Improving the Accuracy of the Solution of a Multidimensional System by Differentiating the XY Probability Density Equations for the Identification of Gold Nanoparticles on Fibers

The results of computer modeling in determining the probability of intersection of distribution ellipses by solving a system of equations with multidimensional correlation components of Raman polarization spectra are presented. A method is proposed to improve the accuracy of identification of gold nanoparticles on polyester fibers taking into account the longitudinal and transverse polarization of laser radiation over the entire range of the Raman spectrum. The method of drawing up on the basis of vector-matrix analysis and solving a system of multidimensional differential correlation equations on the probability density of intersection of peak distributions of Raman spectra in the recognition of gold nanoparticles on the surface of dielectric materials is realized. The implementation of the proposed method allowed to obtain a solution of the system when differentiating by XY the probability density equations of the ellipses of the distribution with an accuracy of 10
^-16
.