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Two Monte Carlo algorithms for computing quantum mechanical expectation values of coordinate operators, i.e., multiplicative operators that do not commute with the Hamiltonian, are presented and compared.
These amplitudes relate to quantum mechanical expectations as (langle alpha _{j} rangleapproxlangle a_{j}rangle_{mathrm{QM}}), where (langlecdotrangle) denotes the expectation with respect to the Wigner quasi distribution and (langlecdotrangle_{mathrm{QM}}) a quantum mechanical expectation value.
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In this appendix we denote expectations with respect to the Wigner function as (langlecdotrangle_{mathrm{W}}) and quantum mechanical expectations as (langlecdotrangle).
Elevation and lowering of the patella have been reported for both techniques, often opposite to mechanical expectations [ 18, 27, 28].
We compute statistical-mechanical expectation values of macroscopic laboratory observables.
The California law also prohibits certain mechanical features, and the expectation is that gun makers and sellers in the state will adapt in the same way as before.
Contrary to the expectations, brilliant mechanical and high temperature resistance might not be observed at the alkali activated slag mortars irrespective of the applied cured conditions.
This is contrary to normal expectations of mechanical regulation of bone formation and resorption.
However, in clear contrast to our expectations, under mechanical loading these growth factors did not play any synergistic role.
For a given fractal mechanical operatorA, we have an expectation value 〈 A 〉 α and a root mean square dispersion ( Δ A ) α, 〈 A 〉 α = 1 Γ ( 1 + α ) ∫ − ∞ ∞ A | ψ α ( x, t ) | 2 ( d x ) α (5.34).
That's the tough thing: if it looks and sounds triple-A, there's an expectation that the mechanical depth and complexity will be at that level too, and that's often the thing that smaller teams can't do.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com