We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory.

The Goursat representation formula in the complex plane, expressing a real–valued biharmonic function in terms of two holomorphic functions and their anti–holomorphic complex conjugates, is generalized to Euclidean space, expressing a real–valued polyharmonic function of order p in terms of p so–called monogenic functions of Clifford analysis. Mathematics Subject Classification (2010). 30G35.

In this paper, we show how ihe machinery of ederior differential sysiemr can k wed i o help soltie nonholonomic motion planning problems. Since the Gorrsat normal form for ezterior differential systems is dual i o chained form for vectorfields, we solve the problem of steering a mobile robot with n trailers by convcriing ihe system int.0 chained form, doing ihe paih-planning in the chained form...

In the paper, we consider a linear nonautonomous Goursat-Darboux system which is a continuous version of discrete Fornasini-Marchesini system. We give some general algorithm for construction a piecewise constant control related to some density result for attainable sets connected with integrable controls and piecewise constant ones. Copyright c ©2005 IFAC

We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting set of singular integro-differential equations on boundary. boundary integral are solved numerically Chebyshev collocation method which augmented by fractional power term, derived asymptotic analysis corner region, to ...