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The rest of the elements of (mathcal{C }) do not make any difference to the statements; e.g., we may just set the weights corresponding the points not so chosen to be (0).
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represents the subspace corresponding to the points not in S. Note the use of "finitely enumerable" here.
Theoretical analysis and numerical simulations show that the investigated system outperforms the corresponding point-to-point system under the same condition.
Then the user could choose any two stations as the start location and the destination by typing the names of the two stations or clicking the mouse at the corresponding points on the screen.
In order to explore this possibility, we plotted, in Fig. 4(a), the pixel values of the corresponding points in the d⊥ versus the confocal image.
This distortion is manifested in inadequate spatial relationships between pixels in the image and the corresponding points in the scene.
Thus, they compute the distances between the corresponding points in the real-world 3-dimensional space.
Müller argues that for each point seen in stereoscopic vision, the two signals from the corresponding points on the two retinas are projected onto a single point.
The biological (evolutionary) distance between two genomes can be obtained through the Euclidean distance among the corresponding points in the genome space.
The latter are attached to the patient's head before the brain scan, and a three-dimensional digitizer matches them to the corresponding points in the image.
Three-dimensional coordinates were determined by finding the corresponding points within the profilometric data set.
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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