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The 1994 ICTP Prize in the field of Mathematics (in honour of Sir Michael Atiyah, UK) was awarded to Chao-Jiang Xu from Wuhan University, Wuhan, P.R. China, for his contributions to nonlinear sub-elliptic problems, symbolic calculus of sub-elliptic operators and diffraction problems for nonlinear waves. He succeeded in establishing the existence and regularity of solutions for highly degenerate quasi-linear sub-elliptic partial differential equations. He developed a theory of non-homogeneous symbolic calculus.