Mathematical Proceedings of the Cambridge Philosophical Society: Volume 102 -

Singularities of convex-polygonally generated shape-densities
Hui-Lin Le
Published online by Cambridge University Press:

24 October 2008, pp. 587-596
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In earlier papers Kendall and Le[3,4] made a geometrical study of the structure and singularities of a convex-polygonally generated shape-density for any convex polygon K. The present work describes the singular tessellation T(K) in algebraic terms, and obtains explicit formulae for the ‘jump functions’ of m̃ across every edge of the tessellation. These results, combined with earlier work by Le[5] on the basic tile, make it possible to find m̃ explicitly in every tile by what we have called the ‘stepping-stone’ method. In a closing section the exact order of the differential singularity is found at the tile boundaries.

Mathematical Proceedings of the Cambridge Philosophical Society