Optimal Transport and Applications to Geometric Optics
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chap...
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| Format: | Elektronički e-knjiga |
| Jezik: | engleski |
| Izdano: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2023.
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| Izdanje: | 1st ed. 2023. |
| Serija: | SpringerBriefs on PDEs and Data Science,
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| Teme: | |
| Online pristup: | https://doi.org/10.1007/978-981-99-4867-3 |
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| 100 | 1 | |a Gutiérrez, Cristian E. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Optimal Transport and Applications to Geometric Optics |h [electronic resource] / |c by Cristian E. Gutiérrez. |
| 250 | |a 1st ed. 2023. | ||
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| 300 | |a 1 online resource (X, 135 p. 1 illus.). | ||
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| 505 | 0 | |a Chapter 1 Introduction -- Chapter 2 The normal mapping or subdifferential.-Chapter 3 Sinkhorn’s theorem and application to the distribution problem -- Chapter4 Monge-Kantorovich distance -- Chapter 5 Multivalued measure preserving maps -- Chapter 6 Kantorovich Dual Problem -- Chapter 7 Brenier and Aleksandrov solutions -- Chapter 8 Cyclical monotonicity -- Chapter 9 Quadratic cost -- Chapter 10 Brenier ’s Polar Factorization Theorem -- Chapter 11 Benamou and Brenier formula -- Chapter 12 Snell’s law of refraction -- Chapter 13 Solution of the far field refractor problem < 1 -- Chapter 14 Proof of the Disintegration Theorem -- Chapter 15 Acknowledgements -- Chapter 16 References. | |
| 520 | |a This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory andintegration, as well as basic knowledge of functional analysis. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Operations research. | |
| 650 | 0 | |a Management science. | |
| 650 | 0 | |a Geometrical optics. | |
| 650 | 0 | |a Wave theory of light. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 1 | 4 | |a Optimization. |
| 650 | 2 | 4 | |a Operations Research, Management Science. |
| 650 | 2 | 4 | |a Classical Optics, Geometric and Wave optics. |
| 650 | 2 | 4 | |a Differential Equations. |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||