Radii of simplices and some applications to geometric inequalities
Radii of simplices and some applications to geometric inequalities
复制标题
单纯形的半径以及在几何不等式中的一些应用
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
T. Theobald
中科院分区：
文献类型：
--
作者：
René Brandenberg;T. Theobald
给出了欧氏空间中多面体在j维子空间上的半径极小投影的一个刻划。应用到单纯形，这个特征允许将外半径的计算减少到外接情况下的计算或低维单纯形的外半径的计算。在本文的第二部分中，我们利用这一特征来确定正则单形的外（n - 1）-半径序列（这是最小封闭圆柱的半径）。这就解决了Weisbach（1983）的一篇论文中的一个错误所引起的问题。在证明中，我们首先将问题归结为对称多项式的约束优化问题，然后将其归结为具有附加整数约束的固定变量数的优化问题。
We provide a characterization of the radii minimal projections of polytopes onto j-dimensional subspaces in Euclidean space . Applied to simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. In the second part of the paper, we use this characterization to determine the sequence of outer (n – 1)-radii of regular simplices (which are the radii of smallest enclosing cylinders). This settles a question which arose from an error in a paper by Weisbach (1983). In the proof, we first reduce the problem to a constrained optimization problem of symmetric polynomials and then to an optimization problem in a fixed number of variables with additional integer constraints.