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Exact(13)
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.
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.
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.
While these studies aim to find the intermediary's optimal strategy (e.g., in terms of revenue or platform value) to invest in IT improvements, quality, or marketing strategies, our paper searches for the revenue-optimal split between the two user groups, after empirically proving all corresponding directions of network effects, considering fixed user fees.
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.
If the angle of departure (AOD) and angle of arrival (AOA) of the paths are integer multiples of 1/L r and 1/L t, most of the entries of channel matrix in angular/spatial domain are 0. Otherwise, some entries of channel matrix in angular/spatial domain are not 0 because of the leakage effect even though there are no paths in the corresponding directions of the entries in channel matrix.
Similar(46)
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.
Joint statistics of the radius vector magnitude and the corresponding direction vector constitute the basis for the present approach.
To obtain the direction of the frictional force vector, the relative velocity vector between the polishing pad and the wafer with corresponding direction was simulated.
From the prediction of radiated power, it is found that the vertical and lateral bending waves of the rail radiate most of the noise for the corresponding direction.
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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