论文标题
关于John Simplex的注释，有正面的扩张
A Note on John Simplex with Positive Dilation
论文作者
论文摘要
我们证明了Johns定理的简单定理$ r^d $，带有正扩张因子$ d+2 $，这改善了先前已知的$ d^2 $上限。鉴于$ d $下限，这种界限很紧。此外，我们举例说，$ d $不是$ d = 2 $的最佳下限。我们的结果回答了有关简单的约翰定理的两个问题，并由\ cite {leme2020 costly}提出了积极的扩张。
We prove a Johns theorem for simplices in $R^d$ with positive dilation factor $d+2$, which improves the previously known $d^2$ upper bound. This bound is tight in view of the $d$ lower bound. Furthermore, we give an example that $d$ isn't the optimal lower bound when $d=2$. Our results answered both questions regarding Johns theorem for simplices with positive dilation raised by \cite{leme2020costly}.
