Let θ : π 1 (R) → PSL(2, C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem.Theorem. Necessary and sufficient for θ to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that θ(π 1 (R)) be nonelementary. A branch point is required if and only if the representation θ does not lift to SL(2, C).

We give a characterization of hyperelliptic surfaces in terms of simple, closed geodesics on the surfaces and graphs associated to these geodesics.

This work focuses on the specific application of Infrared Thermography (IRT) during plasma wind tunnel tests that reproduce hypersonic gas conditions performed in CIRA Scirocco facility. Unfortunately some drawbacks can limit the use of the thermographic set up in Scirocco in some specific nozzle configurations, because it is impossible to obtain a direct view of the test model from the thermal camera. These difficulties are overcome by using a mirror, which, on the contrary, provides a non direct view of the model by the thermal camera. The present work shows that classical mirrors (with reflectivity across the entire visible spectrum) can represent a simple and cheap way to measure the target temperature in these critical geometric conditions.

No abstract

No abstract