Volumes Spanned by Random Points in the Hypercube

Consider the hypercube [0, 1]ⁿ in Rⁿ. This has 2ⁿ vertices and volume 1. Pick N = N(n) vertices independently at random, form their convex hull, and let V_n be its expected volume. How large should N(n) be to pick up significant volume? Let k=2/√≈1.213, and let ? > 0. We shall show that, as n→∞, V_n→0 if N(n)?(k??)ⁿ →1 if N(n) ? (k + ?)ⁿ. A similar result holds for sampling uniformly from within the hypercube, with constant .     

Čerenkov spectroscopic assay of fission isotopes

A erenkov counting technique is presented for the radioassay of¹⁰⁶Ru in aqueous solutions containing nitrate, nitric acid, chloride as well as inactive ruthenium nitrosyl complex carrier. The counting efficiency was found to be a function of colour quenching by these substances in the UV and visible range. Measurements made on a three-channel automatic liquid scintillation spectrometer indicated that the counting efficiency can be calculated by use of the experimentally determined channel ratio of a quenched sample, without prior knowledge of the quencher concentration. The technique can be useful during studies on the removal of¹⁰⁶Ru from nuclear waste solutions. Special settings of discriminator windows enable radioassays in presence of weak -emitters such as¹³⁷Cs. The possibility of determining¹⁰⁶Ru in presence of⁹⁰(Sr/Y) was also investigated.     

A randomized algorithm for fixed-dimensional linear programming

We give a (Las Vegas) randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is , where lim _{d d} = 0. This improves the corresponding worst-case complexity, . The method is based on a recent idea of Clarkson. Two variations on the algorithm are examined briefly.     

Actinide uptake onto zeolite-L and SAPO-34

The characteristics of ion exchange of uranyl and americium, which are -emitting radioactive nuclides, were examined by batch and column methods. SAPO-34 showed good selectivity for uranyl ion at pH 2–3.5, and distribution coefficients of Am³⁺ and UO ₂ ²⁺ increased with equilibrium pH. -irradiation (2 MGy) did not show any significant effect on the uptake of both of actinide ions onto L and SAPO-34. Higher does of -irradiation (up to 10 MGy) created a change of equilibrium pH, and hence uptake, due to radiolysis of water and heat localization generated by -radiation and annealing processes.     

Inorganic ion-exchangers for the removal of zirconium,hafnium and niobium radioisotopes from aqueous solutions

Studies were made on the uptake of zirconium, hafnium and niobium isotopes onto zeolites and amorphous zirconium phosphate. Ion exchange capacities and distribution coefficients were determined and the influence of pH examined. Kinetic experiments were made to determine the rates of uptake of the radioisotopes on the exchangers and to measure the leaching of isotopes from preloaded exchangers by synthetic sea water, simulated pond water and distilled water.     

Interlaboratory GC/MS response factor precision

A quality control procedure for Fused Silica Capillary Column Gas Chromatography/Mass Spectroscopy (FSCC GC/MS) was tested and shown to produce similar response factors at five Spectroscopy (FSCC GC/MS) was tested and shown to produce similar response factors at five laboratories. The average relative standard deviation (RSD) of interlaboratory response factors for fifty three compounds of environmental interest determined at each laboratory at nominal injected weights of 20, 100, and 200 ng was found to be 18.9% for four of the five laboratories which participated in this work. These data demonstrate that similar response factors can be attained in routine GC/MS measurements when adequate quality control is maintained.     

Sodium,rubidium and caesium uptake on Los Trancos clay

The uptake of sodium, caesium and rubidium onto Los Transcos clay was studied using the batch method. Sodium-22, rubidium-86 and caesium-137 were used as tracers. In most of the experiments cation concentrations used were 0.01 N. Triple distilled and deionized water were used and the grain size of all solid particles was 53 m. In all cases a few hours of shaking was enough to reach the equilibrium. The ion exchange isotherm experiments were performed by using ammonium forms of the clays. Results showed that the ammonium form of Los Trancos clay was selective for Cs and Rb uptake but Na was not prefered. Cation uptake kinetics were complete in 1 h.