More precisely, for large degrees d the probability that a randomly chosen polynomial is irreducible is about 1/d.
The p-value is approximated using the asymptotic behavior of (complete and incomplete) Gamma functions for large degrees of freedom, M = 9999.
Our computations required up to 25,000-digit precision, and, for large degrees and correspondingly high precision levels, were rather expensive (over 20 processor-hours in some cases).
To our best knowledge, this value is optimized for photonic crystal sensors array by now and it means our design is a promising candidate for large degree of multiplexing sensing.
Therefore, for small degree authors, the degree differences between those authors and their neighbors are small, and large for large degree authors, which leads to the trend change of (mathrm{DN} k)).
Numerical experiments illustrate the validity of this approach for larger degrees of the filter as compared to similar previous algorithms.
Furthermore, the non-linear model requires computationally more time and effort, especially for larger degrees of freedom system.
For high volume fractions of the network chains (φ > 0.8) the untangled oligomer shows the same degree of orientation as the network, while for larger degrees of swelling the oligomer orientation is smaller than that of the network chains.
He believed for relatively small degrees of shortening the best approach involved acute "forced lengthening, practiced under narcotics…" But for larger degrees, "…it would be dangerous…" [ 2].
To enhance the effect and reduce the recurrence of AHP, modification or augmentations of Parks' dosage were reported by Calhoun and Harley [ 5], Nelson et al [ 19], and others for larger degrees of AHP [ 15– 17, 22, 23, 26, 28].
However, whereas 2 LOD intervals are conservative for two line crosses, the necessary LOD drop increases for larger degrees of freedom in the model (Manichaikul et al. 2006) and we have previously shown they are overly liberal for our 8-way crosses (King et al. 2012b).
