Table of Contents
Physics Research International
Volume 2011, Article ID 874302, 4 pages
http://dx.doi.org/10.1155/2011/874302
Research Article

The Hausdorff Dimension of the Penrose Universe

Department of Mathematics, Technical School Center of Maribor, 2000 Maribor, Slovenia

Received 27 April 2011; Accepted 17 July 2011

Academic Editor: Leonardo Golubovic

Copyright © 2011 L. Marek-Crnjac. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Connes, Noncommutative Geometry, Academic Press, New York, NY, USA, 1994.
  2. J. P. May, E-infinity Ring Spaces and E-Infinity Ring Spectra, Springer, Heidelberg, Germany, 1977.
  3. M. S. El Naschie, “A review of E-infinity theory and the mass spectrum of high energy particle physics,” Chaos, Solitons and Fractals, vol. 19, no. 1, pp. 209–236, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. H. He, “A note on elementary cobordism and negative space,” International Journal of Nonlinear Science and Numerical Simulations, vol. 11, no. 12, pp. 1093–1095, 2010. View at Google Scholar
  5. M. S. El Naschie, “Banach-tarski theorem and cantorian micro space-time,” Chaos, Solitons and Fractals, vol. 5, no. 8, pp. 1503–1508, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. S. El Naschie, “Quantum collapse of wave interference pattern in the two-slit experiment: a set theoretical resolution,” Nonlinear Science Letters A, vol. 2, no. 1, pp. 1–9, 2011. View at Google Scholar
  7. J. H. He, T. Zhong, L. Xu et al., “The importance of the empty set and noncomutative geometry in underpinning the foundations of quantum physics,” Nonlinear Science Letters B, vol. 1, no. 1, pp. 15–24, 2011. View at Google Scholar
  8. M. S. El Naschie, “Superstrings, knots and noncommutative geometry in E-infinity space,” International Journal of Theoretical Physics, vol. 37, no. 12, pp. 2935–2951, 1998. View at Google Scholar
  9. M. S. El Naschie, “Penrose universe and cantorian spacetime as a model for noncommutative quantum geometry,” Chaos, Solitons and Fractals, vol. 9, no. 6, pp. 931–933, 1998. View at Google Scholar · View at Scopus
  10. F. Büyükkılıç and D. Demirhan, “Cumulative diminuations with Fibonacci approach, golden section and physics,” International Journal of Theoretical Physics, vol. 47, no. 3, pp. 606–616, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. V. Jones and V. S. Sunder, Introduction to Subfactors, University Press, Cambridge, UK, 1997.
  12. L. Marek-Crnjac, “E-infinity Cantorian space-time from subfactors and knot theory,” Chaos, Solitons and Fractals, vol. 32, no. 3, pp. 916–919, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Marek-Crnjac, “On a connection between the limit set of the Möbius-Klein transformation, periodic continued fractions, El Naschie's topological theory of high energy particle physics and the possibility of a new axion-like particle,” Chaos, Solitons and Fractals, vol. 21, no. 1, pp. 9–19, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer, New York, NY, USA, 1990.
  15. L. Marek-Crnjac, “The mass spectrum of high energy particles via El Naschie's E-infinity golden mean nested oscillators, the Dunkerly-Southwell eigenvalue theorems and KAM,” Chaos, Solitons and Fractals, vol. 18, no. 1, pp. 125–133, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. R. Coldea, D. A. Tennant, E. M. Wheeler et al., “Golden ratio discovered in a quantum word,” Science, vol. 8, no. 32, Article ID 5962, pp. 177–180, 2010. View at Google Scholar