... Original Russian Text Copyright c 2001 by Grigoryan, Mailybaev On the Weierstrass Preparation Theorem S. S. Grigoryan and A. A. Mailybaev Received May 22, 2000 Abstract--An analytic function of several variables is considered. ... As an application, an explicit formula describing a bifurcation diagram locally up to second-order terms is derived for the case of a double root. Key words: Weierstrass preparation theorem, analytic function of several variables, bifurcation diagram. ... ЗЗЗ hn ! ...

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