XANES calculations of amorphous materials are a good example of the use of FeffMPI because, in principle, each atomic site in the CRN is inequivalent
to every other site because of the statistical disorder in the model.
Let [bar]s, [bar]t denote different sets of propositionally equivalent but temporally inequivalent
global states in M.
We have to ask ourselves what attitude to take towards inequivalent
quantizations of a given classical theory - how many of them are physically significant?
The fact that Kuwait plays host to his conference and other similar regional gatherings is an inequivalent
paradigm of His Highness the Amir's distinctive humanitarian role and eagerness to ease out humanitarian woes, create better living conditions and fight poverty, Al-Badr added.
In this case, |0([xi], t)> and |0> are unitarily inequivalent
and the proper physical vacua are |0([xi], t)> [54, 55].
As we can see in these solutions, the Hamiltonian itself comprises inequivalent
lattice sites that lead to the blowup and the energy gap.
There is good reason to believe that, ultimately, this theory will have corrections that are not found in QED and therefore be inequivalent
at some level of accuracy.
The N1s spectra clearly indicate the existence of three inequivalent
nitrogen heteroatoms either in the sample I or in the sample I/CV.
For the ZnO nanowire with [V.sub.Zn], [V.sub.O], [O.sub.Zn], or [Zn.sub.O] defect, there are three inequivalent
defect positions, which are denoted by [V.sub.Zn1]-[V.sub.Zn3], [V.sub.O1]-[V.sub.O3], [O.sub.Zn1]-[O.sub.Zn3], and [Zn.sub.O1]-[Zn.sub.O3] as shown in Figures 2(a), 2(b), 2(d), and 2(e), respectively, whereas, there are two inequivalent
[Zn.sub.i] and [O.sub.i] defect positions, which are denoted by [Zn.sub.i1]-[Zn.sub.i2] and [O.sub.i1]-[O.sub.i2] as shown in Figures 2(c) and 2(f), respectively
d [equivalent to] [b.sup.2] (mod 4), d nota square in [O.sub.K], d > 0, d' < 0}.For each d [member of] [D.sub.+-], let [h.sub.K] (d) denote the number of inequivalent
primitive binary quadratic forms over [O.sub.k] of discriminant d, and let ([x.sub.d],[y.sub.d]) [member of] [O.sub.k] x [O.sub.k] be the fundamental solution of the Pellian equation [x.sup.2] - [dy.sup.2] = 4.
In this sense geometric product is analogous to bindings employed in HRR or BSC, but we can still proceed in several inequivalent
In this research (41) it was shown that the previous result may be explained by assuming a different degree of ordering of th e [Bi.sup.3+] and [Bi.sup.5+] cations located at the two inequivalent
positions, in the sense that one position is occupied by somewhat more [Bi.sup.3+] than [Bi.sup.5+] and the other position is occupied in the opposite way.