Generating functions and multiplicity formulas: the case of rank two simple Lie algebras

A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown

Stability of Feverfew and its Active Principle Parthenolide: An Elusive Antimigraine Herbal Medicine

Background Feverfew is a traditional herbal remedy for the relief of arthritis, migraine, toothache, and menstrual difficulties. It is widely accepted that parthenolide, a sesquiterpene lactone, is its main active principle. However, the decrease of parthenolide in commercial preparations is a well-known process with no technical solution so far. Aims To review the evidence for the mechanism of the degradation of parthenolide and similar sesquiterpene lactones. Methods Systematic review. Results and Conclusion In conclusion, and without discarding any degradation of parthenolide into non-identifiable fragments, the fate of this compound in dry, powdered feverfew is to undergo a covalent binding to plant proteins resulting in a biologically inactive adduct - in accordance with the direct and indirect data found in the literature. This process seems to be virtually unstoppable, and temperature and light do not seem to be playing a significant role under normal storage conditions according to some authors. In the presence of a high level of humidity, parthenolide may undergo an acid-induced cyclisation giving rise to a guaianolide-type sesquiterpene lactone, a class of compound that is commonly found in Feverfew. Microbial degradations are not likely to play an important role if the formulation complies with Pharmacopoeial microbiological quality requirements. The experimental and clinical data in the literature do not report on any increase in the toxicity of stored feverfew.&nbsp

A remark on proper partitions of unity

In this paper we introduce, by means of the category of exterior spaces and using a process that generalizes the Alexandroff compactification, an analogue notion of numerable covering of a space in the proper and exterior setting. An application is given for fibrewise proper homotopy equivalences.Comment: 15 pages, 1 figur

Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey

Growing progress in sensor technology has constantly expanded the number and range of low-cost, small, and portable sensors on the market, increasing the number and type of physical phenomena that can be measured with wirelessly connected sensors. Large-scale deployments of wireless sensor networks (WSN) involving hundreds or thousands of devices and limited budgets often constrain the choice of sensing hardware, which generally has reduced accuracy, precision, and reliability. Therefore, it is challenging to achieve good data quality and maintain error-free measurements during the whole system lifetime. Self-calibration or recalibration in ad hoc sensor networks to preserve data quality is essential, yet challenging, for several reasons, such as the existence of random noise and the absence of suitable general models. Calibration performed in the field, without accurate and controlled instrumentation, is said to be in an uncontrolled environment. This paper provides current and fundamental self-calibration approaches and models for wireless sensor networks in uncontrolled environments