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This introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle. It systematically introduces three classes of geometrical invariants on Finsler manifolds and their intrinsic relations, analyzes local and global results from classic and modern Finsler geometry, and gives non-trivial examples of Finsler manifolds satisfying different curvature conditions.
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the eff...
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Fluorescence in situ hybridization (FISH) has been developed as a powerful technology which allows direct visualisation or localisation of genomic alterations. The technique has been adopted to a range of applications in both medicine, especially in the areas of diagnostic cytogenetics, and biology. Topics described in this manual include: FISH on native human tissues, such as blood, bone marrow, epithelial cells, hair root cells, amniotic fluid cells, human sperm cells; FISH on archival human tissues, such as formalin fixed and paraffin embedded tissue sections, cryofixed tissue; simultaneous detection of apoptosis and xpression of apoptosis-related genes; comparative genomic ybridization; and special FISH techniques.
In this volume, the editor and contributors describe the use of molecular beam epitaxy (MBE) for a range of key materials systems that are of interest for both technological and fundamental reasons. Prior books on MBE have provided an introduction to the basic concepts and techniques of MBE and emphasize growth and characterization of GaAs-based structures. The aim in this book is somewhat different; it is to demonstrate the versatility of the technique by showing how it can be utilized to prepare and explore a range of distinct and diverse materials. For each of these materials systems MBE has played a key role both in their development and application to devices.
Our CBSE Chemistry Term 1 Sample Paper MCQ Book includes 13 Sample Papers (Solved, Unsolved & Extra) for maximum Term 1 practice with MCQs that are based on the latest paper pattern. After 7 quality checks, these books make the most preferred final revision book for CBSE Class 12 Term 1 Boards.
Leading scholar Paul G. Pickowicz traces the dynamic history of Chinese filmmaking and discusses its course of development from the early days to the present. Moving decade by decade, he explores such key themes as the ever-shifting definitions of modern marriage in 1920s silent features, East-West cultural conflict in the movies of the 1930s, the strong appeal of the powerful melodramatic mode of the 1930s and 1940s, the polarizing political controversies surrounding Chinese filmmaking under the Japanese occupation of Shanghai in the 1940s, and the critical role of cinema during the bloody civil war of the late 1940s. Pickowicz then considers the challenging Mao years, including chapters on...