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end{aligned} end{aligned}We have the same estimates for the case (lambda <-d) and (zin (-1,0)).
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So, for (Phi^{1}_{j}) we have the same estimate as for (Phi_{j}).
In view of Lemma 4, we have the same estimate (35) for solution (u_{3}) as for solution (u_{1}) and (u_{2}).
Agreement follows from the fact that once a process decided, at least n−2t correct processes have the same estimate x, and thus no other value will ever be adopted in line 9.
Methods based on a fused lasso penalty rely on the idea that, in most cases, two successive measurements should have the same estimate.
In addition, respondents with the same raw score will always have the same estimated latent trait level, which is not the case with the 2- and 3-parameter models.
A sensitivity analysis was used to test the reliability of the results, and it reported that the results remained unchanged and had the same estimates after deleting any one of the included studies.
For example, two of the sites (Wolfville, NS and McCarthy, AK) had the same estimated bedrock age (300 my) but significantly different mean 87Sr/86SrF ratios (1-tailed t-test; t5 = −3.82, P = 0.006).
Also, if φ is a (c -comparison func -comparisonTheorem 2.3 we have the same error estimates (1.4)-(1.6) as in [6]-Theorem 1.8.
Since approaches 0 in the two-sided test, both tests have the same parameter estimates and the same number of significant voxels.
We have the same best estimate of control group re-operation rate (i.e. 30%) for the saline solution effect, based on two randomized trials [ 31, 35].
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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