Optimal domain of qq-concave operators and vector measure representation of qq-concave Banach lattices

Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years

An empirical calibration of nebular abundances based on the sulphur emission lines

We present an empirical calibration of nebular abundances based on the strong emission lines of [SII] and [SIII] in the red part of the spectrum through the definition of a sulphur abundance parameter S23. This calibration presents two important advantages against the commonly used one based on the optical oxygen lines: it remains single-valued up to abundances close to solar and is rather independent of the degree of ionization of the nebula.Comment: 10 pages, 8 figures. Accepted for publication in MNRA

Parenting Latino Toddlers and Preschoolers: Clinical and Nonclinical Samples

Parenting practices contribute significantly to the social-emotional development of young children. There is limited literature that addresses the role of culture in parenting, particularly among Latino families who have very young children with significant behavior problems. The current study compared the parenting practices of 30 low-income Latino mothers whose young children had been referred for mental health services for their behavior problems with a similar group of 30 mothers of children without behavior problems. Results showed that mothers in the clinical sample nurtured their children less often and used more frequent verbal and corporal punishment as discipline than the nonclinical sample. The clinical sample also had a significantly higher incidence of mental health problems in their families. Results also showed the significant toll that raising young children with challenging behaviors takes on their mothers. The implications of these findings for the early identification of these children are discussed

Evolution of Vacuum Bubbles Embeded in Inhomogeneous Spacetimes

We study the propagation of bubbles of new vacuum in a radially inhomogeneous background filled with dust or radiation, and including a cosmological constant, as a first step in the analysis of the influence of inhomogeneities in the evolution of an inflating region. We also compare the cases with dust and radiation backgrounds and show that the evolution of the bubble in radiation environments is notably different from that in the corresponding dust cases, both for homogeneous and inhomogeneous ambients, leading to appreciable differences in the evolution of the proper radius of the bubble.Comment: 18 pages, 15 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (new version with a few cosmetic changes w.r.t. the published one