Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Periodic administration of allopurinol is not effective for the prevention of canine leishmaniosis (Leishmania infantum) in the endemic areas

A total of 95 clinically healthy and seronegative for Leishmania infantum dogs, residing an area highly endemic for canine leishmaniosis (CL) and living an outdoor life-style, were split into positive and negative groups, and then were randomly assigned to receive allopurinol (n=51; 20 mg/kg once daily), or placebo (n=44) for I week per month, from April to November. Forty per cent (38/95) of these dogs were not reexamined and retested at the end of the trial for reasons unrelated to CL. None of the remaining 57 dogs exhibited the symptomatic form of the disease at the end of the 1-year follow-up period. Of the 15 allopurinol-treated dogs that were non-infected (negative PCR and tissue smear microscopy) at the beginning of the trial, 6 (40% P=0.03) became PCR-positive, of which 3 became also seropositive, at the end of the observation period. In contrast, only 1 of 7 (14.3%) placebo-treated non-infected dogs became PCR positive at the same time point. Of the 19 allopurinol-treated dogs that were infected (PCR-positive) at the beginning of the trial, 18 (94.7%) remained PCR-positive and one (5.3%) seroconverted, at the end of the observation period. Of the 16 initially infected and placebo-treated dogs, 14 (87.5%) remained PCR positive, of which one (6.7%) also turned positive by tissue smear microscopy. Therefore, it is concluded that the use of allopurinol, at the daily dose of 20 mg/kg, for 1 week per month, during the period of sandfly activity, does not prevent the infection of non-infected dogs by L infantum, and, also, does not help in the elimination of the parasite from dogs with asymptomatic infections. (c) 2005 Elsevier B.V. All rights reserved