# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## On the /Lojasiewicz exponent at infinity of real polynomials

### Tom 94 / 2008

Annales Polonici Mathematici 94 (2008), 197-208 MSC: Primary 14P10. DOI: 10.4064/ap94-3-1

#### Streszczenie

Let $f \colon {\Bbb R}^n \rightarrow {\Bbb R}$ 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 /Lojasiewicz 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 /Lojasiewicz exponent at infinity of $f$ and the problem of computing the global optimum of $f$ is also established.

#### Autorzy

• Ha Huy VuiInstitute of Mathematics
Cau Giay District 10307
Hanoi, Vietnam
e-mail
• Pham Tien SonDepartment of Mathematics
University of Dalat
Dalat, Vietnam
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek