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періодичних видань НАН України
Retroreflecting Curves in Nonstandard Analysis
Репозиторій DSpace/Manakin
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Retroreflecting Curves in Nonstandard Analysis
Посилання:
Retroreflecting Curves in Nonstandard Analysis / R. Almeida, V. Neves, A. Plakhov // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 1. — С. 12-24. — Бібліогр.: 7 назв. — англ.
Підтримка:
The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacao para a Ciencia e a Tecnologia" FCT, cofinanced by the European Community Fund FEDER/POCTI.
Дата:
2009
Переглядів:
756
Завантажень:
357
Анотація:
We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C¹, 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 in nitely close to a given curve.
