Displaying similar documents to “Ample hierarchy”

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

Deformations of free and linear free divisors

Michele Torielli (2013)

Annales de l’institut Fourier

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We study deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates the deformation spaces. This cohomology turns out to be zero for all reductive linear free divisors and to be constructible for Koszul free divisors and weighted homogeneous free divisors.

Supersolvable orders and inductively free arrangements

Ruimei Gao, Xiupeng Cui, Zhe Li (2017)

Open Mathematics

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In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.

Understanding singularitiesin free boundary problems

Xavier Ros-Oton, Joaquim Serra (2019)

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

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Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfacesor boundaries. The most classical example is the melting of ice to water (the Stefan problem). In this case, the freeboundary is the liquid-solid interface between ice and water. A central mathematical challenge in this context is to understand the regularity and singularities of free boundaries. In this paper we provide a gentle introduction to this topic by presenting some classical results...