【摘 要】
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Based on the spectral structure of a class of one-dimensional three-tile quasi-periodic lattice models that are established in 1990 for which the (concurrent) s
【机 构】
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Department of Mathematics, South China University of Technology, Guangzhou 510640
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Based on the spectral structure of a class of one-dimensional three-tile quasi-periodic lattice models that are established in 1990 for which the (concurrent) substitution rules are S → M, M → L, and L → LS, with S, M,and L representing the short, medium, and long tiles of atomic spacings, respectively, we suggest that S is E (egg), M is SI (silkworm) and L is M (moth), for easily understanding. By the use of the number theory, we have rigorously proved the existence of the limit θ = limn→oo Sn-1/Sn ≈ 0.68232789.., where Sn is the number of elements contained in the n-th silk sequence. Some relations among the sequences En, SIn, and Mn are found,where the subscript n means the n-th generation.
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