We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.

The recent article about estimated glomerular filtration rate (GFR) by Levey and colleagues (1) is remarkable. The authors suggest that the new equation may still have some bias and especially may have less precision in patients with GFRs greater than 60 mL/min per 1.73 m 2 . This is even more important if the GFR is greater than 90 mL/min per 1.73 m 2 . In the paper's Methods section, Levey an...

For k ≥ 1, let I g (k) be the k term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k ≥ 1, there exists some Gk ≥ 0 such that I g (k) is generated by elements which are supported on subsurfaces whose genus is at most Gk. We also prove similar theorems for the Johnson filtration of Aut(Fn) and for certain mod-p analogu...

Filtration of natural and colloidal matter is an essential process in today's water treatment processes. The colloidal matter is retained with the help of micro- and nanoporous synthetic membranes. Colloids are retained in a "cake layer"--often coined fouling layer. Membrane fouling is the most substantial problem in membrane filtration: colloidal and natural matter build-up leads to an increas...

This paper presents the results and conclusions from experimental investigations concerning filtration properties of nonwovens. The needled nonwovens were made from polyester fibres (PTE) with average fibre diameter 12 micrometres and polypropylene fibres (PP) with average fibre diameter 32 micrometres. Nonwovens were produced out of each of those fibres or out of a mixture of polyester and pol...