We use a simple approach to estimating the Banach-Mazur distance between convex bodies and simplex.As an application of this approach,we provide a purely analytic proof for the known result sup_(C∈K^n) d_(BM)(C,△)≤...We use a simple approach to estimating the Banach-Mazur distance between convex bodies and simplex.As an application of this approach,we provide a purely analytic proof for the known result sup_(C∈K^n) d_(BM)(C,△)≤n + 2,where d_(BM)(.,.) denotes the Banach-Mazur distance,A denotes an n-dimensional simplex and K^n denotes the class of n-dimensional convex sets in R^n.展开更多
文摘We use a simple approach to estimating the Banach-Mazur distance between convex bodies and simplex.As an application of this approach,we provide a purely analytic proof for the known result sup_(C∈K^n) d_(BM)(C,△)≤n + 2,where d_(BM)(.,.) denotes the Banach-Mazur distance,A denotes an n-dimensional simplex and K^n denotes the class of n-dimensional convex sets in R^n.
文摘为降低重型商用车燃油消耗、减少运输成本,本文协调“人-车-路”交互体系,将车辆与智能网联环境下的多维度信息进行融合,提出了一种基于迭代动态规划(iterative dynamic programming,IDP)的自适应距离域预见性巡航控制策略(adaptive range predictive cruise control strategy,ARPCC)。首先结合车辆状态与前方环境多维度信息,基于车辆纵向动力学建立自适应距离域模型对路网重构,简化网格数量并利用IDP求取全局最优速度序列。其次,在全局最优速度序列的基础上,求取自适应距离域内的分段最优速度序列,实现车辆控制状态的快速求解。最后,利用Matlab/Simulink进行验证。结果表明,通过多次迭代缩小网格,该算法有效提高了计算效率和车辆燃油经济性。