Géométrie des courbes. Note sur la quadrature des sections coniques
Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.
The Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for an infinite thermoelastic plate weakened by a hole having arbitrary shape. The plate considered is conformally mapped to the area of the right half-plane. Many previous discussions of various authors can be considered as special cases of this work. The shape of the hole being an ellipse, a crescent, a triangle, or a cut having the shape of a...
Let be a Galois extension of a countable Hilbertian field . Although need not be Hilbertian, we prove that an abundance of large Galois subextensions of are.
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
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