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Probabilities that Random Spherical Caps are in Contact
http://hdl.handle.net/10232/11767
http://hdl.handle.net/10232/11767e2d2e49b-0e1d-4fae-89e4-3b5e2967f5c6
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
AN00408518_v62_p9-17.pdf (13.5 MB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2011-08-02 | |||||
| タイトル | ||||||
| タイトル | Probabilities that Random Spherical Caps are in Contact | |||||
| タイトル言語 | en | |||||
| 著者 |
磯川, 幸直
× 磯川, 幸直 |
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| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | spherical cap | |||||
| キーワード | ||||||
| 主題言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | zero probability | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| アクセス権 | ||||||
| アクセス権 | open access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
| 要約 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Consider four random spherical caps of common radius on the unit sphere, and assume that their centers, p1, p2, p3, p4, are generated independently and uniformly. Let G be a graph made of four vertices v1, v2, v3, v4, for which vertices vi, and vj are connected by an edge if and only if spherical caps with centers pi, pj are in-contact. We study the following two events: EI that G is composed of a connected triangle of three vertices and an isolated vertex; EII that G is composed of a connected line-segment of four vertices. Since both events occur with zero probability, it is impossible to define the ratio P(EI) : P(EII) by the usual manner. However, by introducing a concept of ε-contactness and later letting ε be arbitrarily small, we can invest a legitimacy to the ratio in an asymptotic sense. On this foundation an exact expression for the ratio will be derived and then it will be evaluated numerically for various radii of speherical caps. |
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| 内容記述言語 | en | |||||
| 収録雑誌名 |
ja : 鹿児島大学教育学部研究紀要. 自然科学編 en : Bulletin of the Faculty of Education, Kagoshima University. Natural science 巻 62, p. 9-17, 発行日 2011-03-14 |
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| 作成日 | ||||||
| 日付 | 2011-03-14 | |||||
| 日付タイプ | Issued | |||||
| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| ISSN | 03896692 | |||||
| NII書誌ID（雑誌） | ||||||
| 収録物識別子タイプ | NCID | |||||
| NC ID | AN00408518 | |||||
| 出版タイプ | ||||||
| 出版タイプ | VoR | |||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
| NDC | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 公開者・出版者 | ||||||
| 出版者 | 鹿児島大学 | |||||
| 出版者言語 | ja | |||||
| 公開者・出版者 | ||||||
| 出版者 | Kagoshima University | |||||
| 出版者言語 | en | |||||
