Fully Nonlinear Pdes In Real And Complex Geometry And Optics
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Fully Nonlinear Pdes In Real And Complex Geometry And Optics
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Author : Luca Capogna
language : en
Publisher: Springer
Release Date : 2013-10-07
Fully Nonlinear Pdes In Real And Complex Geometry And Optics written by Luca Capogna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-07 with Mathematics categories.
The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.
Fully Nonlinear Pdes In Real And Complex Geometry And Optics
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Author : Luca Capogna
language : en
Publisher:
Release Date : 2013-10-31
Fully Nonlinear Pdes In Real And Complex Geometry And Optics written by Luca Capogna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-31 with categories.
The Golden Anniversary Celebration Of The National Association Of Mathematicians
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Author : Omayra Ortega
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-10
The Golden Anniversary Celebration Of The National Association Of Mathematicians written by Omayra Ortega and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Education categories.
This volume is put together by the National Association of Mathematicians to commemorate its 50th anniversary. The articles in the book are based on lectures presented at several events at the Joint Mathematics Meeting held from January 16–19, 2019, in Baltimore, Maryland, including the Claytor-Woodard Lecture as well as the NAM David Harold Blackwell Lecture, which was held on August 2, 2019, in Cincinnati, Ohio.
Mathematical Methods In Liquid Crystal Optics And Lens Design
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Author : Eric Stachura
language : en
Publisher: Springer Nature
Release Date : 2024-08-20
Mathematical Methods In Liquid Crystal Optics And Lens Design written by Eric Stachura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-20 with Mathematics categories.
Freeform lens design has numerous applications in imaging, aerospace, and biomedicine. Due to recent advancements in precision cutting and grinding, the manufacturing of freeform optical lenses with very high precision is now possible. However, there is still a significant lack of mathematical literature on the subject, and essentially none related to liquid crystals. Liquid crystals are appealing for use in imaging due to their flexibility and unique electro-optical properties. This book fills a gap in mathematical literature and attracts focus to liquid crystals for freeform lens design. It provides a rigorous mathematical perspective on liquid crystal optics, focusing on ray tracing in the geometric optics regime. A mathematical foundation is set to study lens design and ray tracing problems in liquid crystals. Additionally, it addresses absolute instruments, which are devices that image without any optical aberrations. These instruments cannot be designed through transformation optics, and until recently, only a handful of examples were known. Mathematically, this is a largely untapped area of research, yet the applications are profound. Finally, the book describes several open directions, revealing the richness of the intersection of liquid crystal optics and mathematical analysis. The content of this book will prove invaluable for researchers of mathematical optics as well as those interested in liquid crystal theory, in addition to those mathematics graduate students aiming to understand the physical basis of light propagation in liquid crystals
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane
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Author : Kari Astala
language : en
Publisher: Princeton University Press
Release Date : 2008-12-29
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane written by Kari Astala and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-29 with Mathematics categories.
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Geometry In Partial Differential Equations
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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1994
Geometry In Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Linear Partial Differential Equations For Scientists And Engineers
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Author : Tyn Myint-U
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Linear Partial Differential Equations For Scientists And Engineers written by Tyn Myint-U and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-05 with Mathematics categories.
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
Critical Technologies Plan
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Author :
language : en
Publisher:
Release Date : 1991
Critical Technologies Plan written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Military research categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Differential Geometry Part 2
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Author : Shiing-Shen Chern
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Differential Geometry Part 2 written by Shiing-Shen Chern and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Contains sections on Complex differential geometry, Partial differential equations, Homogeneous spaces, and Relativity.