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https://doi.org/10.1007/978-1-4612-0189-2Lie group; Lie groups; algebra; classical mechanics; differential geometry; ksa; linear algebra; manifold; sSPURN 发表于 2025-3-22 12:40:32
Preliminaries,Throughout the text the symbol “:=” indicates a defining equality. For example, to define the symbol R. we writeabnegate 发表于 2025-3-22 16:10:08
Bridge to Differential Geometry,Except for a few exercises (marked “optional”), later chapters do not depend crucially on the contents of this chapter. The reader should feel free to skip directly to Chapter 4.epinephrine 发表于 2025-3-22 18:53:52
Symmetries are Lie Group Actions,Every student of physics knows how important symmetries are. Calculations are easier and more enlightening in coordinates that recognize the symmetry of the underlying problem. For instance, calculating the volume of a cylinder is possible in spherical or Cartesian coordinates, but it is much easier in cylindrical coordinates.CREEK 发表于 2025-3-22 22:53:27
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ce validation of computationally predicted miRNAs in citrus, apple, and other fruit crops. Our ongoing research indicates that miR-RACE is also very useful to verify the sequences of putative miRNAs obtained by deep sequencing of small RNA libraries. The protocol of miR-RACE is rapid and can be comp