Displaying similar documents to “Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II.”

Solution of Cubic and Quartic Equations

Marco Riccardi (2009)

Formalized Mathematics

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In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].

On wild ramification in quaternion extensions

G. Griffith Elder, Jeffrey J. Hooper (2007)

Journal de Théorie des Nombres de Bordeaux

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This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain - 1 (along with some partial results for the more general case). This catalog depends upon the , which as defined in [] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only...