5 problems

Let $I$ be an interval. An irreducible polynomial $Q(x)=a_dx^d+\cdots+a_0\in\mathbb{Z}[x]$ with $a_d>0$, all roots in $I$, and $a_d^{-1/d}>t_{\mathbb{Z}}(I)$ is a nonmonic critical…

Let $I$ be an interval. Maximal obstruction existence conjecture. Every interval of length less than $4$ has a maximal obstruction. The paper proves existence when the interval has…

Let $I$ be an interval of length less than $4$. A maximal obstruction for $I$ is an obstruction whose value is maximal among the obstructions considered for $I$; denote its value b…

Let $I=[0,b]$ be an interval with $b e 0$ and $bleq 1$. Define … the smallest integer $n\geq 2$ for which $1/n\leq b$. Zero-endpoint interval conjecture. … The conjecture gives an…

Let $E$subset ${\mathbb R}^2$ be compact and let $H$ be a polarizer. The polarization monotonicity conjecture. … Moreover, equality holds only if $P_H(E)\cong E$ or…