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Then, by Theorem 3.2, every increasing f : [ u 0, v 0 ] → ℓ 2 has a minimum best approximation point and a maximum best approximation point with respect to W ( x, y ) in [ u 0, v 0 ].
In the first best approximation theorem, we establish a sequence { x n } which converges strongly to the unique best approximation point; while in the second best approximation theorem, we obtain the existence of a minimum best approximation point and a maximum best approximation point in order intervals.
Then, f has a minimum best approximation point x ∗ and a maximum best approximation point x ∗ with respect to W ( x, y ) in [ u 0, v 0 ], such that u 0 ⪯ u 1 ⪯ ⋯ ⪯ u n ⪯ ⋯ ⪯ x ∗ ⪯ x ∗ ⪯ ⋯ ⪯ v n ⪯ ⋯ ⪯ v 1 ⪯ v 0, (3.18).
Given u 0, v 0 ∈ L 2 such that u 0 ≺ v 0 ; then, by Theorem 3.2, every increasing f : [ u 0, v 0 ] → L 2 has a minimum best approximation point and a maximum best approximation point with respect to W ( x, y ) in [ u 0, v 0 ].
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where | D 1 | = ∑ ( i, j ) ∈ D 1 1 is the number of pixels in D 1, and | D 2 | = ∑ ( i, j ) ∈ D 2 1 is the number of pixels in D 2. If the energy F reaches a minimum, the best segmentation results are obtained, i.e., the subregion D 1 and subregion D 2. It is noticed that since the selection of D 1 and D 2 is arbitrary, there are lots of pairs ( D 1, D 2 ), so minimizing the energy F is difficult.
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We did the minimum best, then raised our game if we could.
Figure 7 shows the comparison of our results to the median, average, and minimum (best) in original TRECVID2011 MED task.
The detector module׳s mean, standard deviation, minimum (best) and maximum (worst) energy resolution were 10.19%, ±0.68%, 8.36% and 13.45% FWHM, respectively.
'Median,' 'Average,' and 'Min' is the median, average, and minimum (best) of MinNDCs over 60 runs submitted in TRECVID2011 MED task, respectively.
And the wrong idea is end design or destiny, maximum, minimum, best, least, and so on.
Write better and faster with AI suggestions while staying true to your unique style.
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