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Meanwhile, the cost function is lower-bounded since the sum rate of the whole system is upper bounded.
At higher SNR (see Figure 6), the CDF of AIR system is upper bounded by (16) and loosely lower bounded by the (21) (see Appendix B).
By (19), the SEP of the overall system is upper bounded by begin{array}{*{20}l} P_{Etext{to}E}^{mathcal{R}} le frac{3}{2}Qleft({sqrt {2gamma beta_{min }^{mathcal{R}}}} right) = frac{3}{2}Qleft({sqrt {2{gamma_{min {mathcal{R}}}}}} right).
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In this section, we prove that the pth moment of the solution of system (1.2) is upper bounded, and then discuss the stochastic permanence and extinction.
The primary aim for each loading scheme under consideration is to increase the total system value, which is upper bounded by K = 15.
It's all about the middle-class system: Susan is upper-middle-class, Beverly and Laurence are the real middle class, and then Tony and Angela are the lower middle, they're desperately trying to fit in.
The sum MMSE of the MIMO relay system with the direct link is upper bounded by the sum MMSE of the direct link and source-relay-destination link.
For any linear JNCC, applied in our system model, the diversity order d is upper bounded as d ≤ d R = 1 + t min. We use the diversity equivalence between a BF channel and block BEC [24, 25].
The resultant system is fully coupled whereby upper reinforcement layers are affected by the behavior of lower layers.
The most complex trading system is that of the upper Xingu; it includes a dozen tribes, each with its own products.
The extent of approximation introduced by this method of decoupling the system is evaluated, and tight upper bounds on the norm of errors are derived.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com