Geometry of the Triangle Equation on TwoManifolds,2002, arXiv, math-ph/0208041 (to appear
A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference “black and white triangle operators (equations)” on triangulated surfaces with a black and white coloring of triangles. In this work, we develop the theory of these operators and equations, showing their similarity with the complex derivatives @ and @.
ABSTRACT Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modeling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on In Silico models.