Automatic Solution of the System of Equations of the Equivalent Radius of the Distribution Ellipses of Dielectric Materials for the Recognition of Gold Nanoparticles

The presented research is aimed at developing scientific and technical bases for conducting mathematical modeling of nanostructured physical objects of small dimensions. The sensitivity of identification of biologically active nanoparticles of metallic gold to cancer cells is considered based on the results of differentiation of the equivalent radii of intersection of ellipses of the distribution of statistical values of the peaks of Raman spectra together with the XY equations. A method is proposed for the automatic solution of a multidimensional system of nonlinear differential equations for the intersection of ellipsoids of Raman spectrograms of dielectric materials with and without gold nanoparticles. When solving the problem of increasing the accuracy and speed of recognition of gold nanoparticles on the surface of the fibers, the polarization of laser radiation along and across the fibers was taken into account. When solving the system using nonlinear quadratic and XY differential equations of the equivalent radii of the ellipses of the distribution, a high accuracy of R0 and R1 is obtained up to 10
^-15
.