Application Of Homotopy To The Ageing Process Of Human Bone
DOI:
https://doi.org/10.23755/rm.v47i0.874Keywords:
Homomorphism, Homotopy, Homology, Chain complex, Topological Space.Abstract
This article presents the ageing process of human bone which can play a major role in the structure of the human body from the concept of homotopy in algebraic topology. The structure of the human bone, which is precisely connected is consider here to be topologically equivalent to a cylinder. The elegant but complex skeletal shape of the human bone is described by the Cartesian functions of α = S1 X I and H, H' : α -> α. The bone shape of the human body at an early stage. That is the bone shape of the newborn is called α = S1 X I homotopy. The process of continuous ageing bone is considered to be family of homotopy based on its functions. The study discusses algebraic topology of homotopies through the homotopy of stable functions of the human bone from infancy to old age.
References
Allen Hatcher, Algebraic Topology, Cambridge University press – 2002.
Andrew H. Wallace, Algebraic Topology: Homology and Cohomology, University of Pennsylvania – 1970.
J. Dugundji, Topology, Allen and Bacon, Inc. – 1966.
James R. Munkres, A first course in Topology, Prencite – Hall. Inc. New Jersey – 1967.
W. S. Massey, A Basic course in Algebraic Topology, Springer-verlag, New York.
Lewis Brew, William Obeng-Denteh, David Delali Zigli. Application of Homotopy to the Ageing Process of Human Body within the framework of Algebraic Topology. Journal of Mathematics Research – Vol. 11, No. 4; August 2019.
Laurence Boxer, Ismet Karaca, Ahmet Oztel. (2011) Topological Invariants in Digital Images, Journal of Mathematical Sciences: Advances and Application. 11(2), 109-140.
J. L. Giavitto and O. Michel. (2003) Modeling the Topological Organization of Cellular Processes, Bio systems. 70(2), 149-163.
Anas A. M. Arafa, S. Z. Rida, Hegagi Mohamed Ali. Homotopy Analysis Method for solving Biological population Model. Vol. 56, No. 5, November 15, 2011.
F. Guerrero, F. J. Santonja, R. J. Villanueva. Solving a model for the evolution of smoking habit in Spain with homotopy analysis method. 14(2013) 549-558.
Downloads
Published
Issue
Section
License
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:
- Free access for all users worldwide
- Increased visibility and readership
- Rapid publication
- No spatial constraints
- Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)
Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.