Near solutions of polynomial equations
Shih Ping Tung (2006)
Acta Arithmetica
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Displaying similar documents to “The Fedoryuk Condition and the Łojasiewicz Exponent near a Fibre of a Polynomial”
Near solutions of polynomial equations
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Acta Arithmetica
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We study the determinant of pairs of rotants of Anstee, Przytycki and Rolfsen. We consider various notions of rotant orientations.
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Acta Arithmetica
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Collectanea Mathematica
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The reduced length of a polynomial with complex coefficients
A. Schinzel (2008)
Acta Arithmetica
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On the Łojasiewicz exponent near the fibre of polynomial mappings
Ha Huy Vui, Nguyen Hong Duc (2008)
Annales Polonici Mathematici
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We give the formula expressing the Łojasiewicz exponent near the fibre of polynomial mappings in two variables in terms of the Puiseux expansions at infinity of the fibre.
Degrees of Polynomial Solutions of a Class of Riccati - tipe Differential Equations*.
Mira Bhargava (1964)
Collectanea Mathematica
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Addendum to the paper: "On the number of terms of a composite polynomial" (Acta Arith. 127 (2007), 157-167)
Umberto Zannier (2009)
Acta Arithmetica
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On the Łojasiewicz exponent at infinity of real polynomials
Ha Huy Vui, Pham Tien Son (2008)
Annales Polonici Mathematici
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Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of...
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Combinatorial Nullstellensatz approach to polynomial expansion
Fedor Petrov (2014)
Acta Arithmetica
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Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.
Elementary properties of the class of nondeterministic polynomial time computable functions
James P. Jones (1988)
Banach Center Publications
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On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²
Jacek Chądzyński, Tadeusz Krasiński (1992)
Annales Polonici Mathematici
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A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.
A generating function for the generalised Rice's polynomial
V. L. Deshpande, V. M. Bhise (1970)
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Hong Bing Yu (2001)
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