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Our approach presented below works as long as we can neglect edge effects, i.e., X ˜ i ∗ = X i ∗ for most i.
A system like the below works well, and also keeps your house clean!
My photograph of tyre tracks on a beach in Deauville (below) works on the same principle.
Charles Burchfield did so, and Winslow Homer's watercolors are preferred in some quarters to his oils, but, because watercolors are on paper, the art market has always priced them well below works on canvas.
The proof below works for any field of characteristic zero.
The hard drive enclosure below works, in general, the same way.
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Below are works by Anna Gensler (top) and Amy Kurzweil (bottom). .
If I can keep all those people working together, you find out that the people below work all together.
The days of buying properties below working capital are long gone.
All arguments used below work unchanged in the general case, too.
Watch Chef Wentworth below working his magic with Octopus Confit.
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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