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

Laser-induced chemical etching of silicon in NF3 atmosphere

Chemical etching of single-crystal Si in an NF₃ atmosphere is performed by continuous irradiation with an Ar⁺ laser at 514.5 nm. The etching process proves to be a thermally stimulated chemical reaction between solid Si and NF₃ gas. The experimental results show how the depth and width of the etched grooves depend on laser power, scan speed, and gas pressure. The etch rates observed may exceed 25 m/s.     

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.