41,767 research outputs found
Dupin hypersurfaces in Lie sphere geometry
The method of moving frames in Lie sphere geometry has produced significant
results in the classification of Dupin hypersurfaces in spheres. What is the
secret of its effectiveness? The answer emerges in the classification of
nonumbilic isoparametric surfaces in the space form geometries. Using the
method of moving frames, the proof of this classification is an elementary
exercise. The same proof classifies the cyclides of Dupin in M\"obius geometry
and finally in Lie sphere geometry, where all nonumbilic Dupin immersions are
Lie sphere congruent to each other.Comment: To appear in the Shoshichi Kobayashi Memorial Volume of Progress in
Mathematics, Birkhause
New Frontiers In Collection Development Preparing To Meet New Standards
This article describes the general policies which may be included in a comprehensive collection development policy, attempting to follow national guidelines. It also describes one approach to analyzing how well the library collection supports the various parts of the curriculum, and presents a technique to compare a library collection with peer libraries by subject majors. Finally, the Collection Development Plan section provides a format for stating an action plan to develop the collection based upon all of the information gathered
The Minimal Facts Approach to the Resurrection of Jesus: The Role of Methodology as a Crucial Component in Establishing Historicity
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