On properties of principal elements of Frobenius Lie algebras

We investigate the properties of principal elements of Frobenius Lie algebras, following the work of M. Gerstenhaber and A. Giaquinto. We prove that any Lie algebra with a left symmetric algebra structure can be embedded, in a natural way, as a subalgebra of some sl(m,K), for K= R or C. Hence, the work of Belavin and Drinfeld on solutions of the Classical Yang-Baxter Equation on simple Lie algebras, applied to the particular case of sl(m, K) alone, paves the way to the complete classification of Frobenius and more generally quasi-Frobenius Lie algebras. We prove that, if a Frobenius Lie algebra has the property that every derivation is an inner derivation, then every principal element is semisimple, at least for K=C. As an important case, we prove that in the Lie algebra of the group of affine motions of the Euclidean space of finite dimension, every derivation is inner. We also bring a class of examples of Frobenius Lie algebras, that hence are subalgebras of sl(m, K), but yet have nonsemisimple principal elements as well as some with semisimple principal elements having nonrational eigenvalues, where K=R or C.Comment: Latex, 16 pages. The last version appeared at Journal of Lie Theory. Keywords and phrases: Frobenius Lie algebra, affine Lie algebra, Left symmetric Lie algebra, affine motion, symplectic Lie algebra, seaweed Lie algebra, symplectic Lie group, invariant symplectic structure, invariant affine structur

Reduced bio-efficacy of permethrin EC impregnated bednets against an Anopheles gambiae strain with oxidase-based pyrethroid tolerance

BACKGROUND: Insecticide-treated nets (ITNs) are an integral component of malaria control programmes in Africa. How much pyrethroid resistance in malaria vectors will impact on the efficacy of ITNs is controversial. The purpose of this study was to evaluate knockdown and killing effects of ITNs on a metabolic-based resistant or tolerant malaria vector strain. METHODS: Bio-efficacy of 500 mg/m(2 )permethrin EC treated bednets was assessed on the OCEAC laboratory (OC-Lab) strain of Anopheles gambiae s.s.. This strain is resistant to DDT and tolerant to pyrethroids, with elevated mixed function oxidases. The Kisumu reference susceptible strain of A. gambiae s.s. was used as control. Nets were impregnated in February 1998 and used by households of the Ebogo village. Then they were collected monthly over six months for Bio-assays (WHO cone test). Knockdown and mortality rates were compared between the OC-Lab and the Kisumu strains, by means of the Mantel-Haenszel chi-square test. RESULTS: During the whole trial, permethrin EC knockdown rates were impressive (mostly higher than 97%). No significant difference was observed between the two strains. However, the mortality rates were significantly decreased in the OC-Lab strain (40–80%) compared with that of the Kisumu strain (75–100%). The decrease of killing effect on the OC-Lab strain was attributed to permethrin EC tolerance, due to the high oxidase metabolic activity. CONCLUSION: These data suggested an impact of pyrethroid tolerance on the residual activity of ITNs. More attention should be given to early detection of resistance using biochemical or molecular assays for better resistance management

The Development of a Temporal Information Dictionary for Social Media Analytics

Dictionaries have been used to analyze text even before the emergence of social media and the use of dictionaries for sentiment analysis there. While dictionaries have been used to understand the tonality of text, so far it has not been possible to automatically detect if the tonality refers to the present, past, or future. In this research, we develop a dictionary containing time-indicating words in a wordlist (T-wordlist). To test how the dictionary performs, we apply our T-wordlist on different disaster related social media datasets. Subsequently we will validate the wordlist and results by a manual content analysis. So far, in this research-in-progress, we were able to develop a first dictionary and will also provide some initial insight into the performance of our wordlist

The Separation of Powers and Constitutionalism in Africa: The Case of Botswana

This Article examines the doctrine of separation of powers and considers its relevance and significance in African constitutional practice, in particular its operation in Botswana. The Article outlines the doctrine\u27s origins, nature, purposes, and its major modern manifestations. The Article then analyzes the separation of powers in Botswana and considers how the doctrine\u27s operation in Botswana has contributed to the country\u27s solid and sustained constitutional system and its reputation as Africa\u27s most successful democracy