population

The purpose of this study was to analyze the internal consistency and the external and structure validity of the 12-Item General Health Questionnaire (GHQ-12) in the Spanish general population. A stratified sample of 1001 subjects, ages between 25 and 65 years, taken from the general Spanish population was employed. The GHQ-12 and the Inventory of Situations and Responses of Anxiety-ISRA were administered. A Cronbach’s alpha of .76 (Standardized Alpha: .78) and a 3-factor structure (with oblique rotation and maximum likelihood procedure) were obtained. External validity of Factor I (Successful Coping) with the ISRA is very robust (.82; Factor II, .70; Factor III, .75). The GHQ-12 shows adequate reliability and validity in the Spanish population. Therefore, the GHQ-12 can be used with efficacy to assess people’s overall psychological well-being and to detect non-psychotic psychiatric problems. Additionally, our results confirm that the GHQ-12 can best be thought of as a multidimensional scale that assesses several distinct aspects of distress, rather than just a unitary screening measure.

A historical account of types of fuzzy sets and their relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).