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

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8 papers · 1 filter

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.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…

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…

Where not to find the spectrum of the partial theta function

Midpoints and critical points

Degree 6 hyperbolic polynomials and orders of moduli

Further than Descartes' rule of signs

Sign patterns and rigid moduli orders

Degree 5 polynomials and Descartes' rule of signs

Degree $6$ hyperbolic polynomials and orders of moduli