Mendeley出力
＜図書＞
Optimal transportation networks : models and theory
| 責任表示 | Marc Bernot, Vicent Caselles, Jean-Michel Morel |
|---|---|
| シリーズ | Lecture notes in mathematics ; 1955 |
| データ種別 | 図書 |
| 出版情報 | Berlin : Springer , c2009 |
| 本文言語 | 英語 |
| 大きさ | x, 200 p. : ill. (some col.), col. maps ; 24 cm |
| 概要 | "The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, rec...nt approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees." "These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume."--BOOK JACKET.続きを見る |
| 目次 | Introduction: The Models - 2. The Mathematical Models - 3. Traffic Plans - 4. The Structure of Optimal Traffic Plans - 5. Operations on Traffic Plans - 6. Traffic Plans and Distances between Measures - 7. The Tree Structure of Optimal Traffic Plans -and their Approximation - 8. Interior and Boundary Regularity - 9. The Equivalence of Various Models 10. Irrigability and Dimension 11. The Landscape of an Optimal Pattern - 12. The Gilbert-Steiner Problem - 13. Dirac to Lebesgue Segment: A Case Study - 14. Application: Embedded Irrigation Networks - 15. Open Problems.続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6990489 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
中央図 3E | 410.8/L 493/(1955) | 2009 |
|
058212008009733 |
|
|||
|
|
|
理系図3F 数理独自 | SER/LNM/1955 | 2009 |
|
023212008004614 |
|
|||
|
|
|
数理 雑誌室 | SER/LNM/K1955 | 2009 |
|
023212008004638 |
|
書誌詳細
| 一般注記 | Includes bibliographical references (p. 193-197) and index |
|---|---|
| 著者標目 | *Bernot, Marc Caselles, Vicent Morel, Jean-Michel, 1953- |
| 書誌ID | 1001226300 |
| ISBN | 9783540693147 |
| NCID | BA87343338 |
| 巻冊次 | ISBN:9783540693147 |
| 登録日 | 2009.09.18 |
| 更新日 | 2017.02.18 |