S. Dinh

activity

20142024

collaborators

13 papers

math.AG2024

Computation of the Łojasiewicz exponents of real bivariate analytic functions

Si Tiep Dinh, Feng Guo, Hong Duc Nguyen +1

The main goal of this paper is to present some explicit formulas for computing the {Ł}ojasiewicz exponent in the {Ł}ojasiewicz inequality comparing the rate of growth of two real b…

math.OC2022

Characterizations of directional openness for set-valued mappings

Si Tiep Dinh, Tien Son Pham

We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regula…

math.CA2022

Limits of real bivariate rational functions

Si Tiep Dinh, Feng Guo, Hong Duc Nguyen +1

Given two nonzero polynomials $f, g \in R [x, y]$ and a point $(a, b) \in R^{2},$ we give some necessary and sufficient conditions for the existence of the limit $\disp…

math.AG2021

On definable open continuous mappings

Si Tiep Dinh, Tien Son Pham

For a definable continuous mapping $f$ from a definable connected open subset $Ω$ of $R^{n}$ into $R^{n},$ we show that the following statements are equivalent: (i) The…

math.AG2021

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 $f$ with the set of discontinuity of two functions, the multivalued function which associate…

math.AG2021

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 $(R, +, \cdot) .$ Namely, let $f, g_1, \ldots, g_l \colon \mathbb{R}^n \…

math.AG2020

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…

math.OC2020

Stability of closedness of closed convex sets under linear mappings

Si Tiep Dinh, Tien Son Pham

We study the problem of when the continuous linear image of a fixed closed convex set $X \subset R^{n}$ is closed. Specifically, we improve the main results in the papers \ci…

math.AG2018

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 $C^{1}$ semialgebraic functions and relate its existence to the set of asymptotic critical values.

math.AG2016

Łojasiewicz inequalities with explicit exponent for smallest singular value functions

Si Tiep Dinh, Tien Son Pham

Let $F (x) := (f_{ij} (x))_{i = 1, \dots, p; j = 1, \dots, q},$ be a ( $p \times q$ )-real polynomial matrix and let $f (x)$ be the smallest singular value function of $F (x) .$ In this paper, w…

math.AG2015

Łojasiewicz-type inequalities with explicit exponents for the largest eigenvalue function of real symmetric polynomial matrices

Si Tiep Dinh, Tien Son Pham

Let $F (x) := (f_{ij} (x))_{i, j = 1, \dots, p},$ be a real symmetric polynomial matrix of order $p$ and let $f (x)$ be the largest eigenvalue function of the matrix $F (x) .$ We denote by…

math.OC2014

Hölder-Type Global Error Bounds for Non-degenerate Polynomial Systems

Si Tiep Dinh, Ha Huy Vui, Pham Tien Son

Let $F := (f_{1}, \dots, f_{p}) : R^{n} \to R^{p}$ be a polynomial map, and suppose that $S := {x \in R^{n} : f_{i} (x) \leq 0, i = 1, \dots, p} \neq = \emptyset.$ …

math.DS2014

Horizontal gradient of polynomial functions for the standard Engel structure on $R^{4}$

Si Tiep Dinh, Krzysztof Kurdyka

We investigate the set $V_{f}$ of horizontal critical points of a polynomial function $f$ for the standard Engel structure defined by the 1-forms $ω_{3} = d x_{3} - x_{1} d x_{2},$ $ω_4=dx_4-x_3dx_…

Computation of the Łojasiewicz exponents of real bivariate analytic functions

Characterizations of directional openness for set-valued mappings

Limits of real bivariate rational functions

On definable open continuous mappings

Some variational properties of tangent directions at infinity of real algebraic sets

Nichtnegativstellensätze for definable functions in o-minimal structures

Limits of tangent spaces to definable sets

Stability of closedness of closed convex sets under linear mappings

Global mixed Łojasiewicz inequalities and asymptotic critical values

Łojasiewicz inequalities with explicit exponent for smallest singular value functions

Łojasiewicz-type inequalities with explicit exponents for the largest eigenvalue function of real symmetric polynomial matrices

Hölder-Type Global Error Bounds for Non-degenerate Polynomial Systems

Horizontal gradient of polynomial functions for the standard Engel structure on R4

Horizontal gradient of polynomial functions for the standard Engel structure on $R^{4}$