Retroreflecting Curves in Nonstandard Analysis
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...
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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
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| Datum: | 2009 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106530 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Almeida, R. Neves, V. Plakhov, A. 2016-09-30T06:15:53Z 2016-09-30T06:15:53Z 2009 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. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106530 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. 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Retroreflecting Curves in Nonstandard Analysis Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Retroreflecting Curves in Nonstandard Analysis |
| spellingShingle |
Retroreflecting Curves in Nonstandard Analysis Almeida, R. Neves, V. Plakhov, A. |
| title_short |
Retroreflecting Curves in Nonstandard Analysis |
| title_full |
Retroreflecting Curves in Nonstandard Analysis |
| title_fullStr |
Retroreflecting Curves in Nonstandard Analysis |
| title_full_unstemmed |
Retroreflecting Curves in Nonstandard Analysis |
| title_sort |
retroreflecting curves in nonstandard analysis |
| author |
Almeida, R. Neves, V. Plakhov, A. |
| author_facet |
Almeida, R. Neves, V. Plakhov, A. |
| publishDate |
2009 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
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.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/106530 |
| citation_txt |
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. |
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| first_indexed |
2025-12-01T11:56:14Z |
| last_indexed |
2025-12-01T11:56:14Z |
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1850860222901387264 |