Displaying similar documents to “On Root Arrangements of Polynomial-Like Functions and their Derivatives”

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

Ezzaldine, Hayssam, Kostov, Vladimir Petrov (2008)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 12D10. In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs. Research partially supported...

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

Kostov, Vladimir (2003)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 12D10. We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.

Root arrangements of hyperbolic polynomial-like functions.

Vladimir Petrov Kostov (2006)

Revista Matemática Complutense

Similarity:

A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P(n) vanishes nowhere. Denote by xk (i) the roots of P(i), k = 1, ..., n-i, i = 0, ..., n-1. Then in the absence of any equality of the form xi...