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: | Englisch |
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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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862647038204706816 |
|---|---|
| author | Almeida, R. Neves, V. Plakhov, A. |
| author_facet | Almeida, R. Neves, V. Plakhov, A. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-12-01T11:56:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106530 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-01T11:56:14Z |
| publishDate | 2009 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Retroreflecting Curves in Nonstandard Analysis Almeida, R. Neves, V. Plakhov, A. |
| title | 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_short | Retroreflecting Curves in Nonstandard Analysis |
| title_sort | retroreflecting curves in nonstandard analysis |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106530 |
| work_keys_str_mv | AT almeidar retroreflectingcurvesinnonstandardanalysis AT nevesv retroreflectingcurvesinnonstandardanalysis AT plakhova retroreflectingcurvesinnonstandardanalysis |