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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 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 ).
"x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)
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 the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.
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.
Raynaud’s phenomenon, which causes parts of the body like the fingers and the toes to go cold and numb, likely stems from two genes, a study published Thursday in the journal Nature ...
The members of the algebra may be decomposed by grade (as in the formalism of differential forms) and the (geometric) product of a vector with a k-vector decomposes into a (k − 1)-vector and a (k + 1)-vector. The (k − 1)-vector component can be identified with the inner product and the (k + 1)-vector component with the outer product. It is ...