Generalizing this result to infinite lattices, however, requires adding further structure.
2.
For most infinite lattice graphs, " p " c cannot be calculated exactly.
3.
So one may form the infinite lattice of divisors, just as one would for the real fractions.
4.
The same equivalence holds for infinite lattices which satisfy the ascending chain condition ( or the descending chain condition ).
5.
The aforementioned electronic structure calculations are done assuming an infinite lattice and ignore the effects of macroscopic electric fields created by surface charges.
6.
That is, the assumption is that the cell you have chosen is in the midst of an infinite lattice of identical cells.
7.
In essence, the Petersen Middleton theorem shows that a wavenumber-limited function can be perfectly reconstructed from its values on an infinite lattice of points, provided the lattice is fine enough.
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