TY - JOUR
AU - Almeida, R.
AU - Neves, V.
AU - Plakhov, A.
PY - 2009/03/11
Y2 - 2024/10/03
TI - Retroreflecting Curves in Nonstandard Analysis
JF - Журнал математичної фізики, аналізу, геометрії
JA - Журн. мат. фіз. анал. геом.
VL - 5
IS - 1
SE - Статті
DO -
UR - https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm05-0012e
SP - 12-24
AB - <p>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.</p><p><strong>Mathematics Subject Classification: </strong>26E35, 49K30, 49Q10.</p>
ER -