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In the following, we try to solve the problem by alternating the optimization in P (holding Φ constant) and Φ (holding P constant).
The p values (student's t-test) for maximum CSF movement with deep inhalation and deep exhalation are significant when compared to breath holding, p < 0.001 and p < 0.001, respectively.
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Theorem 3.1 Assume that (H) holds, P is normal and for any x ∈ P, A φf)∞ > Bf0.
"I had a gun and so did Ghassemlou... We did not tell the Iranians where the meetings would be held" (p. 219).
Suppose also: (p′) T and g are ( d, ≼ ) -nondecreasing-continuous and commuting atd, at least, one of the following conditions holds: ( p 1 ′ ) T is a ≼-nondecreasing mapping.
( p ˜ ′ ) T and g are ( d, ≼ ) -nonincreasing-continuous and commuting atd, at least, one of the following conditions holds: ( p ˜ 1 ′ ) T is a ≼-nonincreasing mapping.
For an arbitrary matrix M of size K×K, the following relationship always holds, p T M p = c T M ̲ c, (14).
If the manifold ( M, g ) is simple, the following factorizations hold: P - = - 1 2 π I δ ⊥ I 1 ∗, P + = - 1 2 π I 1 ∇ ⊥ I 0 ∗.
E held P's feet fixed to the couch.
E held P's thoracic and lumbar spine fixed to the back support of the chair.
However, the trends did not hold (P > 0.05) for 1-methylethyl GS, another common, but much less abundant, GS.
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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