Eigenvalue Problem in Two Dimension for An Irregular Boundary

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.Comment: 16 pages, 4 figures, v2 matches the journal versio

Effect of Supplementation with Zinc and Other Micronutrients on Malaria in Tanzanian Children: A Randomised Trial

Hans Verhoef and colleagues report findings from a randomized trial conducted among Tanzanian children at high risk for malaria. Children in the trial received either daily oral supplementation with either zinc alone, multi-nutrients without zinc, multi-nutrients with zinc, or placebo. The investigators did not find evidence from this study that zinc or multi-nutrients protected against malaria episodes

Genetic variability of hepatitis C virus before and after combined therapy of interferon plus ribavirin

We present an analysis of the selective forces acting on two hepatitis C virus genome regions previously postulated to be involved in the viral response to combined antiviral therapy. One includes the three hypervariable regions in the envelope E2 glycoprotein, and the other encompasses the PKR binding domain and the V3 domain in the NS5A region. We used a cohort of 22 non-responder patients to combined therapy (interferon alpha-2a plus ribavirin) for which samples were obtained before initiation of therapy and after 6 or/and 12 months of treatment. A range of 25-100 clones per patient, genome region and time sample were sequenced. These were used to detect general patterns of adaptation, to identify particular adaptation mechanisms and to analyze the patterns of evolutionary change in both genome regions. These analyses failed to detect a common adaptive mechanism for the lack of response to antiviral treatment in these patients. On the contrary, a wide range of situations were observed, from patients showing no positively selected sites to others with many, and with completely different topologies in the reconstructed phylogenetic trees. Altogether, these results suggest that viral strategies to evade selection pressure from the immune system and antiviral therapies do not result from a single mechanism and they are likely based on a range of different alternatives, in which several different changes, or their combination, along the HCV genome confer viruses the ability to overcome strong selective [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]