CFP last date
22 April 2024
Reseach Article

Folding of Cantor String

by Renu Chugh, Mandeep Kumari, Ashish Kumar
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 139 - Number 10
Year of Publication: 2016
Authors: Renu Chugh, Mandeep Kumari, Ashish Kumar
10.5120/ijca2016909381

Renu Chugh, Mandeep Kumari, Ashish Kumar . Folding of Cantor String. International Journal of Computer Applications. 139, 10 ( April 2016), 23-27. DOI=10.5120/ijca2016909381

@article{ 10.5120/ijca2016909381,
author = { Renu Chugh, Mandeep Kumari, Ashish Kumar },
title = { Folding of Cantor String },
journal = { International Journal of Computer Applications },
issue_date = { April 2016 },
volume = { 139 },
number = { 10 },
month = { April },
year = { 2016 },
issn = { 0975-8887 },
pages = { 23-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume139/number10/24527-2016909381/ },
doi = { 10.5120/ijca2016909381 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:40:34.825256+05:30
%A Renu Chugh
%A Mandeep Kumari
%A Ashish Kumar
%T Folding of Cantor String
%J International Journal of Computer Applications
%@ 0975-8887
%V 139
%N 10
%P 23-27
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In recent years, folding of various objects have been generated using different approaches. The classical Cantor set is an interesting mathematical construction with links to several areas of analysis and topology. The purpose of this paper is to represent the folding of Cantor string (compliment of Cantor set) using direct folding and folding by cut methods. Moreover, the results governing these types of folding are obtained.

