A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

Let IaS,a"e (d) be a set of centers chosen according to a Poisson point process in a"e (d) . Let psi be an allocation of a"e (d) to I in the sense of the Gale-Shapley marriage problem, with the additional feature that every center xi aI has an appetite given by a nonnegative random variable alpha. Generalizing some previous results, we study large deviations for the distance of a typical point xaa"e (d) to its center psi(x)aI, subject to some restrictions on the moments of alpha.

SYNTHESIS OF N-15-ENRICHED UREA (CO((NH2)-N-15)(2)) FROM (NH3)-N-15, CO, AND S IN A DISCONTINUOUS PROCESS

CO((NH2)-N-15)(2) enriched with the stable isotope N-15 was synthesized based on a reaction involving CO, (NH3)-N-15, and S in the presence of CH3OH. The method differs from the industrial method; a stainless steel reactor internally lined with polytetrafluoroethylene (PTFE) was used in a discontinuous process under low pressure and temperature. The yield of the synthesis was evaluated as a function of the parameters: the amount of reagents, reaction time, addition of H2S, liquid solution and reaction temperature. The results showed that under optimum conditions (1.36, 4.01, and 4.48 g of (NH3)-N-15, CO, and S, respectively, 40 ml CH3OH, 40 mg H2S, 100 degrees C and 120 min of reaction) 1.82 g (yield 76.5%) of the compound was obtained per batch. The synthesized CO((NH2)-N-15)(2) contained 46.2% N, 0.55% biuret, melting point of 132.55 degrees C and did not exhibit isotopic fractionation. The production cost of CO((NH2)-N-15)(2) with 90.0 at. % N-15 was US$ 238.60 per gram.

ABSENCE OF STABILIZATION POINT OF THE SPECIES ACCUMULATION CURVE IN TROPICAL FORESTS

The definition of the sample size is a major problem in studies of phytosociology. The species accumulation curve is used to define the sampling sufficiency, but this method presents some limitations such as the absence of a stabilization point that can be objectively determined and the arbitrariness of the order of sampling units in the curve. A solution to this problem is the use of randomization procedures, e. g. permutation, for obtaining a mean species accumulation curve and empiric confidence intervals. However, the randomization process emphasizes the asymptotical character of the curve. Moreover, the inexistence of an inflection point in the curve makes it impossible to define objectively the point of optimum sample size.

Synthesis of 15N-enriched urea (CO(15NH2)2) from 15NH3, CO, and S in a discontinuous process

CO(15NH2)2 enriched with the stable isotope 15N was synthesized based on a reaction involving CO, 15NH3, and S in the presence of CH3OH. The method differs from the industrial method; a stainless steel reactor internally lined with polytetrafluoroethylene (PTFE) was used in a discontinuous process under low pressure and temperature. The yield of the synthesis was evaluated as a function of the parameters: the amount of reagents, reaction time, addition of H2S, liquid solution and reaction temperature. The results showed that under optimum conditions (1.36, 4.01, and 4.48 g of 15NH3, CO, and S, respectively, 40 ml CH3OH, 40 mg H2S, 100 ºC and 120 min of reaction) 1.82 g (yield 76.5%) of the compound was obtained per batch. The synthesized CO(15NH2)2 contained 46.2% N, 0.55% biuret, melting point of 132.55 ºC and did not exhibit isotopic fractionation. The production cost of CO(15NH2)2 with 90.0 at. % 15N was US$ 238.60 per gram.