The infra-red absorption spectrum of diamond

Proceedings - Mathematical Sciences - The absorption spectra of four typical diamonds, three of them luminescent and the fourth non-luminescent, have been investigated in the infra-red in the...     

Variations on the theme of solvability by radicals

We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points. We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals. We also begin to classify rational functions of prime degree whose inverses are representable by radicals. Original Russian Text ? A.G. Khovanskii, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 86–105. To Vladmir Igorevich Arnold, mathematical idol of my generation     

Variations on the theme of solvability by radicals

We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points. We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals. We also begin to classify rational functions of prime degree whose inverses are representable by radicals.