The mapping is non-invertible since many sequences fold into the same minimum free energy (secondary) structure or shape.
Utterance copy is a difficult inverse problem because the mapping is non-linear and from many to one.
Based on the Cauchy-Schwarz inequality, it is not hard to show that a firmly non-expansive mapping is non-expansive.
On the sound side, a strong version of the sound-based hypothesis would predict that in a language like English, where the orthography-to-phonology mapping is non-transparent, abstract letter representations should be substantially more complicated than in a language such as Finnish, where sound-to-symbol correspondences are almost completely one-to-one.
In order to establish that the general fibre of the Albanese map is non hyperelliptic, it suffices to prove the following lemma.
In this article, it is also proven that the distance between the adjacent subsets A i, Ai+1⊂ X are identical if the p(≥ 2) -cyclic self-mapping is non-expansive [16].
It is interesting to note that the coupling Lindbladian in Eq. (37), though it generates a completely-positive trace-preserving map, is non-Markovian.
This is particularly helpful if the orientation of your map is non-traditional, such as having North located near the bottom.
Microfiche, software, audio/visual material, maps are non-circulating.
The estimated FA maps were non-linearly registered to a standard MNI template.
All remaining markers used in the LepR3 map were non-polymorphic in the 'Topas' x 'Glacier' population.
