On Indecomposable and Imprimitive Modules for Finite Groups - A G-Algebra Approach

One of the most useful results in modular representation theoryof finite groups is Green's indecomposability theorem [4]. Inorder to state it in a simple form, let us fix a complete discretevaluation ring O of characteristic 0 with algebraically closedresidue field F of characteristic p0. Unless stated otherwise,all our modules will be free of finite rank over O or F, respectively.In its most popular form, Green's theorem says the following.     

Measurement of the spectral flux density of negative muons at very low energies

The spectral flux density of negative muons has been measured down to 5 eV.     

Defect Theory for Prime Ideals and Dress"s Induction Theorem

It is due to Thévenaz that a large part of Puig"s theory of pointed groups carries over to the context of Green functors for finite groups, where here maximal ideals play the role of points in the G-algebra situation. The objective of this paper is to generalize the results further to a situation where one replaces maximal ideals by prime ideals. Moreover, we show that also Puig"s version of Sylow"s first theorem for local pointed groups can be extended to this situation, and we demonstrate that Dress"s induction theorem is a consequence of this result.     

Muonic coulomb capture ratios in fluorides and sulfides

Muonic Coulomb capture ratios for 35 fluorides and 13 sulfides have been measured at SIN, Switzerland. We observed a periodic variation with the atomic numberZ of the cation. This is in agreement with recent theoretical calculations.     

Small Cause,Great Impact: Modification of the Guanidine Group in the RGD Motif Controls Integrin Subtype Selectivity

Due to its unique role as a hydrogen‐bond donor and its positive charge, the guanidine group is an important pharmacophoric group and often used in synthetic ligands. The chemical modification of the guanidine group is often considered to destroy its function. Herein, we show that the N‐methylation, N‐alkylation, or N‐acylation of the guanidine group can be used to modify the receptor subtype specificity of the integrin ligand cilengitide. Using the αvβ6/α5β1‐biselective ligand c(isoDGRkphg) and the αvβ6‐specific ligand c(FRGDLAFp(NMe)K(Ac) as examples, we show that the binding affinities of the ligands can be fine‐tuned by this method to enhance the selectivity for αvβ6. Furthermore, we describe a new strategy for the functionalization of integrin ligands. By introducing longer N‐alkylguanidine and N‐acylguanidine groups, we are able to simultaneously identify a hitherto unknown anchoring point and enhance the subtype selectivity of the ligand.     

Measurement of the coulomb capture ratio of muons in 13 fluorides

The Coulomb capture ratios for muons in 13 fluorides have been measured. The results show variations with the atomic number of the fluorinated element similar to those known for oxides.     

Measurement of muonic X-ray intensities and Coulomb capture ratios in chlorides

Muonic X-ray spectra of 32 chlorides have been measured with Ge detectors. Coulomb capture ratios and Lyman X-ray intensities were determined, and correlations to target data established. The experimental capture ratios agree well with the values from a recently proposed formula.