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A Finsler metric on M is a function F : T M → [ 0, + ∞ ) satisfying the following properties: (i) Regularity: F ( x, y ) is smooth in T M ∖ 0. (ii) Positive homogeneity: F ( x, λ y ) = λ F ( x, y ) for λ > 0. (iii) Strong convexity: The fundamental quadratic form g : = g i j ( x, y ) d x i ⊗ d x j, g i j : = 1 2 [ F 2 ] y i y j .
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(i) Imperfect Regularities.
If I go to visit EPA's smart growth office, as I do with some regularity, I have to walk all the way around their huge building to get to an entrance that visitors can use, identify myself, go through a metal detector, and wait for an escort to come down to the entrance and take me up to the office.
The entities described by the mathematical formalism seemed to fit the picture of a collection of fluctuating processes organized into apparently stable structures by statistical regularities — i.e., by regularities of comportment at the level of aggregate phenomena.
Because (a) regular and irregular items were matched on all other factors but regularity (i.e., full-form frequency, lemma frequency, length, etc)., and (b) LANs have been found for misapplications of rules in this and previous studies, we conclude that our LAN for correct regular verbs reflects rule application, which is present for regular participles but not for irregular participles.
Now, I do not blame Williams for not tuning in, because they are awful, but I watch them with regularity, and I can tell you, authoritatively, that this has all been fulsomely discussed.
We prove regularity (i.e., smoothness) of measuresμon Rdsatisfying the equationL*μ=0 whereLis an operator of typeLu=tr(Au″)+B·∇u.
White Regularity is congruent to all other forms of regularity i.e. Black, Brown, Etc etc.
For example, we described aspects of institutionalization (i.e., regularity of performance monitoring activities) and of benefits (i.e., recognition of improved patient outcomes).
The lowest prevalence can be seen in those elderly individuals performing sports activity with high intensity and regularity (i.e., >2 h weekly).
In the second (meaningless), the differently oriented lines were collinear, lending the images a recognizable regularity (i.e., collinearity) even though they were still nonsense objects (Fig. 1).
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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