Sentence examples for p in the first from inspiring English sources

Thus, ((u_{1},v_{1})) is a nontrivial constant-sign solution of problem (P) in the first quadrant of X with (varphi (u_{1},v_{1})>0).

When node ST does not successfully decode x P, PR only directly receives the signal x P in the first time slot.

Suppose we take ourselves to know some claim, q, by inferring it from another claim, p, which we know, but our knowing p in the first place depends on the truth of q.

It follows from (8) and upper semicontinuity of the functions f and p in the first variable that begin{aligned} f overline{x},y) geq 0,quad forall yin X. end{aligned} Hence, x̅ is a solution of EP.

During the second phase, the source and the relay send a new two-symbol full preamble of the above structure, using this time x2(p) and xR(p) (in the first FBMC symbol).

Remark that the result of Theorem 3.2 is valid if we replace the upper semicontinuity of p in the first variable by the bounded above function (xto p x,y)), for all (yin X).

The density of labeled points within a bounded box was calculated for a specified patch P in the second rule.

The first rotation 28 kg/ha P treatment had 91% and the 56 kg/ha P treatment 101% of the volume at age 5 of all the treatments fertilized with P in the second rotation.

Firstly, dehydration of glycerol to acrolein was achieved in high selectivity over a catalyst FeP-P in the first reactor.

That platform idea is one that attracted Vista to Ping in the first place, and this acquisition provides a first step in expanding beyond pure business identity management, where Ping has lived for the last decade.

Moreover, the path process p i sets in P i in the first round is written in every round because in the case the other process p j goes faster than p i in the first round, it will be impossible to p j to know the initial vertex of p i, and hence set P j to the path P i (since a process does not read a shared memory of a previous round).