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Unlike differentiation where analytic solutions can usually be computed, in general finding exact solutions to differential equations is very hard.
We show how such descent directions can be computed in general Lebesgue and Besov spaces, and argue that in the Besov space case determination of descent directions can be interpreted as nonlinear wavelet filtering of the adjoint field.
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Firstly, the relevant visual features are computed, in general forming feature vectors for each video frame as described in Section 1.2.
Statistical significance of differences in mean neuronal volumes in the dup(15) autism, idiopathic autism, and control groups were computed in general linear mixed models using the mixed procedure in version 13.1 of the Stata statistical package [ 65].
The statistical significance of the differences in mean neuronal volumes between autistic and control brains and between pairs of age ranges was computed in general linear mixed models adjusted for autocorrelation of neurons within each brain using the xtmixed procedure in version 12 of the Stata statistical package.
The statistical significance of the differences in mean neuronal volumes between autistic and control brains and between pairs of age ranges was computed in general linear mixed models adjusted for the autocorrelation of measurements within each brain by using the xtmixed procedure in version 12 of the Stata statistical package [ 41].
Instead of the OI that we used in the prestructured version of the SOT, some distance-based index (DI) could be computed in this general version of the SOT.
The parameter values have been computed in standard units for general relevance across different setups, a feature absent in earlier studies.
The groups πn+k(Sn) with n > k + 1 are called the stable homotopy groups of spheres, and are denoted πkS: they are finite abelian groups for k ≠ 0, and have been computed in numerous cases, although the general pattern is still elusive.
By applying the linear Eulerian theory of stability, the critical solution with discrete variables for general truss structures is computed in this paper.
The general Satterthwaite approximation was computed in a mixed-effects regression model (PROC MIXED), with breed, diet and their interaction as fixed effects.
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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