| Co-Investigator(Kenkyū-buntansha) |
ITO Hiroshi Ehime University Faculty of Engineering Associate Professor, 工学部, 助教授 (90243005)
AMANO Kaname Ehime University Faculty of Engineering Professor, 工学部, 教授 (80113512)
SADAMATSU Takashi Ehime University Faculty of Engineering Professor, 工学部, 教授 (10025439)
KAWAMURA Kazuhiro Institute of Math., Univ.of Tsukuba Associate Professor, 数学系, 助教授 (40204771)
INOUE Tomoki Ehime University Faculty of Engineering Associate Professor, 工学部, 助教授 (60253316)
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| Research Abstract |
We intended to develop parallel researches with the paper [S1] for fractal waves (i.e. musical passages, sounds of voices, or picture data with some noises) by finding some effective topological invariants. Although we did not succeed to find the invariants, we summarized our mathematical foundation in [S4], and using the Work Station, which was equipped by this grant, we listed up all fractals in [S3] by the way used in [S2] and found two different kinds of fractals never appeared among CG's in their book. On the other hand, we believe that the space studied in [S5], which is the countable topological product of a space consisting of three points with non T_1-topology, will give some strong influences for our further studies concerning this research.
[S1] Ichiro Tsuda, Mathematics and Medical Science - Around brain waves and pulses (in Japanese), Sugaku Vol. 51, No. 1 (1999), pp. 91- 97.
[S2] H.-O.Peitgen, et. al., Fractals for the Classroom : Strategic Activities, vol. 3, Springer-Verlag, 1999, ISDN 0-387-98420-8.
[S3] Koichi Tsuda, Fractals yielded by three affine maps (in Japanese), to appear in Memoirs of Faculty of Engineering, Ehime University, VOl. 20.
[S4] ibid. , Variations of topological spaces due to Steve Watson, 957th AMS Meeting(# 957-54-36), University of Toronto, Ontario, Canada, September 23, 2000.
[S5] H.Tsuiki, The Computational Dimension of a Topological Space, preprint (Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University).
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