1. Let G and G' be two plane open sets and w(z) a topological map.ping of G onto G'. By Q we denote any quadrilateral in G, i.e. the topological image of a closed square with a distinguished pair of opposite sides. The conformal modulus m of Q is the ratio m=a/b of the sides of a conformally equivalent rectangle 22, the distinguished sides of Q corresponding to the sides of length b. We call th...

In this paper, a revitalization of conformal mapping methods applied to fluid flows in two dimensions is proposed. The present work addresses several important issues concerning their application for vortex particle flow solvers. Difficulties of past conformal based method are reviewed. One difficulty concerns the ability of a mapping procedure to represent complicated shapes. The present paper...

This paper presents a new mapping to construct the self-organizing map on the curved seamless surface. This mapping is developed for the planar triangle surface derived from the conformal selforganizing map [C.-Y. Liou, Y.-T. Kuo, Conformal self-organizing map for a genus-zero manifold, Visual Comput. 21(5) (2005) 340–353]. It shows how to construct a seamless surface for the genus-zero manifol...

The problem of the generation of homogeneous grids for spherical domains is considered in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obt...

Certain aspects of three dimensional asymptotically de Sitter spaces are studied, with emphasis on the mapping between gravity observables and the representation of the conformal symmetry of the boundary. In particular, we show that non-real conformal weights for the boundary theory correspond to space-times that have non-zero angular momentum. Some miscellaneous results on the role of the holo...

A quasi-conformal mapping of the parametric domain onto the underlying physical domain is used to generate a 2D structured mesh with required properties: grid line orthogonality and prescribed mesh point clustering near the domain boundary. The functions implementing the mapping are sought by solving the Dirichlet problem for the elliptic partial differential equations. An additional control fo...