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Journal of Mathematical Chemistry

, Volume 50, Issue 9, pp 2606–2622 | Cite as

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

  • Shigeru Arimoto
  • Mark Spivakovsky
  • Massoud Amini
  • Eiji Yoshida
  • Masaaki Yokotani
  • Tokio Yamabe
Original Paper

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.

Keywords

Repeat space theory (RST) Carbon nanotubes *-algebra Banach algebra C*-algebra Matrix Art 

Mathematics Subject Classification

92E10 15A18 46E15 13G05 14H20 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Shigeru Arimoto
    • 1
  • Mark Spivakovsky
    • 2
  • Massoud Amini
    • 3
  • Eiji Yoshida
    • 1
  • Masaaki Yokotani
    • 1
  • Tokio Yamabe
    • 4
  1. 1.Division of General Education and ResearchTsuyama National College of TechnologyOkayamaJapan
  2. 2.Institut de Mathematiques de Toulouse, Unité Mixte de Recherche CNRS (UMR 5219), UFR MIGUniversité Paul SabatierToulouse Cedex 9France
  3. 3.Department of MathematicsFaculty of Mathematical Sciences, Tarbiat Modares UniversityTehranIran
  4. 4.Institute for Innovative Science and TechnologyGraduate School of Engineering, Nagasaki Institute of Applied ScienceNagasakiJapan

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