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发表于 2025-3-28 16:30:06
Hexagonal Distributions on Hexagonal Latticeysis of geometrical characteristics of the lattice, as a vital prerequisite for the group-theoretic bifurcation analysis of this lattice that will be conducted in Chaps. 6–9. Hexagonal distributions on this lattice, corresponding to those envisaged by Christaller and Lösch in central place theory (S
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发表于 2025-3-28 20:04:50
Irreducible Representations of the Group for Hexagonal Latticewas described in . by the group ., which is the semidirect product of D. by .. In this chapter, the irreducible representations of this group are found according to a standard procedure in group representation theory known as the method of little groups, which exploits the semidirect product structu
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发表于 2025-3-29 01:13:27
Matrix Representation for Economy on Hexagonal Lattice . and .. In this chapter, the matrix representation of this group for the economy on the hexagonal lattice is investigated in preparation for the group-theoretic bifurcation analysis in search of bifurcating hexagonal patterns in Chaps. . and .. Irreducible decomposition of the matrix representatio
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发表于 2025-3-29 05:42:34
Hexagons of Christaller and Lösch: Using Equivariant Branching Lemmabranching lemma as a pertinent and sufficient means to test the existence of hexagonal bifurcating patterns on the hexagonal lattice. By the application of this lemma to the irreducible representations of the group ., all hexagonal distributions of Christaller and Lösch (Chaps. . and .) are shown to