Retroreflecting Curves in Nonstandard Analysis

Автор(и)

  • R. Almeida Department of Mathematics, University of Aveiro Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • V. Neves Department of Mathematics, University of Aveiro Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • A. Plakhov presently visiting Institute of Mathematical and Physical Sciences University of Aberystwyth, Aberystwyth SY23 3BZ, Ceredigion, UK

Ключові слова:

Nonstandard Analysis, retroreflectors, maximum resistance problems, reflection, billiards.

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 infinitely close to a given curve.

Mathematics Subject Classification: 26E35, 49K30, 49Q10.

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Опубліковано

2009-03-11

Як цитувати

(1)
Almeida, R.; Neves, V.; Plakhov, A. Retroreflecting Curves in Nonstandard Analysis. J. Math. Phys. Anal. Geom. 2009, 5, 12-24.

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