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This allows to apply first-order Taylor expansion to each nonlinear operation in order to characterize the effect of the quantization of the inputs of the operations.
An important point is that the way the functions w k have been defined gives that they belong to the Sobolev space W 1, p ( B j ) and this allows to apply the regularity theory available for such solutions.
Stability (A1) and reduction (A2) guarantee estimator reduction (4.18) for η (T ℓ ; U (T ℓ ) ). Together with quasi-orthogonality (A3) and reliability (3.7), this allows to apply (4.24).
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This allowed to apply qualitative and quantitative methods to empirically select and group global job demands and resources which were relevant for all employees: quantitative and qualitative task-related job demands, job resources related to supportive and appreciative manager and peer behavior, respectively, and task-related resources.
This property allows to apply a convenient hyperbolicity criterion that has become known as the "secular equation" [J. Anderson, A secular equation for the eigenvalues of a diagonal matrix perturbation, Lin. Alg. Appl. 246 (1996 49 70]].
The data availability from a sufficiently large number of studies allows to apply this multivariate approach, which requires reported estimates for the bivariate relations among all proxy variables.
If so, this will allow to apply this questionnaire for assessing the results derived from any research study with the aim of assess possible behavioral changes in health habits as a result of a motivational approaching.
This validation allowed to apply the method to new configurations, so to develop systems further on optimised, able to remove higher thermal fluxes in the same processes.
We thought this would allow to apply the questionnaire in both epidemiological and outcome studies and also could provide an opportunity for future research works to compare quality of life among Iranian population and people living in other communities.
This lack does not allow to apply most algorithms for the satisfaction of Quality of Service requirements to new and established flows.
This allows to draw conclusions that apply to more realistic problems, as well.
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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