Sentence examples for each is lower from inspiring English sources

Suppose that for each, is lower semicontinuous on, and that is -convex in its second variable.

Since for each, is lower semicontinuous on, for each fixed, and each, there exist, such that.

By assumption, for each, is lower semicontinuous on, then by [16], for each fixed, and for each, there exist, such that.

(i for each is lower semicontinuous on each nonempty compact subset of ; (ii)for each nonempty finite set and for each with and, (2.12).

(i for each is lower semicontinuous on each nonempty compact subset of ; (ii)for each finite set and for each ; (iii there exists a nonempty compact convex subset of such that for some, there holds (2.20).

For solving the generalized equilibrium problem, let us give the following assumptions for, and the set : (A1) for all ; (A2) is monotone, that is, for all ; (A3) for each is weakly upper semicontinuous; (A4) for each is convex; (A5) for each, is lower semicontinuous; (B1) for each and, there exists a bounded subset and such that for any, (2.4).

Separate studies found different percentages of atypical Lyme disease associated rashes (3, 4, 9 ); each was lower than the percentage found in our study.

"Oh God, welcome Uday and Qusay as martyrs on the day of judgment," a man intoned as the bodies of each were lowered into the ground.

In order to eliminate these pockets, the line must be pitched downward so that the outlet of each span is lower than the maximum sag.

If Amazon's expected revenue from each phone is lower - such as $240, which would be a typical wholesale price for a $600 device - then it could have up to 346,000 unsold phones.

MDT is prolonged because the prior probabilities are lower and the increase in the likelihood of each alternative is lower.