A numerical method of a two-dimensional non-linear controllable system reachable set boundary approximation is considered. In order to approximate the boundary right piecewise linear closed contours are used: a set of broken lines on a plane. As an application of the proposed technique a method of finding linear functional global extremum is described, including its use for systems with arbitrary dimensionality.
A method for estimating the native gold composition in micron‐ and submicron‐sized inclusions in the matrix of a sulfide mineral with electron probe X‐ray microanalysis is proposed. Such inclusion sizes are comparable with or less than the X‐ray generation volume, and therefore, the analytical signal is a mixture of signals from the matrix elements and the inclusion elements, which significantly complicates the quantification. The proposed procedure is based upon the extrapolation of the trend of the dependence of the measured elemental contents in the inclusions, for example, Au or Ag, versus the content of matrix elements, namely, S, Fe, and As. To define the influence of the inclusion size on the intensity of the excited X‐rays, the trajectories of the electrons in a sample were simulated by the Monte Carlo method. It was found that the trends in the behavior calculated by the Monte Carlo method are consistent with the data measurements of an artificial pyrite sample with a sprayed pure gold layer (approximately 1 μm thick) arranged perpendicular to the sample surface. The measurements were performed on a Superprobe JXA‐8200 microanalyzer. The proposed method was demonstrated by analyzing natural, finely dispersed gold inclusions in arsenopyrite. This approach made it possible to evaluate the Au and Ag contents in the approximately 1 μm inclusions and assess the uncertainty of the measurement.
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