Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

Study on hydrogen absorption in Zr powder used for tritium confinement in a production system of tritium for fusion reactors with a high-temperature gas-cooled reactor

ABSTRACT: A tritium production method using a high-temperature gas-cooled reactor loaded with lithium compound particles has been proposed for steadily starting up and stably operating a fusion reactor. In order to confine the produced tritium, small lithium-compound particles are considered to be coated by ceramic materials. The present authors have proposed adding zirconium fine particles into the inside of the ceramic coating to improve tritium confinement performance. In this work, powdered zirconium was exposed to hydrogen or deuterium gas in a closed volume at elevated temperatures and absorption rate constant and Sieverts' constant were evaluated by the pressure drop by absorption. After the experiments, it was found that the powdered zirconium sample became a lump by a sintering effect. By referring literature data for α-zirconium and its oxide, the observed absorption rate was speculated to include the influence of sintering and oxide layer. The obtained Sieverts’ constants were slightly smaller than literature data. By taking into account the observed hydrogen absorption behavior in powdered zirconium, tritium leak from alumina-coated lithium-compound particles containing zirconium fine particles was roughly estimated in some conditions. Tritium permeation rate can be reduced by adding zirconium but the leak suppression effect is limited. Keywords: Hydrogen absorption, Zirconium, Tritium confinemen

Standard Rape Cases in the Criminal Justice System in Campinas, São Paulo

This study presents a longitudinal analysis of the records found in the Women’s Defense Division of the Public Ministry and in the Criminal Courts of the municipality of Campinas, São Paulo State. The study identified both the characteristics of rape (the accused, victims and relations between them), as well as the processes of selection and filtering to which they are submit during their processing. The results found for Campinas reflect rape complaints found in international studies, which indicate that rape is a heterogeneous category, although the aggressors are invariably men and the victims young. On the other hand, when the criminal selection process is analyzed, a filtering of typologies is noticed, found in the complaint phase in three standards for the crime of rape: intrafamiliar, committed by an unknown aggressor and among youth who know each other