Sequence of Fuzzy Topographic Topological Mapping
DOI:
https://doi.org/10.11113/mjfas.v4n2.51Keywords:
Algebraic progression, Geometrical object, Mathematical Induction, Topological space,Abstract
Fuzzy Topographic Topological Mapping, shortly FTTM, is a model for solving neuromagnetic inverse problem. FTTM consist of four topological spaces and connected by three homeomorphisms. FTTM 1 and FTTM 2 were developed topresent 3-D view of an unbounded single current source and bounded multicurrent sources, respectively. Liau Li Yun (2006) showed that FTTM 1 and FTTM 2 are homeomorphic and this homeomorphism will generate another 14 FTTM. She then conjectured if there exist n elements of FTTM then the numbers of new elements are n4 − n . The 1purpose of this paper is to study the geometrical features of FTTM. In the process, several definitions were developed which may be used to prove the conjecture. This paper will show the proof of the conjecture and their extension result.
References
Fauziah. Z., Tahir. A. and Rashidi Shah, A. (2000). Pemodelan Isyarat MEG. Proceeding of The 8th Nasional Simposium of Mathematical Sciences. Kuala Terengganu: Universiti Putra Malaysia.
Fauziah Zakaria (2002). Algorithma Penyelesaian Masalah Songsang Arus Tunggal Tak Terbatas MEG. Universiti Teknologi Malaysia: Tesis Sarjana.
Hamalainen, M, Hari, R, Ilmoniemi, J. I., Knuutila, J and Lounasmaa, O. V. (1993). Magnetoencephalography – theory, instrumen andapplication to non-invasive studies of the networking human brain. Reviews on Modern Physics. 65 (2).430-434.
Kenneth H. Rosen (2000). Elementary Number Theory and its Applications. 4th ed. United State: AT & T Laboratories.
Liau L. Y. (2001). Homeomorfisma S2 Antara E2 Melalui Struktur Permukaan Riemann serta Deduksi Teknik Pembuktiannya bagi Homeomorfisma Pemetaan Topologi Topografi Kabur (FTTM). Universiti
Teknologi Malaysia: Tesis Sarjana.
Liau L. Y. (2006). Group-Like Algebraic Structures of Fuzzy Topographic Topological Mapping for solving Neuromagnetic Inverse Problem. Universiti Teknologi Malaysia: PhD Thesis.
Tahir, A., Rashdi Shah, A., Fauziah, Z. and Liau. L. Y. (2000). Development of Detection Model for Neuromagnetic Fields. Proceeding of BIOMED. September 27-28. Kuala Lumpur: Universiti Malaya.119-
Tahir, A., Rashdi Shah, A., Fauziah, Z., Liau. L. Y. and Wan Eny Zarina, W. A. R. (2004). Homeomorphisms of Fuzzy opographic Topological Mapping (FTTM). Matematika, Jld.20, Bil. 2.
Tarantola, A. and Vallete, B. (1982). Inverse problems:quest for information. J. Geophys. 50.
Wan Eny Zarina, W. A. R., Tahir, A. and Rashidi Shah, A. (2002). Simulating The Neuronal Current Sources In The Brain. Proceeding BIOMED. September 27-28. Kuala Lumpur: Universiti Malaya.
