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Furthermore, these condensed localizations on the C2 and C3 axes somehow exhibited reversed directions to one another; that is, increase on the C2 axis was always correlated with decrease on the C3 axis.
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Since is increasing on, then (2.41).
By Lemma 2.3, is increasing on,.
The function is increasing on,, and, for,.
Hence is increasing on, and therefore, is also increasing on this interval since is increasing on by.
So and is increasing on and the function is increasing on by Lemma 2.1.
Since is increasing on, (2.62) gives a unique satisfying (2.63).
Thus is increasing on and then the inequality (2.2) holds.
Thus, (a) has a minimum point in ; (b) is decreasing on ; (c) is increasing on ; (d).
Then, and is increasing on since a.e. on this interval by (1.9).
Now the pressure is increasing on one of the last sizeable holdouts — lands owned by Native Americans.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com