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On the Łojasiewicz exponent at infinity of real polynomials

100%

Vui H., Son P.

Annales Polonici Mathematici

2008

tom 94

nr 3

197-208

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 computing the global optimum of f is also established.

Topology of families of affine plane curves

100%

Vui H., Son P.

Annales Polonici Mathematici

1999

tom 71

nr 2

129-139

We determine bifurcation sets of families of affine curves and study the topology of such families.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Son P.

2 Vui H.

1 2008

1 1999

Wyniki wyszukiwania

On the Łojasiewicz exponent at infinity of real polynomials

Topology of families of affine plane curves