Liouvillian systems were initially introduced in [3] and can be seen as a natural extension of differential flat systems. Many physical non flat systems seem to be Liouvillian (cf [12, 11, 1, 10]). We present in this paper an alternative definition to this class of systems using the language of diffieties and infinite prolongation theory.

In this work we have tried to solve several problems that involve scalar and vectorial image information lying on the plane or on 3D surfaces. We will present and discuss four novel algorithms devised to solve those problems: tracking of objects in movies, tracking of regions on deforming 3D surfaces, restoration of damaged pictures, removal of objects from images, and solving of PDE’s on impli...

In this work we consider the concept of differential flatness defined by Fliess, Levine, Martin and Rouchon. The structural property of k-flatness (the case in which flat outputs depends up to the kth derivative of the inputs) is studied based on the properties of the dynamic extension algorithm and the Cartan-Kähler theorems on the existence of integral manifolds of exterior differential syste...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...