On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Hydraulic Conditions Required to Move Unanchored Residue Materials

Hydraulic conditions required to initiate movement of unanchored residue materials are identified in the present study. Selected amounts of corn, cotton, pine needles, sorghum, soybean, sunflower, and wheat residue are placed in a flume on a sand surface, and flow is then introduced at the top of the flume in progressive increments. The discharge rate and flow velocity necessary to cause residue movement are determined. The ratio of critical flow depth to residue diameter, critical Reynolds number, critical shear stress, dimensionless shear stress, and boundary Reynolds number are calculated from hydraulic measurements. Regression equations are developed to relate dimensionless shear stress to boundary Reynolds number and residue diameter. Boundary Reynolds number, in turn, is related to residue diameter and cover. Close agreement is found between predicted and actual parameter values obtained from the regression relations. The regression equations can be used to estimate the beginning of motion for other residue materials if residue diameter and cover are known

The Discriminant of an Algebraic Torus

For a torus T defined over a global field K, we revisit an analytic class number formula obtained by Shyr in the 1970's as a generalization of Dirichlet's class number formula. We prove a local-global presentation of the quasi-discriminant of T, which enters into this formula, in terms of cocharacters of T. This presentation can serve as a more natural definition of this invariant.Comment: 17 page

Mutations in PINK1 and Parkin Impair Ubiquitination of Mitofusins in Human Fibroblasts

PINK1 and Parkin mutations cause recessive Parkinson's disease (PD). In Drosophila and SH-SY5Y cells, Parkin is recruited by PINK1 to damaged mitochondria, where it ubiquitinates Mitofusins and consequently promotes mitochondrial fission and mitophagy