Central and Non-central Limit Theorems in a Free Probability Setting

Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wigner integrals, where Hermite processes are replaced by non-commutative Tchebycheff processes. This includes the non-commutative fractional Brownian motion and the non-commutative Rosenblatt process.     

Mass spectrometry characterisation of fatty acids from metabolically engineered soybean seeds

Improving the quality and performance of soybean oil as biodiesel depends on the chemical composition of its fatty acids and requires an increase in monounsaturated acids and a reduction in polyunsaturated acids. Despite its current use as a source of biofuel, soybean oil contains an average of 25 % oleic acid and 13 % palmitic acid, which negatively impacts its oxidative stability and freezing point, causing a high rate of nitrogen oxide emission. Gas chromatography and ion mobility mass spectrometry were conducted on soybean fatty acids from metabolically engineered seed extracts to determine the nature of the structural oleic and palmitic acids. The soybean genes FAD2-1 and FatB were placed under the control of the 35SCaMV constitutive promoter, introduced to soybean embryonic axes by particle bombardment and down-regulated using RNA interference technology. Results indicate that the metabolically engineered plants exhibited a significant increase in oleic acid (up to 94.58 %) and a reduction in palmitic acid (to <3 %) in their seed oil content. No structural differences were observed between the fatty acids of the transgenic and non-transgenic oil extracts.

Insight into the reaction mechanism of the conversion of methylbutynol on silica-alumina

The conversion of methylbutynol (MBOH) over commercially available silicaalumina solids was studied. The formation of 3-methyl-3-butene-2-one (MIPK) was explained in terms of the cooperative action of both Br?nsted acidic and coordinatively unsaturated surface sites. With increasing silica content the number of defect sites decreases and well ordered silica-alumina is formed.     

Kinetic Spectrofluorimetric Determination of Nitrite in Water Samples and Nitrogen Dioxide in the Atmosphere Sampled by the Liquid Droplet Method

 A simple, sensitive and selective kinetic spectrofluorimetric determination of NO₂ sampled by the droplet method in the atmosphere was proposed on the basis of the reaction of safranin O with nitrite. By this reaction, a diazonium salt is formed, which causes a fluorescent reddish-orange dye color of the solution to change into a non fluorescent blue color. The reaction was monitored fluorimetrically by measuring the decrease in fluorescence intensity of safranin O at (λ_ex/λ_em = 536 nm/579 nm) by a fixed-time method. The experimental conditions were optimized. Under the optimum conditions in the concentration range of 7.5–400 ng/ml, a linear calibration curve (r² = 0.9978) was obtained with a detection limit of 7.5 ng/ml. The method was applied successful ly to the determination of nitrite in spiked water and NO₂ in the atmosphere, as sampled by a liquid droplet method. Received August 23, 1999. Revision February 29, 2000.