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Then we show the regularity of the integration map that convolves functionals with the partial measures of the finite range decomposition.
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One may note that the inhomogeneous approach relieves the considerations with regard to the regularity of the interval length, and an integration is done over elapsed time after the beginning of the study.
To solve this difficulty, we had to assume that the function p is regular enough; this allows us, via an integration by parts to increase the regularity of the nonlinear term N ( t ) at the expense of Lipschitz regularity on p. Step 1. Proof of ( 21 ) and ( 22 ).
To deal with the issue of dimensionality in a complex problem, we use either Monte Carlo sampling or sparse quadratures for the integration over the prior probability density function, depending on the regularity of the integrand function.
The latter involves the spatial integration of the source term, analytically manipulated to take advantage from the regularity of the free-surface elevation, usually smoother than the bottom elevation.
Movement professes the regularity of the bar line but violates that regularity at every moment.
We loved the comforting regularity of the side-dish pairings.
It happened with the frequency and regularity of the equinoxes.
Kelly makes jokes about the regularity of the old men.
"It was meant to break the regularity of the building.
High pH value benefits for the regularity of the products.
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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