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Families of differential forms on complex spaces

Vincenzo Ancona, Bernard Gaveau (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On every reduced complex space X we construct a family of complexes of soft sheaves Λ X ; each of them is a resolution of the constant sheaf X and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of X . The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.

First kind integral equations for the numerical solution of the plane Dirichlet problem

Søren Christiansen (1989)

Aplikace matematiky

We present, in a uniform manner, several integral equations of the first kind for the solution of the two-dimensional interior Dirichlet boundary value problem. We apply a general numerical collocation method to the various equations, and thereby we compare the various integral equations, and recommend two of them. We give a survey of the various numerical methods, and present a simple method for the numerical solution of the recommended integral equations.

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