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The above Hao Z-C inequality is refined by using Corollary 2.7 as follows: Theorem 3.1.
These candidate lines were finally refined by using the Gaussian probability decision and distance metric decision.
For getting a more accurate transmission map, it is refined by using a guided image filtering.
In the subsequent search, values of design variables found from the preliminary search were further refined by using a nonlinear searching technique.
In the Akatsuki Level-3 data, spacecraft navigation data are refined by using a limb-fitting technique (Ogohara et al. 2012).
The spectra was further refined by using a delay time of 50 μs and gate time of 2 ms to avoid autofluorescence.
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To improve the electron beam confinement with an additional horizontal focusing force, the geometrical shape of the ferromagnet pieces were refined by use of a newly developed 3D code.
Alignments for each mtDNA and nuclear gene were generated using MUSCLE v3.7 [ 104], then refined by eye using the translated amino acid sequences.
Sequences were aligned automatically using ClustallW [ 30], and the alignment was then refined by eye using MEGA 4 [ 31].
The alignments were then refined by hand using MacClade 4.06 [ 86].
The rbcL nucleotide and protein sequences were prealigned with clustalw and refined by eye using the multiple alignment sequence editor SeaView [ 41].
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