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And marketing experts say that--almost by accident--McDonald's was among the first major fast-food operators to make use of a formula that costs little but pays huge dividends in customer count: limited time promotions.
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Applications are constructed by making use of a transformation formula for fractional derivatives as well as generalized fractional derivatives.
Our analysis makes use of an analytic formula for the irradiance in terms of spherical-harmonic coefficients of the illumination, and shows, under appropriate assumptions, that the principal components or eigenvectors are identical to the spherical harmonic basis functions evaluated at the surface normal vectors.
Siscoe et al. (2006) and Li et al. (2006) calculated Carrington's recovery from the results of their simulation using a solar wind structure that could have caused the Carrington storm development; they made use of an empirical formula, Burton's model (Burton et al. 1975).
The second representation is obtained by making use of a new transformation formula for the fractional derivative recently published by Tremblay et al. [16].
These representations are found by making use of a new transformation formula for fractional derivatives published recently by the authors [16].
Here we make use of this formula to (a) improve the accuracy of computing pressure in two kinds of existing time-discrete projection methods implicit in viscosity only, and (b) devise new higher-order accurate time-discrete projection methods that extend a slip-correction idea behind the well-known finite-difference scheme of Kim and Moin.
Schools with higher-needs children have received more dollars for each child, but because of budget cuts, the city has not been able to make use of the formula fully.
To derive over λ k, we make use of the formula of the n th derivative of the Lambert-W function given by (2).
They made use of a mixture of magic formulas, chants, and prayers and of traditional healing methods, such as administering medicinal herbs or bleeding.
The proofs make use of Duhamel's formula and dispersion estimates for the linear propagator, as well as chain and Leibniz rules for fractional derivatives of compositions ∥DαF u)∥Lp and products ∥Dα fg)∥Lp, 0 < α < 1 and 1 < p < ∞.
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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