Proof Set p ¯ ∗ = N p / ( N − p ) if N > p, and in the case of N ≤ p, p ¯ ∗ > p is an arbitrarily fixed constant.
Pfa and Pd in the case of real received signals, and unequal and unknown amplitudes and phases.
We only consider U Ω, a, 6 ( P ) in the case m ≥ 1, since U Ω, a, 6 ( P ) ≡ 0 for m = 0.
Open image in new window Fig. 1 A min-cost flow model for P in the case r = 2, s = 2, t = 3.
Open image in new window Fig. 2 A Hitchcock model for P in the case r = 2, s = 2, t = 3 (the edges, i.e. the variables, with i′ > j′ are omitted).
Antibiotic resistance is likely to inflict a cost on the carrying individual [ 32- 37], which we denote c C in the case of chromosome-carried resistance and c P in the case of plasmid-carried resistance.
Results obtained from liquid liquid extraction experiments show that the new compound effectively extracts both Au and Pd, improving in the case of Pd the results obtained when using the more substituted ligand.
In order to prove that { x n } is a Cauchy sequence in ( X, d ), we consider the distance d ( x n, x n + p ) in the cases p = 2 m + 1 and p = 2 m.
Then they also defined the generalized functions (delta_{1}^{(k+1)}(P)) and (delta_{2}^{(k+1)}(P)) as in the cases (p, q< 1) and (p, q = 1), respectively.
The tail of the binomial distribution to be summed up was chosen based on the observed number of "successes" m, which could be either less or more than 13* p. In the case m >13 *p, we set P' = 1-P, otherwise the original P was used.
