Message
Find your own winning way in
the game of theoretical thinking that involves lots of mathematics
and scientific discovery. While playing this game, we apply
the dialogue engineering (or dialectical) technique. Dialogue
may be sometimes monologue, where dialogue occurs between
one and oneself, and , of course, dialogue may be actual
dialogue in seminar talks and other presentations. My main
research theme can be termed as dialogue engineering.
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Publications(January 2001 - December 2001)
- S. YUKITA, "Linear Cellular Automata on Cayley Graphs,"
Japan J. Indust. Appl. Math., Vol. 18, No. 1, pp. 15-24,
February 2001.
Abstract - Linear cellular
automata on Cayley graphs of some class of groups are
studied. The injectivity and surjectivity of parallel
maps are shown to be determined by their local maps. The
main theorems are non-Euclidean extensions of Ito, Osato,
and Nasu's results on the injectivity and surjectivity
of linear cellular automata The proofs are based on Machi
and Mignosi's Garden of Eden theorem and properties of
unique product groups. Examples of groups that allow the
Ito-Osato-Nasu type theorem and of groups that do not
are given.
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