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Both properties can be proven in exactly the same way as in [34], Corollary 7.4, thus we only sketch the proof for (X^{mathrm{w}}): (i) Smoothness of the transition probability densities: Due to Assumption (10) the transition probability of two (or more) consecutive steps (psi^{mathrm{w}}_{Delta t}circpsi^{mathrm{w}}_{Delta t}) of our integrator has a smooth density.
(i) Smoothness.
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A key issue that needs to be considered is how to determine the degree of smoothness (i.e., smoothing parameter, λ) in the smoothing process.
I lacked the smoothness of a guy I once saw who sat next to an attractive girl, peeked over at her loose-leaf binder, and after a minute turned and said, "Malaria!
Once I've accomplished the above foot smoothness, I always use a foot and leg spray at both the beginning of the day (unless running late) and always at the end of the day.
We prove regularity (i.e., smoothness) of measuresμon Rdsatisfying the equationL*μ=0 whereLis an operator of typeLu=tr(Au″)+B·∇u.
Traditional FGS rate control techniques lack a systematic approach to making tradeoffs between image quality, motion smoothness (i.e., the frame rate), and video smoothness (PSNR difference between consecutive frames), according to limitations on system resources and users' preferences.
Several authors have obtained estimates of the upper constant (K_{2}) in (1) for the ordinary second modulus of smoothness, i.e., for (sigmaequiv1).
Edit boxes in the "Deconvolution" panel are used to set the "Tolerance for ABIC optimization", as well as the initial values for ln u) (i.e., smoothness), position shift, and length correction.
The most important feature when choosing a covariance function is its smoothness, i.e. how much the value of the function sampled at a point x ∗ correlates with the same function at points close to x ∗.
The algorithm searches for the optimum solution efficiently in the three-dimensional parameter space (i.e., smoothness, position shift, and length correction) using "Reflection", "Expansion", "Contraction", and "Reduction" of tetrahedrons depending on the values on the nodes without information of gradient at each node.
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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