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Exact(27)
If either directional derivative is negative, then we solve for the minimum along the corresponding direction.
The ball instantly rolls in the corresponding direction; your finger's distance from center controls the speed.
Each value in the tern is a measure of the nucleus alignment in the corresponding direction.
u i,i ∈ {x,y,z} describes the movement in the corresponding direction.
Therefore, if Δϕ and Δθ are small, the corresponding direction finding precision is satisfactory.
Fig. 11 Largest γ value and axes direction of the largest and smallest amplitude for the corresponding direction.
Similar(32)
where and are the and components of the velocity or optical flow of respectively, and and are the derivatives of the image at in the corresponding directions.
To do so, a unit load is applied on the centerline of the rail head in the vertical direction and another in the lateral direction, for calculating the displacements caused in the corresponding directions with the FEM model.
Thus, the singular vectors give a geometric description of where the trajectory lies, and the singular values are a measure of the extent of the trajectory in the corresponding directions.
Assuming (10) holds true, it is seen that part of the cosines in (7), namely those associated to values of k close to the ends of the interval (−⌈N/2 − 1⌉, ⌊N/2⌋) become greater than one in absolute value, i.e., the corresponding directions ϕ k are not real.
FTs of particle images yield a set of central sections in the corresponding directions.
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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