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We can think about the new functions [x]n as a new basis in the linear space of polynomials.
The condition for a point to be classed as outside the current basis vector and selected as a new basis vector is derived and embedded in the recursive procedure.
If these 3 elements are now taken as a new basis instead of 0 and 1, a clever construction shows that 7 \((= 2^{3}-1)\) such sets exists and, in a next step, 127 \((= 2^{7}-1)\) pops up.
In fact, this article was driven by a startup press release I saw recently, highlighting a startup's "geo-fencing technology" as a new basis for discount coupons.
Indeed, elucidating the mechanisms of cell death and of their regulatory pathways has now emerged as a new basis for future breeding strategies aimed at cell survival, of interest for biotechnology.
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These data are of importance as they can provide a new basis for the rationalization of a therapeutic strategy for this disease.
If it works, it could help to put transatlantic relations on a new basis, rather as Mr Bush's policy has already done with Russia.
These data suggest that this approach is effective, and may be adopted into routine care and should serve as a new pathophysiological basis for the management of decompensated refractory CHF.
Therefore, guaranteed food safety information and attributes should emerge as a new index and basis for future trade in the beef industry.
Two-dimensional orthogonal triangular functions are used in [3, 18] as a new set of basis functions to approximate solutions of nonlinear two-dimensional integral equations.
(4) If the basis for payment is revised as the result of a reconsideration, the new basis for payment is final and is not subject to further reconsideration.
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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