Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

Exactness of SWKB for shape invariant potentials

The supersymmetry-based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.     

Comparison of monomethoxy‐, dimethoxy‐, and trimethoxysilane anchor groups for surface‐initiated RAFT polymerization from silica surfaces

The immobilization of reversible addition–fragmentation chain transfer (RAFT) agents on silica for surface‐initiated RAFT polymerizations (SI‐RAFT) via the Z‐group approach was studied systematically in dependence of the functionality of the RAFT‐agent anchor group. Monoalkoxy‐, dialkoxy‐, and trialkoxy silyl ether groups were incorporated into trithiocarbonate‐type RAFT agents and bound to planar silica surfaces as well as to silica nanoparticles. The immobilization efficiency and the structure of the bound RAFT‐agent film varied strongly in dependence of the used solvent (toluene vs. 1,2‐dimethoxyethane) and the anchor group functionality, as evidenced by atomic force microscopy, transmission electron microscopy, dynamic light scattering, and UV/Vis spectroscopy. Surface‐initiated RAFT polymerizations using functionalized silica nanoparticles revealed that grafted oligomers, which often occur in SI‐RAFT, are not formed within the crosslinked structures that originate from the immobilization, and that RAFT‐agent films that show less aggregation during the immobilization are more efficient during SI‐RAFT in terms of polymer grafting density. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 103–113