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The precipitation-deformation correlation and the samples absolute deformation monitoring showed a common expansion mechanism for the different cement compositions.
Our results showed that caleosin genes from different species did not share a common expansion model.
Additionally, several segmentally and tandem-duplicated gene pairs were identified from seven species, and further analysis revealed that caleosins of different species did not share a common expansion model.
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Besides common expansions, a significant number of lineage-dependent family expansions were observed (Additional file 1: Figure S5).
The 2D subspace problem is easy to handle, as shown above; but the search for (18) may be quite difficult, because the projection operator would make the objective function nondifferentiable and lose the common Taylor expansion, consequently it is nontrivial to search for proper stepsize α.
Using the decay estimates on the differences of the functions (u^{mathfrak{d}_{p}}) and (f^{mathfrak{d}_{p}}), we show the existence of a common asymptotic expansion (hat{u} epsilon) = sum_{m geq0} h_{m} epsilon^{m}/m! inmathbb {F}left[hspace{-1.8pt}left[epsilonright]hspace{-1.8pt}right]) (resp.
This insight into the sources and pathways of common ragweed expansion may help to better understand its invasion success and provides baseline data for future studies on the evolutionary processes involved during range expansion in novel environments.
In addition, we noted that each sequence showed more intra-species rather than inter-species homology suggesting that although the sequences in each species had originated from a common ancestor, expansion in the number of family members had occurred after the species had diverged [ 14].
The most common such expansion is of a CAG repeat encoding glutamine, resulting in the 'polyglutamine diseases' which include Huntington's disease (HD), spinal bulbar muscular atrophy, dentatorubral-pallidoluysian atrophy and spinocerebellar ataxia (SCA) types 1, 2, 3, 6, 7 and 17 (Fig. 1).
The CGG repeat would be replicated on the lagging strand template, which would predict that contractions of CGGs would be more common than expansions.
It appears that these functions share a common formal asymptotic expansion in the perturbation parameter.
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