The convergence rate for the strong law of large numbers: General lattice distributions

LetX ₁,X ₂, ... be a sequence of independent random variables with common lattice distribution functionF having zero mean, and let (S _n ) be the random walk of partial sums. The strong law of large numbers (SLLN) implies that for any and >0

Ultrasound treatment acceleration of solvent extraction for fumigant residues from wheat

Concerns about consumer and worker safety and the fate of fumigants have fuelled strong efforts to determine their residues in foodstuffs. Fumigants are usually extracted from commodities with solvent at room temperature (25 degrees C). In this paper, solvent extraction of methyl bromide, phosphine, carbonyl sulfide, and carbon disulfide using ultrasonic acceleration or heating was evaluated. Wheat samples plus solvent, in gas-tight bottles, were placed in an ultrasonic chamber or an oven (50 degrees C), and fumigants were released into the headspace over the solvent. Completeness of extraction was demonstrated within 2 h for ultrasonic extraction, 7-20 h for 50 degrees C heating, and 8-35 h for room temperature extraction. The rapidity of extraction was mainly due to ultrasonic vibration rather than increased temperature.     

Co-precipitation in some binary sulphate systems

Studies have been made of the distribution behaviour of tracers with alkaline earth sulphates, using the technique of precipitation from homogeneous solution. The co-precipitation of strontium with barium sulphate and of lead, lanthanum, and yttrium, separately, with barium sulphate, and with strontium sulphate, were investigated. Although there was qualitative correlation between the observed values of the distribution coefficient and the theoretical solubility product ratios for each of the binary systems studied, the divergence between theory and observation was so great that it seems unlikely that there is any quantitative correlation.     

Synthesis of substituted 5-aminomethyl tetrahydro-isoquinolines and dihydro-isoindoles

The synthesis of ten substituted aminomethylene tetrahydro-isoquinolines is described, proceeding in eight steps from 5-hydroxyisoquinoline via reductive amination of N-Boc tetrahydro-isoquinoline 5-carboxaldehyde. Likewise, reductive amination was used to prepare four substituted dihydro-isoindoles from the corresponding aldehyde. The dihydro-isoindole ring system was conveniently accessed via a 2+2+2 cycloaddition reaction.     

Radical copolymerization of 2-acryloyl thioxanthone with methyl methacrylate

A novel monomer, 2-acryloyl thioxanthone (TXA), was prepared by reaction of 2-hydroxy thioxanthone with acryloyl chloride. Copolymerization of TXA with methyl methacrylate (MMA) in DMF at 80°C was studied in order to evaluate relative reactivities of these monomers. Values of 1.36 and 0.5 were found for the respective reactivity ratios of MMA and TXA, respectively. The resonance stabilization and polar properties were determined and discussed in terms of spectroscopic data.