Hassen Cheriha

activity

20182020

most citedDescartes' rule of signs, Rolle's theorem and sequences of admissible pairs

5 citations · 6 across the 4 of their papers we have counts for

collaborators

4 papers

math.CA2020★ 1 cited

Degree 5 polynomials and Descartes' rule of signs

Hassen Cheriha, Yousra Gati, Vladimir Petrov Kostov

For a univariate real polynomial without zero coefficients, Descartes' rule of signs (completed by an observation of Fourier) says that its numbers $p os$ of positive and $n e g$ of n…

math.CA2019

A non-realization theorem in the context of Descartes' rule of signs

Hassen Cheriha, Yousra Gati, Vladimir Petrov Kostov

For a real degree $d$ polynomial $P$ with all nonvanishing coefficients, with $c$ sign changes and $p$ sign preservations in the sequence of its coefficients ( $c + p = d$ ), Descartes'…

math.CA2019

On Descartes' rule of signs

Hassen Cheriha, Yousra Gati, Vladimir Petrov Kostov

A sequence of $d + 1$ signs $+$ and $-$ beginning with a $+$ is called a {\em sign pattern (SP)}. We say that the real polynomial $P := x^{d} + \sum_{j = 0}^{d - 1} a_{j} x^{j}$ , $a_{j} \neq = 0$ , defin…

math.CA2018★ 5 cited

Descartes' rule of signs, Rolle's theorem and sequences of admissible pairs

Hassen Cheriha, Yousra Gati, Vladimir Petrov Kostov

Given a real univariate degree $d$ polynomial $P$ , the numbers $p o s_{k}$ and $n e g_{k}$ of positive and negative roots of $P^{(k)}$ , $k = 0$ , $\dots$ , $d - 1$ , must be admissible, i.e. the…