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Research conducted by the principal investigator during the period June 1, 1979 to May 31, 1980, resulted in the following research articles which have either appeared in print, or have been accepted in refereed mathematical journals, in this period: Inequalities for polynomials with a prescribed zero; On the Enestrom-Kakeya Theorem and Its Sharpness; Bounds for incomplete polynomials vanishing at both endpoints of an interval; Remarks on some conjectures of G. G. Lorentz; On incomplete polynomials; An extension of the Enestrom-Kakeya Theorem and its sharpness; On zeros of generalized Bessel polynomials; Incomplete factorizations of matrices and connections with H- matrices; On two conjectures on the zeros of generalized Bessel polynomials; Incomplete polynomials: an electrostatic approach; An introduction to the Convergence Theory of Pade' Approximants.