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If you apply for financial aid, the official cost of attendance below will be used to determine aid eligibility.

If you apply for financial aid, the official cost of attendance below will be used to determine aid eligibility, namely, borrowing capacity.

Some of the auxiliary results provided below will be used in the main theorem proofs.

For the sake of simplicity and convenience, in the following discussion, the notations below will be used h u = sup n ∈ Z + { h ( n ) }, h l = inf n ∈ Z + { h ( n ) }, (1.2).

Several validated questionnaires described below will be used for outcome assessments.

In addition, objective physical measurements as described below will be used.

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We give several lemmas below which will be used in the proof of our main results.

Below, C will be used to denote various positive constants, whose value may vary from one application to another.

We recall this theorem below that will be used in the proof of the main theorems in this paper.

For all secondary end points and analyses, a p value below 0.05 will be used.

After some refinement of wording, these checklists have been finalized (below) and will be used by trained research staff to determine the elements contained in the nutrition and physical activity policies.

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