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Exact(10)
Obviously, for any polynomial p, f, (Delta_{c}f), and (Delta_{c}^{n}f) share p and ∞ CM.
We say that f and g share p CM, provided that (f z -p z)) and (g(z)-p(z)) have the same zeros counting multiplicity.
If for each pair of functions f and g in ℱ, P ( f ) f ( k ) and P ( g ) g ( k ) share p ( z ) in D, then ℱ is normal in D. Lemma 2.1 (see [14]).
Since f ( z ) and g ( z ) are entire functions of order zero and share p ( z ) CM, we have F ( z ) − p ( z ) G ( z ) − p ( z ) = η, (11).
If n ≥ 2 d + 2 and for each pair of functions f and g in ℱ, f n f ′ and g n g ′ share p ( z ) in D, then ℱ is normal in D. In 2012, Wu and Xu [13] got the following theorem.
If for each pair of functions f and g in ℱ, f f ( k ) and g g ( k ) share p ( z ) in D, then ℱ is normal in D. Remark 1.1 Theorem 1.1 still holds when p ( z ) is a nonzero finite constant.
Similar(50)
Breastfeeding and household tobacco use were significantly associated with bed-sharing (p = 0.003 and p = 0.04, respectively).
Participants with unstable housing were less likely to report use of methadone (p = 0.014), to report syringe sharing (p = 0.027) and to use heroin daily (p = 0.013).
Also, women who injected themselves reported lower Injection Burden then when this was done by the husband or shared (p = 0.002).
We find a highly significant sharing (P = 2.28e-20) of segment and interaction domain endpoints, with 60.8% (571/939) of interaction domain endpoints also being segment endpoints.
Despite a singular report of the only other shared P lineage, the youngest and elsewhere predominant P1, this contradicts an origin of haplogroup P in central/southern Sahul (Australia) followed by (back- migrations to northern Sahul (NG).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com