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If no mapping exists, then additional processing is required to identify similarities and overlap.
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Mathematically, it is said that the points on the sphere are mapped onto the plane; if a one-to-one correspondence of points exists, then the map is called conformal.
If God exists, then something exists.
It barely existed then".
If a transcript was mapped to multiple genomic loci, then only the best mapping was retained; if more than one nearly identical best mapping existed (difference in BLAT scores < 5%), then the transcript was discarded to avoid ambiguity.
Now, we use Theorem 3.3 with a mapping A, then there exists a unique PPF dependent fixed point φ ∈ S ( F 0 ) of A, that is, A φ = φ ( c ) and α ( φ ( c ), A φ ) ≥ 1.
From S E) = S X) is complete and (3.16) and (3.17) are holds, we use Corollary 3.3 with a mapping Θ, then there exists a unique fixed point z ∈ S X) such that Θz = z.
If we additionally suppose that f is a harmonic mapping, then there exists a holomorphic function (g:mathbb {H}to mathbb {C}) such that (f z)= operatorname {Re}g z) +icy).
If is a continuous mapping, then there exists such that for all.
If is an order contraction mapping, then there exists a unique random fixed point in.
If T is a generalized weakly contractive mapping, then there exists a unique (z in X) such that (z=Tz) and (varphi z)=0).
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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