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Numerically, they yield two solutions, neither of which may be demographically valid.
Equation (8) yields two solutions, as shown in Eq. (9).
The general kinematics function is shown to yield six solutions.
Refinement of the data set by maximum-likelihood methods yielded three solutions, one major class comprising 42% of the molecules selected for representation in Figure 5 and two other classes representing 30 and 28% of the data set.
(Which is why Dirac's equation actually yields four solutions, one for each possible combination of spin and charge).
This then yields four candidate solutions of (I j,α j ), and the candidate that maximizes the likelihood in Equation 4 is selected as the solution of the examined pel.
However, one can note that the algorithm may yield four, at most, solutions of the point p (x, y, z), and this can be explained as follows.
From Kelly's research, these new solutions yield forty times performance improvements around query.
Since in an integral domain a·b = 0 implies that either a = 0 or b = 0, the simpler equations x − 2 = 0 and x + 1 = 0 can be solved to yield the two solutions x = 2 and x = −1 of the original equation.
The crates yielded two copies of the Green statue.
This yields two kinds of problems.
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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