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Notice that, since 0 < α < β.
Notice that, since the power of the channel symbols is normalized, the SNR is 1/N0.
Notice that, since A is a g-monotone mapping, and T is a λ-inverse strongly monotone, we have.
Notice that, since φ x ^ m in (8) is a function of m, its PD is also a function of m.
Notice that, since X is transformed into a clique, G is chordal bipartite if and only if G′ is strongly chordal- 1,1).
Notice that, since we choose V the unitary matrix, the theorem is true if and only if (A^{rm T}A=D) holds.
Notice that, since there are (omega ) retail firms, total demand for each intermediate input equals begin{aligned} omega tilde{y}_{t}(j equiv y_{t}(j)=left( frac{P_{At}(j)}{P_{At}} right) ^{-epsilon }Y_{t}.
Notice that, since our estimation approach implies that, once we control for (mathbf {z,}) a does not depend on the composition of labour inputs, (tw_{-1}) also becomes a predetermined variable.13.13
Notice that, since approximate fixed point sequence always exists in the single-valued case for the theorems we have revisited, our results can be regarded as abstract extensions of corresponding results for single-valued nonexpansive mappings.
Notice that, since the predicted values have been used for ({widetilde{y}}_{it}) and (phi _{t-1}, the standard errors of the estimated coefficients in the second stage should be corrected by bootstrap.
Notice that, since we have changed the functional form of the stand-in household's utility function, these parameters are not easily comparable to those used in the previous sections.
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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