Dirichlet’s problem on a cracked trapezium

This paper deals with solving Poisson’s equation with conditions on Dirichlet’s limits in an isosceles trapezium with two cracks. The large singular finite elements method used gives satisfactory results in all the domain of study. Numerical values obtained are very accurate for the constraint function and its first derivatives except at the ends of cracks where major changes were registered.Keywords: Large elements, finite elements, singularities, crack

A worldwide map of Plasmodium falciparum K13-propeller polymorphisms

Recent gains in reducing the global burden of malaria are threatened by the emergence of Plasmodium falciparum resistance to artemisinins. The discovery that mutations in portions of a P. falciparum gene encoding kelch (K13)-propeller domains are the major determinant of resistance has provided opportunities for monitoring such resistance on a global scale.; We analyzed the K13-propeller sequence polymorphism in 14,037 samples collected in 59 countries in which malaria is endemic. Most of the samples (84.5%) were obtained from patients who were treated at sentinel sites used for nationwide surveillance of antimalarial resistance. We evaluated the emergence and dissemination of mutations by haplotyping neighboring loci.; We identified 108 nonsynonymous K13 mutations, which showed marked geographic disparity in their frequency and distribution. In Asia, 36.5% of the K13 mutations were distributed within two areas--one in Cambodia, Vietnam, and Laos and the other in western Thailand, Myanmar, and China--with no overlap. In Africa, we observed a broad array of rare nonsynonymous mutations that were not associated with delayed parasite clearance. The gene-edited Dd2 transgenic line with the A578S mutation, which expresses the most frequently observed African allele, was found to be susceptible to artemisinin in vitro on a ring-stage survival assay.; No evidence of artemisinin resistance was found outside Southeast Asia and China, where resistance-associated K13 mutations were confined. The common African A578S allele was not associated with clinical or in vitro resistance to artemisinin, and many African mutations appear to be neutral. (Funded by Institut Pasteur Paris and others.)