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

On the classification of 2-solvable Frobenius Lie algebras

We discuss the classification of 2-solvable Frobenius Lie algebras. We prove that every 2-solvable Frobenius Lie algebra splits as a semidirect sum of an n-dimensional vector space V and an n-dimensional maximal Abelian subalgebra (MASA) of the full space of endomorphisms of V. We supply a complete classification of 2-solvable Frobenius Lie algebras corresponding to nonderogatory endomorphisms, as well as those given by maximal Abelian nilpotent subalgebras (MANS) of class 2, hence of Kravchuk signature (n-1,0,1). In low dimensions, we classify all 2-solvable Frobenius Lie algebras in general up to dimension 8. We correct and complete the classification list of MASAs of sl(4, R) by Winternitz and Zassenhaus. As a biproduct, we give a simple proof that every nonderogatory endormorphism of a real vector space admits a Jordan form and also provide a new characterization of Cartan subalgebras of sl(n, R).Comment: V2: 26 pages, Latex. Title slightly changed. Typos corrected. More details on the proof that every nonderogatory real endomorphism/matrix admits a Jordan form. To appear at Journal of Lie Theor

Outcome of life-threatening malaria in African children requiring endotracheal intubation

BACKGROUND: Little is known about children undergoing critical care for malaria. The purpose of this survey was to evaluate the outcome in African children requiring endotracheal intubation for life-threatening malaria. METHODS: All children with a primary diagnosis of severe malaria (2000 WHO definition) requiring endotracheal intubation, hospitalised over a five-year period, within a tertiary-care hospital in Dakar, Senegal, were enrolled in a retrospective cohort study. RESULTS: 83 consecutive patients were included (median PRISM h(24 )score: 14; IQR: 10–19, multiple organ dysfunctions: 91.5%). The median duration of ventilation was 36 hrs (IQR: 4–72). Indications for intubation were deep coma (Glasgow score ≤7, n = 16), overt cortical or diencephalic injury, i.e, status epilepticus/decorticate posturing (n = 20), severe brainstem involvement, i.e., decerebrate posturing/opisthotonus (n = 15), shock (n = 15), cardiac arrest (n = 13) or acute lung injury (ALI) (PaO(2)/FiO(2 )<300 Torr, n = 4). Death occurred in 50 cases (case fatality rate (CFR), 60%) and was associated with multiple organ dysfunctions (median PELOD(h24 )scores: 12.5 among non-survivors versus 11 among survivors, p = 0.02). Median PRISM(h24 )score was significantly lower when testing deep coma against other indications (10 vs 15, p < 0.001), ditto for PELOD(h24 )score (2.5 vs 13, p = 0.02). Multivariate analysis identified deep coma as having a better outcome than other indications (CFR, 12.5% vs 40.0 to 93.3%, p < 0.0001). Decerebrate posturing/opisthotonus (CFR 73.3%, adjusted relative risk (aRR) 10.7, 95% CI 2.3–49.5) were associated with a far worse prognosis than status epilepticus/decorticate posturing (CFR 40.0%, aRR 5.7, 95% CI 1.2–27.1). Thrombocytopaenia (platelet counts <100,000/mm(3)) was associated with death (aRR 2.6, 95% CI 1.2–5.8) and second-line anticonvulsant use (clonazepam or thiopental) with survival (aRR 0.4, 95% CI 0.2–0.9). Complications, mostly nosocomial infections (n = 20), ALI/ARDS (n = 9) or sub-glottic stenosis (n = 3), had no significant prognostic value. CONCLUSION: In this study, the outcome of children requiring intubation for malaria depends more on clinical presentation and progression towards organ failures than on critical care complications per se. In sub-Saharan Africa, mechanical ventilation for life-threatening childhood malaria is feasible, but seems unlikely to dramatically improve the prognosis

