Modular circle quotients and PL limit sets.
Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.
Linear tetrahedral finite elements whose dihedral angles are all nonobtuse guarantee the validity of the discrete maximum principle for a wide class of second order elliptic and parabolic problems. In this paper we present an algorithm which generates nonobtuse face-to-face tetrahedral partitions that refine locally towards a given Fichera-like corner of a particular polyhedral domain.