Y. Gati

activity

20032026

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

5 citations · 7 across the 10 of their papers we have counts for

collaborators

11 papers

math.CA2026

Where not to find the spectrum of the partial theta function

Yousra Gati, Vladimir Petrov Kostov

The spectrum of Ramanujan's partial theta function $θ (q, x) := \sum_{j = 0}^{\infty} q^{j (j + 1) /2} x^{j}$ , $q \in D_{1}$ (the unit disk centered at the origin), $x \in C$ , is…

math.CA2025

Midpoints and critical points

Yousra Gati, Vladimir Petrov Kostov

For a degree $5$ real polynomial with roots $x_{1} \leq \dots \leq x_{5}$ and roots $ξ_{1} \leq \dots \leq ξ_{4}$ of its derivative, we set $z_{j} := (x_{j} + x_{j + 1}) /2$ , $1 \leq j \leq 4$ . We prov…

math.NA2025

Numerical approach for solving problems arising from polynomial analysis

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods…

math.CA2023

Degree $6$ hyperbolic polynomials and orders of moduli

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

We consider real univariate degree $d$ real-rooted polynomials with non-vanishing coefficients. Descartes' rule of signs implies that such a polynomial has $c ~$ positive and…

math.CA2023

Further than Descartes' rule of signs

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

The {\em sign pattern} defined by the real polynomial $Q := Σ_{j = 0}^{d} a_{j} x^{j}$ , $a_{j} \neq = 0$ , is the string $σ (Q) := (sgn (a_{d}), \dots, sgn (a_{0}))$ . The quantities $…

math.CA2020★ 1 cited

Sign patterns and rigid moduli orders

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

We consider the set of monic degree $d$ real univariate polynomials $Q_{d} = x^{d} + \sum_{j = 0}^{d - 1} a_{j} x^{j}$ and its {\em hyperbolicity domain} $Π_{d}$ , i.e. the subset of values of the coef…

Where not to find the spectrum of the partial theta function

Midpoints and critical points

Numerical approach for solving problems arising from polynomial analysis

Degree 6 hyperbolic polynomials and orders of moduli

Further than Descartes' rule of signs

Sign patterns and rigid moduli orders

Degree $6$ hyperbolic polynomials and orders of moduli