@article{Almeida_Neves_Plakhov_2009, place={Харків, Україна}, title={Retroreflecting Curves in Nonstandard Analysis}, volume={5}, url={https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm05-0012e}, abstractNote={We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class $C^1$, except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.
Mathematics Subject Classification: 26E35, 49K30, 49Q10.}, number={1}, journal={Журнал математичної фізики, аналізу, геометрії}, author={Almeida, R. and Neves, V. and Plakhov, A.}, year={2009}, month={Бер}, pages={12–24} }