Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II.
Rudykh, G.A., Semenev, Eh.I. (2001)
Siberian Mathematical Journal
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Displaying similar documents to “A perturbed integral geometry problem in a three-dimensional space.”
Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II.
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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].
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On wild ramification in quaternion extensions
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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 (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...