A new proof on sequence of fuzzy topographic topological mapping
Keywords:Fuzzy topographic topological mapping, Number Theory, Sequence, Differential Equation,
AbstractFuzzy Topological Topographic Mapping (FTTM) is a model for solving neuromagnetic inverse problem. FTTM consists of four components and connected by three algorithms. FTTM version 1 and FTTM version 2 were designed to present 3D view of an unbounded single current and bounded multicurrent source, respectively. In 2008, Suhana proved the conjecture posed by Liau in 2005 such that, if there exists n number of FTTM, then n4-n new elements of FTTM will be generated from it. Suhana also developed some new definitions on geometrical features of FTTM, and discovered some interesting algebraic properties. In this paper, new proof on sequence of FTTM will be presented. In the proof, the sequence of FTTM is transformed into a system of differential equation.
Ahmad, T., Ahmad, R. S., Zakaria, F., and Yun., L. L. Development of detection model for neuromagnetic fields. Proceeding of Biomed September 27-28, 2000, Kuala Lumpur, Universiti Malaya, 2000.
Zakaria, F., Algoritma Penyelesaian Masalah Songsang Arus Tunggal Tak Terbatas MEG, M.S.thesis, Universiti Teknologi Malaysia, 2002.
Rahman, W. E. Z. W. A., Ahmad, T., and Ahmad, R. S., Simulating the Neuronal Current Sources in the Brain. Proceeding BIOMED. September 27-28, 2002, Kuala Lumpur Universiti Malaysia, 2002.
Yun, L. L., Homeomorfisma s2 antara e2 Melalui Struktur Permukaan Riemann Serta Deduksi Teknik Pembuktiannya Bagi Homeomorfisma Pemetaan Topologi Topografi Kabur, M.S. thesis, Universiti Teknologi Malaysia, 2001.
Ahmad, T., Ahmad, R. S., Yun, L.L., Zakaria, F., and Rahman, W. E. Z. W. A., Matematika, 21(1) (2005) 35–42.
Jamaian, S. S. 2008. Generalized fuzzy topographic topological mapping. M.S. thesis, Universiti Teknologi Malaysia, 2008.
Jamaian, S. S., Ahmad, T., and Talib, J., Journal of Mathematics and Statistics, 6(2) (2010) 151-156.
Hein, J.L., Discreate Mathematics (2nd Edition), Jones and Bartlett Publishers, 2003.
Sanugi, B., Matematika, 9(1) (1993) 23-27.
Lambert, J., Kaedah Pengiraan Dalam Persamaan Pembeza Biasa (Terjemahan), Dewan Bahasa dan Pustaka, Malaysia, 1990.