In this paper, differential invariants of null Cartan curves are studied in (n+2) dimensional Lorentzian similarity geometry. The fundamental theorem for a curve geometry is investigated and the characterization all self-similar parameterized by de Sitter parameter Minkowski space-time given.

In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to e...