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汽车行驶的时间问题
A Problem of the Time of Running Car
【摘要】 就d>2R的情形解决如下组合几何极值问题:某平原地区有一个很大的湖泊.湖泊周围有两个村庄A,B.村庄A到村庄B的直线距离为已知.一辆汽车从A村庄出发以已知匀速速度驶向村B庄.问:若这辆汽车以最短路径行驶到达B村庄至多需要多少时间?
【Abstract】 For the case d>2R,the aim of this paper is to solve the following extreme Value problem of combinatorial geometry: There exists a large lake in some plain,and there are two villages named A and B on the lakeside.Assume the line distance between A and B is given.A car wishes to travel from A to B at the given uniform velocity.We ask: If this car can reach B along the shortest route,how much long this car at most needs the time?
【关键词】 区域;
最短路径;
上确界;
S-凸函数;
不等式;
【Key words】 district; shortest path; supremum; Schur-convex function;
【Key words】 district; shortest path; supremum; Schur-convex function;
【基金】 国家自然科学基金(10171073);四川省教育厅自然科学基金(2005A201)
- 【文献出处】 数学的实践与认识 ,Mathematics in Practice and Theory , 编辑部邮箱 ,2006年08期
- 【分类号】O157.5
- 【被引频次】1
- 【下载频次】64