Journal of Mathematics and Statistics

Generalized Finite Sequence of Fuzzy Topographic Topological Mapping

Tahir Ahmad, Siti Suhana Jamian and Jamalludin Talib

DOI : 10.3844/jmssp.2010.151.156

Journal of Mathematics and Statistics

Volume 6, Issue 2

Pages 151-156

Abstract

Problem statement: Fuzzy Topographic Topological Mapping (FTTM) was developed to solve the neuromagnetic inverse problem. FTTM consisted of four topological spaces and connected by three homeomorphisms. FTTM 1 and FTTM 2 were developed to present 3-D view of an unbounded single current source and bounded multicurrent sources, respectively. FTTM 1 and FTTM 2 were homeomorphic and this homeomorphism will generate another 14 FTTM. We conjectured if there exist n elements of FTTM, then the numbers of new elements are n4-n. Approach: In this study, the conjecture was proven by viewing FTTMs as sequence and using its geometrical features. Results: In the process, several definitions were developed, geometrical and algebraic properties of FTTM were discovered. Conclusion: The conjecture was proven and some features of the sequence appear in Pascal Triangle.

Copyright

© 2010 Tahir Ahmad, Siti Suhana Jamian and Jamalludin Talib. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.