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Tame semiflows for piecewise linear vector fields

Daniel Panazzolo (2002)

Annales de l’institut Fourier

Let $ℰ$ be a disjoint decomposition of $ℝ^{n}$ and let $X$ be a vector field on $ℝ^{n}$ , defined to be linear on each cell of the decomposition $ℰ$ . Under some natural assumptions, we show how to associate a semiflow to $X$ and prove that such semiflow belongs to the o-minimal structure $ℝ_{an, exp}$ . In particular, when $X$ is a continuous vector field and $Γ$ is an invariant subset of $X$ , our result implies that if $Γ$ is non-spiralling then the Poincaré first return map associated $Γ$ is also in $ℝ_{an, exp}$ .

Tangential Markov inequalities on semialgebraic curves and some semialgebraic surfaces

Agnieszka Kowalska (2012)

Annales Polonici Mathematici

We give another proof of the fact that any semialbraic curve admits a tangential Markov inequality. We establish this inequality on semialgebraic surfaces with finitely many singular points.

Tangential Markov inequality in $L^{p}$ norms

Agnieszka Kowalska (2015)

Banach Center Publications

In 1889 A. Markov proved that for every polynomial p in one variable the inequality $| | p^{'} {| |}_{[- 1, 1]} {\leq (d e g p) ² | | p | |}_{[- 1, 1]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs and surfaces,...

The K-moment problem for compact semi-algebraic sets.

Konrad Schmüdgen (1991)

Mathematische Annalen

The moment problem for non-compact semialgebraic sets.

Powers, Victoria, Scheiderer, Claus (2001)

Advances in Geometry

The nonreduced order spectrum of a commutative ring.

James McEnerney, Gilbert Stengle (1997)

Revista Matemática de la Universidad Complutense de Madrid

Theoreme de Pfister pour les varietes et anneaux de Witt reduits.

L. Mähe (1986)

Inventiones mathematicae

Topological methods in representation theory.

Vilonen, Kari (1998)

Documenta Mathematica

Topological types of fewnomials

Michel Coste (1998)

Banach Center Publications

Triangulation in o-minimal fields with standard part map

Lou van den Dries, Jana Maříková (2010)

Fundamenta Mathematicae

In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.

Two interesting oriented matroids.

Richter-Gebert, Jürgen (1996)

Documenta Mathematica

Displaying 1 – 11 of 11

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