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Möbius inversion on a multiplicative semigroup and inverse lattice problems in physics
Author(s) -
Zhaodou Chen,
Yanan Shen,
Shaojun Liu
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199802)21:3<269::aid-mma964>3.0.co;2-#
Subject(s) - mathematics , multiplicative function , semigroup , lattice (music) , inverse , inversion (geology) , pure mathematics , inverse semigroup , mathematical physics , mathematical analysis , physics , geometry , paleontology , structural basin , acoustics , biology
The generalized Möbius function and Möbius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Möbius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.