### A functional equation arising from the Joukowski transformation

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Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles,...

We establish sufficient conditions on the two weights w and v so that the Beurling-Ahlfors transform acts continuously from $L\xb2\left({w}^{-1}\right)$ to L²(v). Our conditions are simple estimates involving heat extensions and Green’s potentials of the weights.

An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing...

We consider the space of holomorphic functions at the origin which extend analytically on the universal covering of $\u2102\setminus \omega \mathbb{Z}$, $\omega \in {\u2102}^{\u2606}$. We show that this space is stable by convolution product, thus is a resurgent algebra.