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end{aligned} then for (lambda_{2}leq1-alpha ) ((lambda_{1}>-alpha)), (k_{lambda} x,y frac{1}{y^{1-lambda_{2}}}) is decreasing for (y>0) and strictly decreasing for the large enough variable y.
end{aligned} for (lambda_{2}leq j_{0}-gamma) ((lambda_{1}>-gamma)), (k_{lambda} x,y frac{1}{y^{j_{0}-lambda_{2}}}) is decreasing for (y>0) and strictly decreasing for the large enough variable y.
end{aligned} then for (lambda_{1}leq i_{0}-gamma) ((lambda_{2}>-gamma)), (k_{lambda} x,y frac{1}{x^{i_{0}-lambda_{1}}}) is decreasing for (x>0) and strictly decreasing for the large enough variable x.
end{aligned} then for (lambda_{1}leq1-alpha) ((lambda_{2}>-alpha)), (k_{lambda} x,y frac{1}{x^{1-lambda_{1}}}) is decreasing for (x>0) and strictly decreasing for the large enough variable x.
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If a sample size is large enough, variables will undoubtedly demonstrate statistical significance.
When 2TW is large enough, a chi-square variable can be approximated as a Gaussian variable.
Although several other variables had regression coefficients comparable in magnitude or larger, the SEs associated with those variables were large enough that none of the other variables included in the full model were significant at the p = 0.05 level, nor were there any trending patterns (p ≤ 0.1; Supplemental Material Table 8).
In both cases, when μ is large enough to make the variable fusion inactive in (5), then the classifier only finds a compromise between the empirical risk and the L1 norm of the classifier.
In fact, the L1-SVM is a particular case of our fused SVM, when the μ parameter is chosen large enough to relax the variable fusion constraint (3), typically by taking μ>2λ.
Although QSS implies that (some of) the terms of the right-hand side of the ODE are large and leaves the left-hand side (derivative term) negligible, the derivative term may still be large enough for the state variable in QSS to change considerably during the time-span of a simulation; the key is that these changes mainly occur on a slow manifold.
The variation in productivity as a dependent variable may then not be large enough to be explained by variables other than location or climate.
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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