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In this paper, a double-well potential functional is employed for distance regularization inside the topology optimization loop, which can enforce the signed distance property of the level set function in a narrow band along the design boundaries while keeping the level set function flat in the rest area of the computational domain.
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The variation in external noise produced curves with the typical structure of TvC functions, flat at low levels of external noise and increasing at higher levels of external noise.
Open image in new window Fig. 10 Maximum von Mises equivalent stress versus a function of flat length Open image in new window Fig. 11 Maximum equivalent plastic strain versus flat length.
That one-dimensionality is also a function of flat and occasionally tone-deaf writing, which hits a low point when a cop says, at a particularly tragic juncture, "Sometimes I think the world is held together by nothing but God's tears".
One can see that the function gets flat fast.
This is reasonable, since the logistic function becomes flat when (vert Vvert ) is large.
In contrast, the initial likelihood function was flat and thus difficult to optimize.
Open image in new window Fig. 2 Schematic of transforming influence function from flat seam to inclined seam.
First, if the wholesale electricity supply function is flat, then the peak-time electricity price could become even lower than the default price.
Another interpretation of the supply equations is that the long-run supply function is flat implying firms set price as a mark-up of their cost.
The transformation involves a mathematical projection of the symmetric influence function for flat seam, f s, onto the inclined seam to form the new asymmetric influence function of f′ s as shown in Fig. 2.
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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