, dissecting mappings on the test functions space,the usual distributions was generalized to pan-linear distributions,and then the forms,structure and basic differential properties of pan-linear distributions were discussed.

It was proved that for any analytic map / from one Ba-nach space E (real or complex) to space F of the same type and any z∈E ,if α(z,f)≤1/13, then z is a approximate Zero point, and if α(z,f)≤9-61/16,then z is a second classapproximate Zero point of f.

Projection families of analytic mappings from transcendental elliptic surfaces to finitely-deformed surfaces;