Nearrings and a construction of triply factorized groups

In this thesis a connection between triply factorised groups and nearrings is investigated. A group G is called triply factorised by its subgroups A, B, and M, if G = AM = BM = AB, where M is normal in G and the intersection of A and B with M is trivial. There is a well-known connection between triply factorised groups and radical rings. If the adjoint group of a radical ring operates on its additive group, the semidirect product of those two groups is triply factorised. On the other hand, if G = AM = BM = AB is a triply factorised group with abelian subgroups A, B, and M, G can be constructed from a suitable radical ring, if the intersection of A and B is trivial. In these triply factorised groups the normal subgroup M is always abelian. In this thesis the construction of triply factorised groups is generalised using nearrings instead of radical rings. Nearrings are a generalisation of rings in the sense that their additive groups need not be abelian and only one distributive law holds. Furthermore, it is shown that every triply factorised group G = AM = BM = AB can be constructed from a nearring if A and B intersect trivially. Moreover, the structure of nearrings is investigated in detail. Especially local nearrings are investigated, since they are important for the construction of triply factorised groups. Given an arbitrary p-group N, a method to construct a local nearring is presented, such that the triply factorised group constructed from this nearring contains N as a subgroup of the normal subgroup M. Finally all local nearrings with dihedral groups of units are classified. It turns out that these nearrings are always finite and their order does not exceed 16.

The construction of TRIGA-TRAP and direct high-precision Penning trap mass measurements on rare-earth elements and americium

Nuclear masses are an important quantity to study nuclear structure since they reflect the sum of all nucleonic interactions. Many experimental possibilities exist to precisely measure masses, out of which the Penning trap is the tool to reach the highest precision. Moreover, absolute mass measurements can be performed using carbon, the atomic-mass standard, as a reference. The new double-Penning trap mass spectrometer TRIGA-TRAP has been installed and commissioned within this thesis work, which is the very first experimental setup of this kind located at a nuclear reactor. New technical developments have been carried out such as a reliable non-resonant laser ablation ion source for the production of carbon cluster ions and are still continued, like a non-destructive ion detection technique for single-ion measurements. Neutron-rich fission products will be available by the reactor that are important for nuclear astrophysics, especially the r-process. Prior to the on-line coupling to the reactor, TRIGA-TRAP already performed off-line mass measurements on stable and long-lived isotopes and will continue this program. The main focus within this thesis was on certain rare-earth nuclides in the well-established region of deformation around N~90. Another field of interest are mass measurements on actinoids to test mass models and to provide direct links to the mass standard. Within this thesis, the mass of 241-Am could be measured directly for the first time.

The role of NPxY domains in LRP1 receptor maturation and function

Analyses of low density lipoprotein receptor-related protein 1 (LRP1) mutant mouse embryonic fibroblasts (MEFs) generated from LRP1 knock-in mice revealed that inefficient maturation and premature proteasomal degradation of immature LRP1 is causing early embryonic lethality in NPxY1 and NPxY1+2 mutant mice. In MEFs, NPxY2 mutant LRP1 showed efficient maturation but, as expected, decreased endocytosis. The single proximal NPxY1 and the double mutant NPxY1+2 were unable to reach the cell surface as an endocytic receptor due to premature degradation. In conclusion, the proximal NPxY1 motif is essential for early sorting steps in the biosynthesis of mature LRP1.rnThe viable NPxY2 mouse was used to provide genetic evidence for LRP1-mediated amyloid-β (Aβ) transport across the blood-brain barrier (BBB). Here, we show that primary mouse brain capillary endothelial cells (pMBCECs) express functionally active LRP1. Moreover, demonstrate that LRP1 mediates [125I]-Aβ1-40 transcytosis across pMBCECs in both directions, whereas no role for LRP1-mediated Aβ degradation was detected. Aβ transport across pMBCECs generated from NPxY2 knock-in mice revealed a reduced Aβ clearance in both directions compared to WT derived pMBCECs. Finally, we conclude that LRP1 is a bona-fide receptor involved in bidirectional transcytosis of Aβ across the BBB.rn