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Extra info for Abdus Salam - Weak and Electromagnetic Interactions. Published in Elementary Particle Theory: Proceedings of the 8th Nobel Symposium
Math. 142 (2002), 433-434. Note this contains instructions for accessing the bibliography via the web. Mignotte, M. (1991), An inequality on the greatest roots of a polynomial, Elem. Math. 46, 85-86 ———— (1999), Polynomials, An Algorithmic Approach, Springer- Verlag Mishra, B. (1993), Bounds on the Roots, in Algorithmic Algebra, SpringerVerlag, 306-308 Parodi, M. (1949), Sur les limites des modules des racines des ´equations alg´ebriques, Bull. Sci. Math. Ser. 11. References for Chapter 1. I. (1970), A bound for the moduli of the zeros of polynomials, Canad.
Thus V(x) can only change at a zero of f1 (x). 3 with k=2 (for if it were, f1 (x) = 0). Hence f2 (x) has the same sign on both sides of x0 . So if x0 is a zero of f1 (x) of even multiplicity, then V(x) does not change as x passes through x0 (for f1 (x) does not change sign), while there is no contribution to the Cauchy index (for ff21 remains equal to +∞, or −∞ ). But, if x0 is of odd multiplicity, f1 (x) changes sign at x0 . If f1 and f2 have the same sign to the left of x0 , V(x) increases by 1 while the Cauchy index has a contribution of -1 ( ff12 jumps from +∞ to −∞).
Ser. 11. References for Chapter 1. I. (1970), A bound for the moduli of the zeros of polynomials, Canad. Math. Bull 13, 541-542 Reich, S. P. (1971), Locating Zeros of Polynomials, Amer. Math. C. (1974), Upper bounds on the moduli of the zeros of a polynomial, Math. Mag. M. (1991), A Remark on the Zeros of a Polynomial, Zeit. Angew. Math. Mech. 71, T832-835 van der Sluis, A. (1970), Upperbounds for Roots of Polynomials, Numer. Math. L. (1924), An inequality for the roots of an algebraic equation, Ann.