5 problems

Cazacu–Flynn–Lam's conjecture. The sharp constant satisfies

Let $C(N)$ be the sharp constant in the second order Hydrogen uncertainty principle … For $N\in\{2,3\}$, the paper establishes $C(N)<(N+1)^2/4$. The dimension-four strict-bound con…

Bennett--Jeavons--Olver--Soffer conjecture. The function $f_\star^{(s)}$ is a maximizer of

For $0<x<1$, the functions $\frac{\arcsin x}{x}$ and $\frac{\arctan x}{x}$ are defined, and the associated inequality is considered. Chao-Ping Chen's conjecture. If $0<x<1$, then ……

Xie's conjecture. The optimal constant should be