在固定的台球和折叠
On pinned billiard balls and foldings
摘要：
我们考虑"钉球"系统，即，具有固定位置和伪速度的球。伪速度的变化规律与运动球之间的全弹性碰撞速度的变化规律相同。对于不同的钉扎球对的碰撞次数是以外生的方式选择的。利用$n$，$d$和球心的位置，给出了$d$维空间中$n$钉扎球系统的最大伪碰撞次数的一个显式上界.作为第一步，我们研究折叠，即，将沿着折痕折叠一张纸的想法形式化的映射。
英文摘要：
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times of collisions for different pairs of pinned balls are chosen in an exogenous way. We give an explicit upper bound for the maximum number of pseudo-collisions for a system of $n$ pinned balls in a $d$-dimensional space, in terms of $n$, $d$ and the locations of ball centers. As a first step, we study foldings, i.e., mappings that formalize the idea of folding a piece of paper along a crease.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
