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.

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

Pengekstrakan cecair-cecair dengan menggunakan turus pengekstrakan cakera berputar melibatkan salah satu dari cecair diserakkan dalam bentuk titisan di dalam cecair yang satu lagi. Taburan yang terbentuk akibat dari putaran cakera yang terdapat dalam turus tersebut menghasilkan titisan anak yang berbagai-bagai saiz. Taburan saiz bagi titisan anak tersebut akan ditentukan dengan kaedah simulasi Monte Carlo.