6 papers · 1 filter
On definable open continuous mappings
Si Tiep Dinh, Tien Son Pham
For a definable continuous mapping from a definable connected open subset of into we show that the following statements are equivalent: (i) The…
Some variational properties of tangent directions at infinity of real algebraic sets
Si Tiep Dinh, Tien Son Pham
In this paper, we relate the set of asymptotic critical values of a polynomial function with the set of discontinuity of two functions, the multivalued function which associate…
Nichtnegativstellensätze for definable functions in o-minimal structures
Si Tiep Dinh, Tien Son Pham
This paper addresses to Nichtnegativstellensätze for definable functions in o-minimal structures on Namely, let $f, g_1, \ldots, g_l \colon \mathbb{R}^n \…
Limits of tangent spaces to definable sets
Si Tiep Dinh, Olivier Le Gal, Tien Son Pham
We study the set of tangent limits at a given point to a set definable in any o-minimal structure by characterizing the set of exceptional rays in the tangent cone to the set at th…
Global mixed Łojasiewicz inequalities and asymptotic critical values
Si Tiep Dinh, Krzysztof Kurdyka, Tien Son Pham
In this paper, we prove a version of global Łojasiewicz inequality for semialgebraic functions and relate its existence to the set of asymptotic critical values.
Łojasiewicz inequalities with explicit exponent for smallest singular value functions
Si Tiep Dinh, Tien Son Pham
Let be a ()-real polynomial matrix and let be the smallest singular value function of In this paper, w…