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The resulting algorithm thus maximizes the robust stability margin and simultaneously synthesizes smooth weights along with a stabilizing controller.
For accurate fitting of transfer functions to magnitude data, smooth weights also allow low-order transfer functions to be used when such smooth variations in their magnitude responses are computed point-wise in frequency.
The background noise contribution to the log ratio of intensities in channel 1 and 2 is thus proportional to 1 / SNR 1 2 + 1 / SNR 2 2. A SNR filter can be supplemented with filters in other variables, and much more elaborate spot quality tests exist [ 13, 15, 19, 20], which could be turned into smooth weights confined between 0 and 1 (as was done in [ 13, 15]).
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That is, we first establish the multiplicity of positive solutions for nonlinear elliptic equations with a positive smooth weight function involving concave and convex nonlinearities in weighted Sobolev spaces, and the proof of the two positive solutions for the problem ( E λ f, h ) is given.
Suppose also that (e^{-varphi }) is a smooth weight function on (Omega ).
These values seemed to be sufficient for obtaining a smooth weighting function.
Different sets of controllers combined by smooth weight functions are used for the plant at different load conditions.
Perez and Palacin proposed an estimation for a quantile function by using the Bernstein polynomials as smooth weight functions [9].
Let (Omega ) be a domain with smooth real codimension-(1) boundary with Levi defining function (rho ), and let (e^{-varphi }) be a smooth weight function.
For the second level, the binary mask marking the specular regions in the image is converted to a smooth weighting mask.
A low cost solution that we propose in order to return to pseudo-elliptical apertures consists of applying a smooth weighting function rather than an on-off function to select the data that will contribute to focusing a point in the migrated space.
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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