Superspace description of wagnerite-group minerals (Mg,Fe,Mn) 2 (PO 4 )(F,OH)

Reinvestigation of more than 40 samples of minerals belonging to the wagnerite group (Mg, Fe, Mn)2(PO4)(F,OH) from diverse geological environments worldwide, using single-crystal X-ray diffraction analysis, showed that most crystals have incommensurate structures and, as such, are not adequately described with known polytype models (2b), (3b), (5b), (7b) and (9b). Therefore, we present here a unified superspace model for the structural description of periodically and aperiodically modulated wagnerite with the (3+1)-dimensional superspace group C2/c(0[beta]0)s0 based on the average triplite structure with cell parameters a [asymptotically equal to] 12.8, b [asymptotically equal to] 6.4, c [asymptotically equal to] 9.6 Å, [beta] [asymptotically equal to] 117° and the modulation vectors q = [beta]b*. The superspace approach provides a way of simple modelling of the positional and occupational modulation of Mg/Fe and F/OH in wagnerite. This allows direct comparison of crystal properties.

Skolemization for Substructural Logics

The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices. However, it is shown here (following similar ideas of Baaz and Iemhoff for first-order intermediate logics in [1]) that first-order substructural logics with a semantics satisfying certain witnessing conditions admit a “parallel” Skolemization procedure where a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate) of formulas with multiple new function symbols. These logics typically lack equivalent prenex forms. Also, semantic consequence does not in general reduce to satisfiability. The Skolemization theorems presented here therefore take various forms, applying to the left or right of the consequence relation, and to all formulas or only prenex formulas.

Description of the SAGhE Cohort: A Large European Study of Mortality and Cancer Incidence Risks after Childhood Treatment with Recombinant Growth Hormone.

BACKGROUND The long-term safety of growth hormone treatment is uncertain. Raised risks of death and certain cancers have been reported inconsistently, based on limited data or short-term follow-up by pharmaceutical companies. PATIENTS AND METHODS The SAGhE (Safety and Appropriateness of Growth Hormone Treatments in Europe) study assembled cohorts of patients treated in childhood with recombinant human growth hormone (r-hGH) in 8 European countries since the first use of this treatment in 1984 and followed them for cause-specific mortality and cancer incidence. Expected rates were obtained from national and local general population data. The cohort consisted of 24,232 patients, most commonly treated for isolated growth failure (53%), Turner syndrome (13%) and growth hormone deficiency linked to neoplasia (12%). This paper describes in detail the study design, methods and data collection and discusses the strengths, biases and weaknesses consequent on this. CONCLUSION The SAGhE cohort is the largest and longest follow-up cohort study of growth hormone-treated patients with follow-up and analysis independent of industry. It forms a major resource for investigating cancer and mortality risks in r-hGH patients. The interpretation of SAGhE results, however, will need to take account of the methods of cohort assembly and follow-up in each country.