Abstract. Let RG denote the group ring of the group G over the ring R. Using an isomorphism between RG and a certain ring of n × n matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order 8 over any finite field of chracteristic 2 is determined in terms of split extensions of cyclic groups.
This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If RG is a group ring, where R is commutative and S is a set of generators of G then necessary and sufficient conditions on a map from S to RG are established, such that the map can be extended to an R-derivation of RG. Derivations are shown to be trivial for semisimple group algebras of abelian groups. The derivations of finite group algebras are constructed and listed in the commutative case and in the case of dihedral groups. In the dihedral case, the inner derivations are also classified. Lastly, these results are applied to construct well known binary codes as images of derivations of group algebras.
In this paper, newly discovered mechanisms of atresia and cell death processes in bovine ovarian follicles are investigated. For this purpose the mRNA expression of receptor interacting protein kinases 1 and 3 (RIPK1 and RIPK3) of the granulosa and theca cells derived from healthy and atretic follicles are studied. The follicles were assigned as either healthy or atretic based on the estradiol to progesterone ratio. A statistically significant difference was recorded for the mRNA expression of a RIPK1 and RIPK3 between granulosa cells from healthy and atretic follicles. To further investigate this result a systems biology approach was used. The genes playing roles in necroptosis, apoptosis and atresia were chosen and a network was created based on human genes annotated by the IMEx database in Cytoscape to identify hubs and bottle-necks. Moreover, correlation networks were built in the Cluepedia plug-in. The networks were created separately for terms describing apoptosis and programmed cell death. We demonstrate that necroptosis (RIPK—dependent cell death pathway) is an alternative mechanism responsible for death of bovine granulosa and theca cells. We conclude that both apoptosis and necroptosis occur in the granulosa cells of dominant follicles undergoing luteinisation and in the theca cells from newly selected follicles.
PLA (polylactide) is a bioresorbable polymer used in implantable medical and drug delivery devices. Like other bioresorbable polymers, PLA needs to be processed carefully to avoid degradation. In this work we combine in-process temperature, pressure, and NIR spectroscopy measurements with multivariate regression methods for prediction of the mechanical strength of an extruded PLA product. The potential to use such a method as an intelligent sensor for real-time quality analysis is evaluated based on regulatory guidelines for the medical device industry. It is shown that for the predictions to be robust to processing at different times and to slight changes in the processing conditions, the fusion of both NIR and conventional process sensor data is required. Partial least squares (PLS), which is the established ’soft sensing’ method in the industry, performs the best of the linear methods but demonstrates poor reliability over the full range of processing conditions. Conversely, both random forest (RF) and support vector regression (SVR) show excellent performance for all criteria when used with a prior principal component (PC) dimension reduction step. While linear methods currently dominate for soft sensing of mixture concentrations in highly conservative, regulated industries such as the medical device industry, this work indicates that nonlinear methods may outperform them in the prediction of mechanical properties from complex physicochemical sensor data. The nonlinear methods show the potential to meet industrial standards for robustness, despite the relatively small amount of training data typically available in high-value material processing.
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