Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings |
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Authors: | G Alpan |
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Abstract: | Let \({\varepsilon}\) be a (small) positive number. A packing of unit balls in \({{\mathbb{E}^{3}}}\) is said to be an \({\varepsilon}\)-quasi-twelve-neighbour packing if no two balls of the packing touch each other but for each unit ball B of the packing there are twelve other balls in the packing with the property that the distance of the centre of each of these twelve balls from the centre of B is smaller than \({2+\varepsilon}\). We construct \({\varepsilon}\)-quasi-twelve-neighbour packings of unit balls in \({{\mathbb{E}^{3}}}\) for arbitrary small positive \({\varepsilon}\) with some surprising properties. |
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