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of three-dimensional hydrodynamic models
Polynomial reformulation of the Kuo criteria for
v- sufficiency of map-germs
In the paper a set of necessary and sufficient conditions for
v-sufficiency (equiv. sv-sufficiency) of jets
of map-germs $f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is
proved which generalize both the Kuiper-Kuo and the Thom
conditions in the function case ($m=1$) so as the Kuo
conditions in the general map case ($m>1$). Contrary to the Kuo
conditions the conditions proved in the paper do not require to
verify any inequalities in a so-called horn-neighborhood of the
(a'priori unknown) set $f^{-1}(0)$. Instead, the proposed
conditions reduce the problem on v-sufficiency of jets
to evaluating the local Łojasiewicz exponents for some
constructively built polynomial functions.