References
  1. Abu Saleem, M. 2007 Some geometric transformations on manifolds and their algebraic structures, Ph.D. Thesis, University of Tanta, Egypt.
  2. Attiya, H. I. 2012. Folding of Hyperbolic Manifolds, Int. J. Contem. Math. Sciences, Vol.7, N. 36, 1791-1799.
  3. Cantor, G. 1879. Uber unendliche lineare Punktmannich- faltigkeiten, Part 1, Math. Ann. Vol.15, 1-7.
  4. Cantor, G. 1880. Uber unendliche lineare Punktmannich-faltigkeiten, Part 2, Math. Ann. Vol.17, 355-358.
  5. Cantor, G. 1882. Uber unendliche lineare Punktmannich- faltigkeiten, Part 3, Math. Ann. Vol.20, 113-121.
  6. Cantor, G.1883. Uber unendliche lineare Punktmannich-faltigkeiten, Part 4, Math. Ann. Vol.21, 51-58.
  7. Cantor, G. 1883 Uber unendliche lineare Punktmannich-faltigkeiten, Part 5, Math. Ann., Vol. 21, 545-591.
  8. Cantor, G. 1884.Uber unendliche lineare Punktmannich-faltigkeiten, Part 6, Math. Ann. , Vol. 23, 453-488.
  9. DI-Francesco, P. 2000. Folding and coloring problem in mathematics and physics, Bull. Amer. Math. Soc. Vol. 37, 251–307.
  10. Edgar, G. 2008 Measure Topology and Fractal Geometry, Springer Verlag, New York, USA.
  11. El-Ahmady, A. E. and Al- Hazmi, N. S. A. 2012 Retraction of one dimensional Manifold, Appl. Math., Vol. 3, 1135-1143.
  12. El-Ghoul, M., El-Ahmady, A. E. and Rafat, H. 2004. Folding-retraction of chaotic dynamical manifold and the VAK of vacuum fluctuation, Chaos Solitons Fractals, Vol. 20, 209–217.
  13. El-Ghoul, M., El-Ahmady, A. E. and Abu-Saleem, M. 2007. Folding on the Cartesian product of manifolds and their fundamental group, Appl. Sci., Vol. 9, 86–91.
  14. El-Ghoul, M., El-Ahmady, A. E., Rafat, H. and Abu-Saleem, M. 2005. The fundamental group of the connected sum of manifolds and their foldings, Chungcheong Math. Soc., Vol. 18, 161–172.
  15. El-Ghoul, M. 1993. Folding of fuzzy graphs and fuzzy spheres, Fuzzy Sets Syst., Vol. 58, 355-363.
  16. El-Ghoul, M. 1985. Folding of manifold, Ph.D Thesis, University of Tanta, Egypt.
  17. El-Ghoul, M. 2002. Fractional dimension of a manifold, Chaos Solitons Fractals, Vol.14,77-80.
  18. El-Ghoul, M. 2001. Fractional folding of a manifold, Chaos Solitons Fractals Vol. 12,1019–1023.
  19. El-Ghoul, M., and Shamara, H. M. 1988. Folding of some types of fuzzy manifolds and their retractions, Fuzzy Sets Syst., Vol. 97, 387-391.
  20. El-Ghoul, M. 1998. The deformation retract and topological folding of a manifold, Commun. Fac. Sci. Univ. Ankara Ser. A, 37, 1-4.
  21. El-Ghoul, M. 1995. The deformation retract of the complex projective space and its topological folding, J. Mater Sci., Vol. 30, No. 4, 45-48.
  22. El-Ghoul, M. 1997. The limit of folding of a manifold and its deformation retract, J. Egypt Math. Soc., Vol. 5, No. 2, 133-140.
  23. El-Ghoul, M. Unfolding of graphs and uncertain graph, The Australian Senior Mathematics Journal Sandy Bay 7006 Tasmania Australia (accepted).
  24. El-Ghoul, M. and Zeen El-Deen, M. R. 1999. On some local properties of Fuzzy Manifold and its folding, Le Matematiche, Vol. LIV- Fasc.II, 201-209.
  25. El-Kholy, E. M. and Al-Khusoni, 1991. Folding of CW-complexes, J. Inst. Math. Comp. Sci.(Math Ser), Vol. 4, No.1, 41-48.
  26. El-Kholy, E. M. 1981. Isometric and topological folding of manifold, Ph. D. Thesis, University of Southampton, UK.
  27. El-Kholy, E.M. and El-Ghoul, M. 1984. Simpilicial folding, J. Fac. Education, Ain ShamsUn., 7 (part. II) , 127-139.
  28. Horiguchi, T. and Morita, T. 1984. Devil’s staircase in one dimensional mapping, Physica A, Vol.126, No.3, 328-348.
  29. Horiguchi, T. and Morita, T. 1984. Fractal dimension related to Devil’s staircase for a family of piecewise linear mappings, Physica A, Vol.128, No.1-2, 289-295.
  30. Lapidus, M. L. and van Frankenhuijsen, M. 2000. Fractal Geometry and Number Theory: Complex dimensions of fractal strings and zeros of zeta functions. Birkhh¨auser, Boston .
  31. Lapidus, M. L. and van Frankenhuijsen, M. 2006. Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and spectra of fractal strings. Springer, Monographs in Mathematics, Springer-Verlag, New York.
  32. Lapidus, M.L. and Hung, L. 2008. Non-Archimedean Cantor set and string, J Fixed Point Theory Appl., Vol.3, No.1, 181–190.
  33. Rani, M. and Prasad, S. 2010. Superior Cantor sets and superior Devil’s staircases, Int.  J. Artif. Life Res., Vol.1, No.1, 78-84.
  34. Robertson, S. A. 1977. Isometric folding of Riemannian manifolds, Proc. Roy. Soc Edinburgh, Vol. 77, 275–289.
  35. Robertson, S. A. and El-Kholy, E. M. 1986. Topological folding, Commun. Fac. Sci. Univ. Ank., Series A1, Vol. 35, 101-107.
  36. Smith, H. J. S. 1875. On the integration of discontinuous functions, Proc. Lon. Math. Soc., Vol. 6, No.1, 140–153.
Index Terms

Computer Science
Information Sciences

Keywords

Cantor set Cantor string Folding methods Retraction.