This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.
A reconstruction of the Chinese sky of two thousand years ago, based on analysis of the first star catalogue in China and other sources. Presented in six well-sized star maps for 100 BC, it is especially important for the history of astronomy. The Han sky, with five times more constellations than Ptolemy knew, reflects diverse human activities. The way in which constellations were grouped discloses a systematic cosmology, uniting universe and the state. The work of the three Han schools is comparable to Ptolemy's Almagest. With three detailed Appendices on the constellations of the three schools, well illustrated to demonstrate the relation between sky and human society, this book is valuable not only for astronomy historians and sinologists, but in general for scholars interested in the ancient cultures of Asia.
This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.
A reconstruction of the Chinese sky of two thousand years ago, based on analysis of the first star catalogue in China and other sources. Presented in six well-sized star maps for 100 BC, it is especially important for the history of astronomy. The Han sky, with five times more constellations than Ptolemy knew, reflects diverse human activities. The way in which constellations were grouped discloses a systematic cosmology, uniting universe and the state. The work of the three Han schools is comparable to Ptolemy's Almagest. With three detailed Appendices on the constellations of the three schools, well illustrated to demonstrate the relation between sky and human society, this book is valuable not only for astronomy historians and sinologists, but in general for scholars interested in the ancient cultures of Asia.
This book enriches unsupervised outlier detection research by proposing several new distance-based and density-based outlier scores in a k-nearest neighbors’ setting. The respective chapters highlight the latest developments in k-nearest neighbor-based outlier detection research and cover such topics as our present understanding of unsupervised outlier detection in general; distance-based and density-based outlier detection in particular; and the applications of the latest findings to boundary point detection and novel object detection. The book also offers a new perspective on bridging the gap between k-nearest neighbor-based outlier detection and clustering-based outlier detection, laying the groundwork for future advances in unsupervised outlier detection research. The authors hope the algorithms and applications proposed here will serve as valuable resources for outlier detection researchers for years to come.
This book advances research on mobile robot localization in unknown environments by focusing on machine-learning-based natural scene recognition. The respective chapters highlight the latest developments in vision-based machine perception and machine learning research for localization applications, and cover such topics as: image-segmentation-based visual perceptual grouping for the efficient identification of objects composing unknown environments; classification-based rapid object recognition for the semantic analysis of natural scenes in unknown environments; the present understanding of the Prefrontal Cortex working memory mechanism and its biological processes for human-like localization; and the application of this present understanding to improve mobile robot localization. The book also features a perspective on bridging the gap between feature representations and decision-making using reinforcement learning, laying the groundwork for future advances in mobile robot navigation research.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.