Displaying similar documents to “Approximation by continuous rational maps into spheres”

Rational points on the unit sphere

Eric Schmutz (2008)

Open Mathematics

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It is known that the unit sphere, centered at the origin in ℝn, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the coordinates: for every point ν on the unit sphere in ℝn, and every ν > 0; there is a point r = (r 1; r 2;…;r n) such that: ⊎ ‖r-v‖∞ < ε.⊎ r is also a point on the unit sphere; Σ r i 2 = 1.⊎ r has rational coordinates; r i = a i b i for some integers a i, b i.⊎ for all i , 0 ⩽ a i ⩽ b i ⩽ ( 32 1 / 2 l o g 2 n ε ) 2 l o g 2 n . One consequence...

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...

Approximation of holomorphic maps by algebraic morphisms

J. Bochnak, W. Kucharz (2003)

Annales Polonici Mathematici

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Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.

Introduction

Pascale Roesch (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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