Displaying similar documents to “Swiss cheeses, rational approximation and universal plane curves”

Characterization of linear rational preference structures.

Jacinto González Pachón, Sixto Ríos-Insua (1992)

Extracta Mathematicae

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We consider the multiobjective decision making problem. The decision maker's (DM) impossibility to take consciously a preference or indifference attitude with regard to a pair of alternatives leads us to what we have called doubt attitude. So, the doubt may be revealed in a conscient way by the DM. However, it may appear in an inconscient way, revealing judgements about her/his attitudes which do not follow a certain logical reasoning. In this paper, doubt will be considered...

Counting rational points near planar curves

Ayla Gafni (2014)

Acta Arithmetica

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We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².

Completions of normed algebras of differentiable functions

William J. Bland, Joel F. Feinstein (2005)

Studia Mathematica

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We look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We also consider some associated problems of polynomial and rational approximation.