Let F (z) = z−H(z) with order o(H(z)) ≥ 1 be a formal map from C to C and G(z) the formal inverse map of F (z). We first study the deformation Ft(z) = z − tH(z) of F (z) and its formal inverse Gt(z) = z + tNt(z). (Note that Gt=1(z) = G(z) when o(H(z)) ≥ 2.) We show that Nt(z) is the unique power series solution of a Cauchy problem of a PDE, from which we derive a recurrent formula for Gt(z). Se...

Let F (z) = z−H(z) with order o(H(z)) ≥ 1 be a formal map from C to C and G(z) the formal inverse map of F (z). We first study the deformation Ft(z) = z − tH(z) of F (z) and its formal inverse Gt(z) = z + tNt(z). (Note that Gt=1(z) = G(z) when o(H(z)) ≥ 2.) We show that Nt(z) is the unique power series solution of a Cauchy problem of a PDE, from which we derive a recurrent formula for Gt(z). Se...

We present a new formula for the Cauchy index of rational function on an interval using subresultant polynomials. There is no condition endpoints and also involves in some cases less

where / i s the boundary function for jpand da is Lebesgue measure on the sphere. When m = 1, (1) easily transforms into the Cauchy integral formula. In dimension m9 the formula extends to be defined on all / in L , always yielding holomorphic functions. If we identify holomorphic functions with their boundary values, the extended operator can be regarded as the orthogonal projection from L to ...

This letter presents a new statistical model for urban scene synthetic aperture radar (SAR) images by combining the Cauchy distribution, which is heavy tailed, with Rician backscattering. The literature spans various well-known models most of are derived under assumption that consists multitudes random reflectors. idea specifically fails scenes since they accommodate heterogeneous collection st...

We provide a complete answer to the problem which consists in finding an unpointed convex cone lying at minimal bounded Pompeiu–Hausdorff distance from a pointed one. We give also a simple and useful characterization of the radius of pointedness of a convex cone. A corresponding characterization for the radius of solidity of a convex cone is then derived by using a duality argument. c © 2007 El...