Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Phạm, Tiên Sȯn"'
The main goal of this paper is to present some explicit formulas for computing the {{\L}}ojasiewicz exponent in the {{\L}}ojasiewicz inequality comparing the rate of growth of two real bivariate analytic function germs.
Externí odkaz:
http://arxiv.org/abs/2405.06302
Consider the problem of minimizing a lower semi-continuous semi-algebraic function $f \colon \mathbb{R}^n \to \mathbb{R} \cup \{+\infty\}$ on an unbounded closed semi-algebraic set $S \subset \mathbb{R}^n.$ Employing adequate tools of semi-algebraic
Externí odkaz:
http://arxiv.org/abs/2308.05349
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are established. A compl
Externí odkaz:
http://arxiv.org/abs/2307.15861
Autor:
Nguyen, Minh Tung, Pham, Tien-Son
We first study Clarke's tangent cones at infinity to unbounded subsets of $\mathbb{R}^n.$ We prove that these cones are closed convex and show a characterization of their interiors. We then study subgradients at infinity for extended real value funct
Externí odkaz:
http://arxiv.org/abs/2211.08677
Autor:
Dinh, Si Tiep, Pham, Tien Son
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 regularity, H\"older continuity of the inverse mapping, coderivatives and va
Externí odkaz:
http://arxiv.org/abs/2207.12240
Given two nonzero polynomials $f, g \in\mathbb R[x,y]$ and a point $(a, b) \in \mathbb{R}^2,$ we give some necessary and sufficient conditions for the existence of the limit $\displaystyle \lim_{(x, y) \to (a, b)} \frac{f(x, y)}{g(x, y)}.$ We also sh
Externí odkaz:
http://arxiv.org/abs/2202.04889
Autor:
Dinh, Si Tiep, Pham, Tien Son
For a definable continuous mapping $f$ from a definable connected open subset $\Omega$ of $\mathbb R^n$ into $\mathbb R^n,$ we show that the following statements are equivalent: (i) The mapping $f$ is open. (ii) The fibers of $f$ are finite and the J
Externí odkaz:
http://arxiv.org/abs/2106.01593
Autor:
Truong, Xuan Duc Ha, Pham, Tien Son
In this paper, we show that some fundamental results for smooth mappings (e.g., the Brouwer degree formula, the implicit function and inverse function theorems, the mean value theorem, Sard's theorem, Hadamard's global invertibility criteria, Pourcia
Externí odkaz:
http://arxiv.org/abs/2105.11652
Autor:
Dinh, Si Tiep, Pham, Tien Son
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 to each value $t$ the set of tangent directions at infinity of the fi
Externí odkaz:
http://arxiv.org/abs/2105.10345
Autor:
Dinh, Si Tiep, Pham, Tien Son
This paper addresses to Nichtnegativstellens\"atze for definable functions in o-minimal structures on $(\mathbb{R}, +, \cdot).$ Namely, let $f, g_1, \ldots, g_l \colon \mathbb{R}^n \to \mathbb{R}$ be definable $C^p$-functions ($p \ge 2$) and assume t
Externí odkaz:
http://arxiv.org/abs/2105.08278