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In other words, even though the formulation in (18) does not explicitly set the page BERs to be identical, it implicitly minimizes the difference between all page BERs.
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Even though the above formulation is for forward transitions only, we can perform all sparse dynamic programming operations in reverse order (with switched indices); as a result we can split each of the two processes described above into further two processes, one for forward and another one for backward transitions.
Even though the space time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares space time decoupled finite element models.
Interestingly, the design criteria similar to (17) but for wall-2 chooses this as a multipath blind zone even though the multipath preserver formulation for wall-2 does not take into account whether a point of reflection is in the shadow region; the experimental design however does.
The average insulin dose remained unchanged for each patient throughout the duration of the study when compared with pretreatment/baseline even though the specific insulin formulation varied (Lantus long-acting insulin with multiple daily injections of Humalog, Humulin injectable or pump, or Novolog injectable).
Even though, there is an integer solution to the linear relaxation of the expanded formulation that is also feasible for the linear relaxation of the objective function.
Bias in estimates of the population mean was negligible for all the methods used, even though their formulations did not always preclude this possibility.
For example one child preferred to take half a tablet even though a liquid formulation was available because taking the liquid involved a large volume of a liquid whose taste they did not like.
Even though the current study provides important baseline information to aid in the formulation of relevant policies and future research, it has limitations as well.
Swelling and erosion results from DTZ formulations display different results even though the same polymers were used.
Even though the patients in our study were using different formulations of the same atypical antipsychotic, the real-life treatment patterns differed considerably between the two formulations of quetiapine.
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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