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pro vyhledávání: '"Parusiński, A"'
In this article, we show the H\"older invariance of the Henry-Parusinski invariant. For a single germ $ f$, the Henry-Parusinski invariant of $ f $ is given in terms of the leading coefficients of the asymptotic expansion of $ f $ along the branches
Externí odkaz:
http://arxiv.org/abs/2402.08301
Autor:
Parusiński, Adam, Rainer, Armin
In previous work, we proved that the continuous roots of a monic polynomial of degree $d$ whose coefficients depend in a $C^{d-1,1}$ way on real parameters belong to the Sobolev space $W^{1,q}$ for all $1\le q
Externí odkaz:
http://arxiv.org/abs/2410.01326
Autor:
Parusiński, Adam, Rainer, Armin
Hyperbolic polynomials are monic real-rooted polynomials. By Bronshtein's theorem, the increasingly ordered roots of a hyperbolic polynomial of degree $d$ with $C^{d-1,1}$ coefficients are locally Lipschitz and this solution map ``coefficients-to-roo
Externí odkaz:
http://arxiv.org/abs/2410.01321
Autor:
Moh, T. T.
The said paper entitled "A Proof Of The Plane Jacobian Conjecture" is not true.
Comment: 2 pages
Comment: 2 pages
Externí odkaz:
http://arxiv.org/abs/math/0512533
Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application, we prove t
Externí odkaz:
http://arxiv.org/abs/2310.20284
Autor:
Parusiński, Adam, Rainer, Armin
This survey revolves around the question how the roots of a monic polynomial (resp. the spectral decomposition of a linear operator), whose coefficients depend in a smooth way on parameters, depend on those parameters. The parameter dependence of the
Externí odkaz:
http://arxiv.org/abs/2308.01299
Autor:
Parusiński, Adam, Rainer, Armin
Publikováno v:
Pacific J. Math. 330 (2024) 317-353
We show that definable Whitney jets of class $C^{m,\omega}$, where $m$ is a nonnegative integer and $\omega$ is a modulus of continuity, are the restrictions of definable $C^{m,\omega}$-functions; "definable" refers to an arbitrary given o-minimal ex
Externí odkaz:
http://arxiv.org/abs/2306.09156
Autor:
Parusiński, Adam, Rainer, Armin
Whitney's extension problem, i.e., how one can tell whether a function $f : X \to \mathbb R$, $X \subseteq \mathbb R^n$, is the restriction of a $C^m$-function on $\mathbb R^n$, was solved in full generality by Charles Fefferman in 2006. In this pape
Externí odkaz:
http://arxiv.org/abs/2306.09155
The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answers. In this paper, we study the effective Putinar's Positivestellensatz
Externí odkaz:
http://arxiv.org/abs/2212.09551
We present a description of singular horizontal curves of a totally nonholonomic analytic distribution in term of the projections of the orbits of some isotropic subanalytic singular distribution defined on the nonzero annihilator of the initial dist
Externí odkaz:
http://arxiv.org/abs/2208.01392