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Raynaud, Michel (1985). "Hauteurs et isogénies" [Heights and isogenies]. In Szpiro, Lucien (ed.). Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell [Seminar on arithmetic pencils: the Mordell conjecture]. Astérisque (in French). Paris: Société Mathématique de France. pp. 199–234. ISSN 0303-1179. MR 0801923.
In 1985, he proved Raynaud's isogeny theorem on Faltings heights of isogenous elliptic curves. [5] With David Harbater and following the work of Jean-Pierre Serre, Raynaud proved Abhyankar's conjecture in 1994. [6] [7] [8] The Raynaud surface was named after him by William E. Lang in 1979. [9] [10]
In general, this makes them hard to solve. Nonetheless, several effective techniques for obtaining exact solutions have been established. The simplest involves imposing symmetry conditions on the metric tensor, such as stationarity (symmetry under time translation) or axisymmetry (symmetry under rotation about some symmetry axis).
Diagonally Implicit Runge–Kutta (DIRK) formulae have been widely used for the numerical solution of stiff initial value problems; [6] the advantage of this approach is that here the solution may be found sequentially as opposed to simultaneously.
In mathematics, a Raynaud surface is a particular kind of algebraic surface that was introduced in William E. Lang () and named for Michel Raynaud ().To be precise, a Raynaud surface is a quasi-elliptic surface over an algebraic curve of genus g greater than 1, such that all fibers are irreducible and the fibration has a section.
Clairaut, Alexis Claude (1734), "Solution de plusieurs problèmes où il s'agit de trouver des Courbes dont la propriété consiste dans une certaine relation entre leurs branches, exprimée par une Équation donnée.", Histoire de l'Académie Royale des Sciences: 196– 215.
Raynaud’s occurs in 2% to 5% of the population, more commonly in women, and takes two forms. Primary Raynaud’s is by far the most common and is typically diagnosed in teenage girls and women ...
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.