Analytical Mathematical Transformation of Correlated Data into Uncorrelated Raman Fiber Spectra for Determination of Nanoparticles of Low-Concentrated Colloidal Silveritle

Analytical forms of multidimensional systems of mathematical transformation equations into uncorrelated form are obtained with their simultaneous solution for equivalent ellipse radii of distributions R0 and R1, as well as probability densities p0 and p1 with the detection of colloidal silver nanoparticles at a concentration of 5% on polyester fibers with multidimensional correlation statistical data of Raman polarization spectra. Analytical forms prove the identification of equations of equivalent radii of ellipses of data spreads when converting them into an uncorrelated form due to the absence of these equations of radii of the mean term, which is present in equations with correlation. The Bayes hypothesis on multiplying non-correlative multidimensional statistical polarization data obtained by transformation in the X and Y directions is used. For a 5% concentration of colloidal silver, the resolution of the identification of silver nanoparticles was obtained by the probability densities of the intersection of the distribution ellipses p0 and p1 up to 10-1-10-64, and by the equivalent radii of the distribution ellipses R0 and R1 up to 0.0304-4.344.