is called a closure operation on , correspondingly is called a closure space, is a closure of , and for simplicity, is indicated by .
composes a complete lattice with respect to relation , denoted by . The intersection operation and union operation on lattice are defined as follows.
where and are set intersection and union operations, respectively.
where is an open neighborhood of .
we have
(7.17)
And, .
(7.18)
Table 7.1
The Results of the Lower Bound of Energy via GA
Name | Length | Sequence | f | LB1 | LB2 | E |
HP-20 | 20 | HPHP2H2PHP2HPH2P2HPH | 3 | -12 | invalid | -9 |
HP-24 | 24 | H2P2(HP2)6H2 | 3 | -16 | 3-12=-9 | -9 |
HP-25 | 25 | P2HP2 (H2P4)3H2 | 4 | -16 | 4-12=-8 | -8 |
HP-36 | 36 | P3H2P2H2P5H7P2H2P4H2P2H P2 | 10 | -25 | 10-24=-14 | -14 |
HP-48 | 48 | P2H (P2H2)2P5H10P6(P2H2)2HP2H5 | 17 | -36 | 17-40=-23 | -23 |
HP-50 | 50 | H2(PH)3PH4P(PH3)3P(HP3)2HPH4(PH)4H | 17 | -48 | 17-41=-24 | -21 |
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