Zobrazeno 1 - 10
of 176
pro vyhledávání: '"Kurdyka, Krzysztof"'
Let $X\subset\mathbb{R}^n$ be a convex closed and semialgebraic set and let $f$ be a polynomial positive on $X$. We prove that there exists an exponent $N\geq 1$, such that for any $\xi\in\mathbb{R}^n$ the function $\varphi_N(x)=e^{N|x-\xi|^2}f(x)$ i
Externí odkaz:
http://arxiv.org/abs/1812.04874
In this paper, we prove a version of global \L ojasiewicz inequality for $C^1$ semialgebraic functions and relate its existence to the set of asymptotic critical values.
Externí odkaz:
http://arxiv.org/abs/1811.07264
Publikováno v:
Mathematische Annalen, 374 no. 1-2 (2019), pp. 211-251
We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real algebraic set-up. We construct a motivic measure on the space of real an
Externí odkaz:
http://arxiv.org/abs/1807.05160
Publikováno v:
In Bulletin des sciences mathématiques November 2022 180
Let $X\subset \mathbb R^n$ be a connected locally closed definable set in an o-minimal structure. We prove that the following three statements are equivalent: (i) $X$ is a $C^1$ manifold, (ii) the tangent cone and the paratangent cone of $X$ coincide
Externí odkaz:
http://arxiv.org/abs/1703.05421
It is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that the homeomorphism can be chosen in such a way that the analytic and algebraic germs are tangent with any prescribed order of ta
Externí odkaz:
http://arxiv.org/abs/1602.06933
Autor:
Kucharz, Wojciech, Kurdyka, Krzysztof
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher dimensions.
Externí odkaz:
http://arxiv.org/abs/1602.01986
Autor:
Kucharz, Wojciech, Kurdyka, Krzysztof
Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in spheres. We pro
Externí odkaz:
http://arxiv.org/abs/1512.05963
Autor:
Kucharz, Wojciech, Kurdyka, Krzysztof
Stratified-algebraic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more flexible. We give a characterization of the compact real algebraic varieties having the following property: There ex
Externí odkaz:
http://arxiv.org/abs/1511.04238
Let $W$ be a subset of the set of real points of a real algebraic variety $X$. We investigate which functions $f: W \to \mathbb R$ are the restrictions of rational functions on $X$. We introduce two new notions: ${\it curve-rational \, functions}$ (i
Externí odkaz:
http://arxiv.org/abs/1509.05905