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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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| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/106530 |
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irk-123456789-1065302016-10-01T03:01:44Z Retroreflecting Curves in Nonstandard Analysis Almeida, R. Neves, V. Plakhov, A. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106530 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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English |
| 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. |
| format |
Article |
| author |
Almeida, R. Neves, V. Plakhov, A. |
| spellingShingle |
Almeida, R. Neves, V. Plakhov, A. Retroreflecting Curves in Nonstandard Analysis Журнал математической физики, анализа, геометрии |
| author_facet |
Almeida, R. Neves, V. Plakhov, A. |
| author_sort |
Almeida, R. |
| title |
Retroreflecting Curves in Nonstandard Analysis |
| 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 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT almeidar retroreflectingcurvesinnonstandardanalysis AT nevesv retroreflectingcurvesinnonstandardanalysis AT plakhova retroreflectingcurvesinnonstandardanalysis |
| first_indexed |
2023-10-18T20:13:09Z |
| last_indexed |
2023-10-18T20:13:09Z |
| _version_ |
1796149285176213504 |