A NEW LOOK AT NEWTON'S INEQUALITIES

New families of inequalities involving the elementary symmetric functions are built as a consequence that all zeros of certain real polynomials are real numbers.

[1]  A. Cauchy.  Cours d'analyse de l'École royale polytechnique , 1821 .

[2]  J. Sylvester,et al.  XVIII. On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure , 1853, Philosophical Transactions of the Royal Society of London.

[3]  I. On Newton's rule for the discovery of imaginary roots of equations , 1865, Proceedings of the Royal Society of London.

[4]  F. Cajori.  A history of mathematics , 1989 .

[5]  Thomas L. Heath,et al.  Thirteen Books of Euclid's Elements , 1911, The Mathematical Gazette.

[6]  Euclid,et al.  The thirteen books of Euclid's Elements, Vol 1 Books 1-2 , 1908 .

[7]  G. Gibson.  The Thirteen Books of Euclid's Elements , 1927, Nature.

[8]  G. Pólya.  Mathematics and Plausible Reasoning , 1958 .

[9]  On some geometric inequalities , 1964 .

[10]  Inequalities Associated with the Triangle , 1965, Canadian Mathematical Bulletin.

[11]  I. G. MacDonald,et al.  Symmetric functions and Hall polynomials , 1979 .

[12]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[13]  Tateaki Sasaki,et al.  Calculation of Discriminants of High Degree Equations , 1981 .

[14]  G. Pólya,et al.  Problems and theorems in analysis , 1983 .

[15]  John McKay.  On computing discriminants , 1987 .

[16]  Normalized symmetric functions, Newton's inequalities, and a new set of stronger inequalities , 1989 .

[17]  F. Brenti,et al.  Unimodal, log-concave and Pólya frequency sequences in combinatorics , 1989 .

[18]  J. Risler,et al.  Real algebraic and semi-algebraic sets , 1990 .

[19]  Israel M. Gelfand,et al.  Noncommutative Symmetrical Functions , 1995 .

[20]  Generalized Means and Convexity of Inversion For Positive Operators , 1998 .

[21]  OF Epartment,et al.  A NEW LOOK AT NEWTON’S INEQUALITIES , 2000 .