Geodesic
Generalization of p-regularity notion and tangent cone description in the singular case
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 2.

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The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p gt; 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
Keywords: p-regularity, singularity, nonlinear mapping, p-factor operator, curves, surfaces 
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Grzegorczyk, Wiesław; Medak, Beata; Tret’yakov, Alexey A. Generalization of p-regularity notion and tangent cone description in the singular case. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 2. http://geodesic.mathdoc.fr/item/AUM_2012_66_2_a2/

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