Sentence examples for bound for the sum from inspiring English sources

Thus, we only need to bound in (D.84) to reach the outer bound for the sum secrecy rate: (D.117).

It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense thatsup{∥U*AU+V*BV∥:U and V are unitaries}= min{∥A+μI∥+∥B-μI∥:μ∈C}.Consequences of the result related to spectral sets, the von Neumann inequality, and normal dilations are discussed.

Next, we prove that the bound for the sum is optimal in each case.

for all, and is the best possible lower power mean bound for the sum.

Next, we prove that is the best possible lower power mean bound for the sum.

Therefore, is the best possible upper power mean bound for the sum.

The summed stress score, summed rest scores, and summed difference score were not statistically different for FBP and WBR (P >.05).

"Know all Men by these Presents," begins the legal boilerplate of the St . Louisfree negro bond affidavits, "that we, Moses Dickson as principal, and John How as security, are firmly bound" for the "full sum of five hundred dollars".

Then, we employ matrix permanents to derive a closed-form tight upper bound for the ergodic sum capacity.

Figure 14 shows the asymptotic lower bound for the normalized sum capacity versus η for QPSK inputs and for β = 1 and 3.

Here, we first devise the optimal transmit scheme for each BS, and then derive a closed-form upper bound for the ergodic sum capacity using the matrix permanents.