Sur la continuité des fonctions de variables complexes

Thèse--Univ. de Paris.Mode of access: Internet

3D-mappings by means of monogenic functions and their approximation

We consider quasi-conformal 3D-mappings realized by hypercomplex di erentiable (monogenic) functions and their polynomial approximation. Main tools are the series development of monogenic functions in terms of hypercomplex variables and the generalization of L. V. Kantorovich's approach for approximating conformal mappings by powers of a small parameter. .This work was partially supported by the R&D Unit Matematica e Aplicacoes (UIMA) of the University of Aveiro, through Portuguese Foundation for Science and Technology (FCT

Limits in categories of Vietoris coalgebras

Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one - intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness. When the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete. As a practical application, we use these developments in the specification and analysis of non-deterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.publishe