The Łojasiewicz exponent of the gradient at infinity

• Autorzy: Rodak T.
• Języki publikacji: EN

Abstrakty

EN

Let f [a member of a set] C[x, y] and deg f = deg[sub y] f [is more than or equal to] 2. In this paper we prove that the Łojasiewicz exponent L[infinity] (grad f) of the gradient of f at infinity is attained on the curve f'y=0.

Słowa kluczowe

EN

magnetic resonanse imaging; gradient

PL

wykładnik Łojasiewicza; gradient

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 1
• Strony: 93--98
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Rodak T.

• Faculty of Mathematics, Łódź University, S. Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] M. Bogusławska, On the Łojasiewicz exponent of the gradient of holomorphic functions, Bull. Pol. Ac. Math., 47 (1999) 337-343.
• [2] J. Chądzyński, T. Krasiński, Exponent of growth of polynomial mappings of C2 into C2, in: Singularities, Banach Center Publ., 20, PWN, Warszawa (1988) 147-160.
• [3] J. Chądzyński, T. Krasiński, The gradient of a polynomial at infinity, preprint no. 2002/01, Faculty of Mathematics, University of Łódź (http://www.imul.uni.lodz.pl).
• [4] T. C. Kuo, Y. C. Lu, On analytic function germs of two complex variables, Topology, 16 (1977) 299-310.
• [5] T. C. Kuo, A. Parusiński, Newton polygon relative to an arc, in: Real and complex singularieties (São Carlos 1998), CRC Res. Notes Math., 412 (2000) 76-93.
• [6] A. Płoski, On the maximal polar quotient of an analytic plane curve, Kodai Math. J., 24 (2001) 120-133.