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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 and integration, as well as basic knowledge of functional analysis.
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 and integration, as well as basic knowledge of functional analysis.
Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.
Explores the connection between optimal transport and geometric optics, focusing on the design of free-form lenses
Offers self-contained presentation, with detailed explanations and full proofs of the theorems and results
Leverages optimal transport principles for the design of non-rotationally symmetric lenses
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.
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 148 |
| Reihe: | SpringerBriefs on PDEs and Data Science |
| Inhalt: |
x
135 S. 1 s/w Illustr. 135 p. 1 illus. |
| ISBN-13: | 9789819948666 |
| ISBN-10: | 9819948665 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Gutiérrez, Cristian E. |
| Auflage: | 1st ed. 2023 |
| Hersteller: |
Springer Singapore
Springer Nature Singapore SpringerBriefs on PDEs and Data Science |
| Maße: | 235 x 155 x 9 mm |
| Von/Mit: | Cristian E. Gutiérrez |
| Erscheinungsdatum: | 10.12.2023 |
| Gewicht: | 0,236 kg |
Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.
Explores the connection between optimal transport and geometric optics, focusing on the design of free-form lenses
Offers self-contained presentation, with detailed explanations and full proofs of the theorems and results
Leverages optimal transport principles for the design of non-rotationally symmetric lenses
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.
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 148 |
| Reihe: | SpringerBriefs on PDEs and Data Science |
| Inhalt: |
x
135 S. 1 s/w Illustr. 135 p. 1 illus. |
| ISBN-13: | 9789819948666 |
| ISBN-10: | 9819948665 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Gutiérrez, Cristian E. |
| Auflage: | 1st ed. 2023 |
| Hersteller: |
Springer Singapore
Springer Nature Singapore SpringerBriefs on PDEs and Data Science |
| Maße: | 235 x 155 x 9 mm |
| Von/Mit: | Cristian E. Gutiérrez |
| Erscheinungsdatum: | 10.12.2023 |
| Gewicht: | 0,236 kg |
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