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Repeat space theory applied to carbon nanotubes and related molecular networks. III

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Abstract

The present article is part III of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. In this part III, four problems concerning the above-mentioned extension of the RST have been formulated. Affirmative solutions of these problems imply (i) asymptotic analysis of carbon nanotubes (CNTs) via the new techniques of normed repeat space, Banach algebra, and C*-algebra becomes possible; (ii) a new linkage is formed between the investigations of CNTs and those of ‘spectral symmetry’. In the present paper, we give affirmative solutions to all of the four problems, together with (a) estimates of the norms of matrix sequences representing CNTs, (b) Challenging Problem A#, which complements Problems A, (c) several pictures of ‘CNT Matrix Art’ which has heuristic power to lead one to get the affirmative answers to the problems formulated in an abstract algebraic manner.

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Authors and Affiliations

  1. Division of General Education and Research, Tsuyama National College of Technology, 624-1 Numa, Tsuyama, Okayama, 708-8509, Japan

    Shigeru Arimoto, Eiji Yoshida & Masaaki Yokotani

  2. Institut de Mathematiques de Toulouse, Unité Mixte de Recherche CNRS (UMR 5219), UFR MIG, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 9, France

    Mark Spivakovsky

  3. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran

    Massoud Amini

  4. Institute for Innovative Science and Technology, Graduate School of Engineering, Nagasaki Institute of Applied Science, 3-1 Shuku-machi, Nagasaki, 851-0121, Japan

    Tokio Yamabe

Authors
  1. Shigeru Arimoto
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  2. Mark Spivakovsky
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  3. Massoud Amini
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  4. Eiji Yoshida
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  5. Masaaki Yokotani
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  6. Tokio Yamabe
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Correspondence to Shigeru Arimoto.

Additional information

The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.

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Arimoto, S., Spivakovsky, M., Amini, M. et al. Repeat space theory applied to carbon nanotubes and related molecular networks. III. J Math Chem 50, 2606–2622 (2012). https://doi.org/10.1007/s10910-012-0050-6

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  • DOI: https://doi.org/10.1007/s10910-012-0050-6

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