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The vector S 0 represents the direction of the incident beam (– z -axis) and forms the radius of the Ewald sphere of length 1/ λ.
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We now have also learned that (4/3π)^(1/3) MEANS the constant of proportion of the volume of a cube equal in volume to a sphere of different basis length r.
Furthermore, Lazarides and Schatz calculated optical spectra for linear aggregates of 13-nm gold spheres of different lengths (up to ten spheres) [ 5].
For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π/2, and all its angles are right angles, which violates the Pythagorean theorem because a2 + b2 ≠ c2.
Now any sphere of endeavour can now be taken to those bafflingly convoluted lengths in the name of telly – lengths that would make most right-thinking individuals question the very sanity of the world.
All of the forces act within a sphere of cutoff radius r C, which also defines the system's length scale.
And you are a sphere, of course.
Yes – in the sphere of public authority.
Science falls outside my sphere of competence.
It hugs a single sphere of ice.
A sphere of aware light.
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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