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It is conjectured since long that for any convex body $P\subset \mathbb{R}^n$ there exists a point in its interior which belongs to at least $2n$ normals from different points on the boundary of $P$. The conjecture is known to be true for $n=2,3,4$.
Externí odkaz:
http://arxiv.org/abs/2406.01773
Publikováno v:
Automation and Remote Control, Volume 84, Issue 3, Pages 221-236 (2023)
The task of intercepting a target moving along a rectilinear or circular trajectory by a Dubins' car is formulated as a time-optimal control problem with an arbitrary direction of the car's velocity at the interception moment. To solve this problem a
Externí odkaz:
http://arxiv.org/abs/2304.06169
Publikováno v:
International Tax Review. 5/11/2020, pN.PAG-N.PAG. 1p.
Autor:
Tokarev, Alexander atokarev@kpmg.ru, Nasonov, Ivan inasonov@kpmg.ru
Publikováno v:
International Tax Review. 9/11/2017, p38-38. 1p.