Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Prospective individual patient data meta-analysis of two randomized trials on convalescent plasma for COVID-19 outpatients

Data on convalescent plasma (CP) treatment in COVID-19 outpatients are scarce. We aimed to assess whether CP administered during the first week of symptoms reduced the disease progression or risk of hospitalization of outpatients. Two multicenter, double-blind randomized trials (NCT04621123, NCT04589949) were merged with data pooling starting when = 50 years and symptomatic for <= 7days were included. The intervention consisted of 200-300mL of CP with a predefined minimum level of antibodies. Primary endpoints were a 5-point disease severity scale and a composite of hospitalization or death by 28 days. Amongst the 797 patients included, 390 received CP and 392 placebo; they had a median age of 58 years, 1 comorbidity, 5 days symptoms and 93% had negative IgG antibody-test. Seventy-four patients were hospitalized, 6 required mechanical ventilation and 3 died. The odds ratio (OR) of CP for improved disease severity scale was 0.936 (credible interval (CI) 0.667-1.311); OR for hospitalization or death was 0.919 (CI 0.592-1.416). CP effect on hospital admission or death was largest in patients with <= 5 days of symptoms (OR 0.658, 95%CI 0.394-1.085). CP did not decrease the time to full symptom resolution

Educators\' selection and evaluation of natural sciences textbooks

No Abstract. South African Journal of Education Vol. 28 (2) 2008 pp. 175-18