All Questions

Imagine there are numbers $a_1,\ldots,a_n \in \mathbb R$ and you want to know whether they are all positive. You cannot access the numbers themselves, but you can choose any symmetric polynomials you ...

Examine the polynomial $$ x^{\tau+1}-\left(1+m\right)x^{\tau}+mx^{\tau-1}+\left(1-m\right)\alpha=0\,. $$ with positive parameters $\tau,\alpha$ and $m<1$, and denote $\left|x_{\max}\left(\tau,\...

Examine the polynomial $$ x^{\tau+1}-x^{\tau}+\alpha=0\, $$ and denote by $\left|x_{\max}\left(\tau,\alpha\right)\right|$ as the maximal magnitude of a root of this equation. For $\tau>1$, I ...