Prise en charge de l’hematome extradural a Dakar. A propos de 40 cas

Introduction L’hématome extradural est une affection rare mais grave car engage rapidement le pronostic vital. Il s’agit d’une urgence thérapeutique nécessitant par conséquent une prise en charge rapide.Objectif L’objectif de ce travail est d’évaluer les aspects épidémiologiques, diagnostiques et thérapeutiques de l’hématome extradural depuis l’avènement du scanner dans notre pays.Patients et méthode Il s’agit d’une étude rétrospective multicentrique réalisée dans quatre de nos hôpitaux durant une période de huit ans, de juillet 1994 à juin 2002. Nous avons pu collecter 40 dossiers de patients traumatisés cranioencéphaliques présentant un hématome extradural à la tomodensitométrie cérébrale.Résultats Sur 1296 patients ayant consulté pour un traumatisme cranio-encéphalique toute gravité confondue, 40 ont présenté un hématome extra dural soit 3,09%. L’age moyen était de 26.1 ans avec une fréquence maximale entre 11 et 20 ans. Le sex. Ratio est de 9.1. Les accidents de la voie publique représentent l’étiologie la plus fréquente avec 55% des cas. Le délai de consultation est long avec une moyenne de 2 à 3 jours. L’examen clinique retrouve des signes d’hypertension intracrânienne chez 87,5% des patients, un déficit moteur chez 30% des patients, des troubles de la conscience dans 55% des cas. Les résultats scannographiques ont montré une localisation temporo pariétale prédominante (72,5%) . 87,5% des patients ont bénéficié d’une prise en charge chirurgicale. L’évolution est favorable dans 75% des cas. Nous avons noté 20% de mortalité.Conclusion L’hématome extradural constitue l’urgence neurochirurgicale type. Son pronostic est bon si traité précocement

Plasmodium falciparum susceptibility to standard and potential anti-malarial drugs in Dakar, Senegal, during the 2013–2014 malaria season

International audienceBackground: In 2006, the Senegalese National Malaria Control Programme recommended artemisinin-based combination therapy (ACT) as the first-line treatment for uncomplicated malaria. Since the introduction of ACT, there have been very few reports on the level of Plasmodium falciparum resistance to anti-malarial drugs. An ex vivo susceptibility study was conducted on local isolates obtained from the Hôpital Principal de Dakar (Dakar, Senegal) from November 2013 to January 2014. Methods: Eighteen P. falciparum isolates were sussessfully assessed for ex vivo susceptibility to chloroquine (CQ), quinine (QN), monodesethylamodiaquine (MDAQ), the active metabolite of amodiaquine, mefloquine (MQ), lumefantrine (LMF), artesunate (AS), dihydroartemisinin (DHA), the active metabolite of artemisinin derivatives, pyronaridine (PND), piperaquine (PPQ), and, Proveblue (PVB), a methylene blue preparation, using the HRP2-based ELISA test. Results: The prevalence of isolates with reduced susceptibility was 55.6% for MQ, 50% for CQ, 5.6% for QN and MDAQ, and 0% for DHA, AS and LMF. The mean IC 50 for PND, PPQ and PVB were 5.8 nM, 32.2 nM and 5.3 nM, respectively. Conclusions: The prevalence of isolates with a reduced susceptibility to MQ remains high and stable in Dakar. Since 2004, the prevalence of CQ resistance decreased, but rebounded in 2013 in Dakar. PND, PPQ and PVB showed high in vitro activity in P. falciparum parasites from Dakar

Plasmodium fakiparum In Vitro Resistance to Monodesethylamodiaquine, Dakar, Senegal, 2014

International audienceWe successfully cultured 36 Plasmodium falciparum isolates from blood samples of 44 malaria patients admitted to the Hopital Principal de Dakar (Dakar, Senegal) during August December 2014. The prevalence of isolates with in vitro reduced susceptibility was 30.6% for monodesethylamodiaquine, 52.8% for chloroquine, 44.1% for mefloquine, 16.7% for doxycycline, 11.8% for piperaquine, 8.3% for artesunate, 5.9% for pyronaridine, 2.8% for quinine and dihydroartemisinin, and 0.0% for lumefantrine. The prevalence of isolates with reduced in vitro susceptibility to the artemisinin-based combination therapy partner monodesethylamodiaquine increased from 5.6% in 2013 to 30.6% in 2014. Because of the increased prevalence of P. falciparum parasites with impaired in vitro susceptibility to monodesethylamodiaquine, the implementation of in vitro and in vivo surveillance of all artemisinin-based combination therapy partners is warranted