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Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces

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Abstract

This study provides an as complete as possible set of precise definitions, within the mathematics developed for quantum similarity purposes. The topics are embedded in the structure of vector semispaces and the possibility of constructing generalized scalar products on them. This scenario allows describing precisely several items and procedures like: (a) the concept of point clouds, (b) the holographic properties of the so called unit shells of vector semispaces, (c) the cosine of a vector set, (d) the description of point cloud huts and (e) opens the way towards the tensorial representation of molecular structures.

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Authors and Affiliations

  1. Institut de Química Computacional, Universitat de Girona, 17071, Girona, Catalonia, Spain

    Ramon Carbó-Dorca & Emili Besalú

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  1. Ramon Carbó-Dorca
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  2. Emili Besalú
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Correspondence to Ramon Carbó-Dorca.

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Carbó-Dorca, R., Besalú, E. Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces. J Math Chem 50, 210–219 (2012). https://doi.org/10.1007/s10910-011-9906-4

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  • DOI: https://doi.org/10.1007/s10910-011-9906-4

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