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The LLRs delivered by the IC are, hence, very small.
In the case k=0 and l=0, the received signal comprises of noise only and the PDF for both limiting and nullifying detector is hence {small{begin{aligned} p z_{C,0}|H_{0})& = frac{beta (1-c)}{2sqrt{2 pi z_{C,0}} sigma} e^{-frac{z_{C,0}}{2 sigma^{2}}} Pi 0, eta) &quad+ (1-frac{sqrt{eta}}{b}) c beta delta z_{C,0} - kappa eta).
The finite-size effects are hence of smaller order.
Alignment constants of the sensitive coordinates are determined to submicron precision and are hence much smaller than the intrinsic resolution of the detectors used.
For larger values of γ, the length of a domain in the denominator is amplified, hence, smaller domains would produce larger objective values than bigger domains with similar interaction frequencies.
If d f >l, the exponential argument is negative and hence small, so the first term is approximately k 1.
In this case the ionic concentration in the CNTs' cavities is rather low (1 mM); hence, small gold nanoparticles were formed (2- to 10-nm mean diameter).
The number of training cases required for near optimal classification for such datasets is smaller and hence smaller proportions devoted to the training set could be near optimal (for n = 100 - 200).
The Cu-Cu distance is small hence it is also considered as a bond.
The size of the device is small hence it can be applicable for Dense Wavelength Division Multiplexing in Photonic Integrated Circuits (PICs).
We assume that the difference between any pair of disordered mode frequencies is small, hence the resonance condition is almost satisfied.
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