APPLICATION OF OPTIMIZATION METHOD IN MULTIDIMENSIONAL SPACE TO THE PROBLEM OF DETERMINING FULLERENE CONCENTRATION IN FULLERENE-CONTAINING MIXTURE

The work proposes a method for the quantitative processing of experimental data from ultraviolet spectroscopy of substituted fullerene mixtures, taking into account errors in the experimental data. This task can be written as a system of Vierordt equations (a system of linear equations). The coefficients of the system are the extinction coefficients of individual substituted fullerenes, which are difficult to measure accurately. Therefore, the mathematical model of the problem contains significant errors that affect the reliability and stability of the solution. To minimize the influence of errors, the work [1] proposes a method, which involves reducing the considered system of linear equations to a linear programming problem. This study generalizes the work [1] and proposes to use linear programming problems to find interval values of correction factors for parameters containing errors. Since decreasing the discrepancy reduces the solution error only for well-conditioned coefficient matrices, the values of correction coefficients that minimize the condition number of the coefficient matrix are found in the obtained intervals. The found correction values allowed to significantly improve the conditionality of the system coefficient matrix and obtain a more accurate solution. By using the refined extinction coefficients, the distribution of molar fractions of fullerene fragments and fullerene-containing compounds in the mixture of products formed by the attachment of cyanoisopropyl radicals was obtained, as well as the distribution of molar fractions of fullerene fragments of different degrees of substitution for samples of fullerene-containing polymethyl methacrylate and the distribution of molar fractions of fullerene fragments of different degrees of substitution for samples of fullerene-containing polystyrene. The results are correct and consistent with the theory, both for low-molecular-weight mixtures and for fullerene-containing polymers.