Geodesic
On Descartes' rule of signs for hyperbolic polynomials
Serdica Mathematical Journal, Tome 49 (2023) no. 4, pp. 251-268
Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

Voir la notice de l'article

We consider univariate real polynomials with all real roots and with two sign changes in the sequence of their coefficients which are all non-vanishing. Assume that one of the changes is between the linear and the constant term. By Descartes' rule of signs, such degree \(d\) polynomials have 2 positive and \(d-2\) negative roots. We consider the possible sequences of the moduli of their roots on the real positive half-axis. When these moduli are distinct, we give the exhaustive answer to the question which positions can the moduli of the two positive roots occupy.
Keywords: real polynomial in one variable, hyperbolic polynomial, sign pattern, Descartes' rule of signs, 26C10 
@article{SMJ2_2023_49_4_a2,
     author = {Kostov, Vladimir},
     title = {On {Descartes'} rule of signs for hyperbolic polynomials},
     journal = {Serdica Mathematical Journal},
     pages = {251--268},
     year = {2023},
     volume = {49},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2023_49_4_a2/}
}
TY  - JOUR
AU  - Kostov, Vladimir
TI  - On Descartes' rule of signs for hyperbolic polynomials
JO  - Serdica Mathematical Journal
PY  - 2023
SP  - 251
EP  - 268
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2023_49_4_a2/
LA  - en
ID  - SMJ2_2023_49_4_a2
ER  - 
%0 Journal Article
%A Kostov, Vladimir
%T On Descartes' rule of signs for hyperbolic polynomials
%J Serdica Mathematical Journal
%D 2023
%P 251-268
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/SMJ2_2023_49_4_a2/
%G en
%F SMJ2_2023_49_4_a2
Kostov, Vladimir. On Descartes' rule of signs for hyperbolic polynomials. Serdica Mathematical Journal, Tome 49 (2023) no. 4, pp. 251-268. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_4_a2/