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If the incident and refracted rays are extended to intersect any line SS parallel to the normal, the lengths PQ and PR along the rays will be proportional to the refractive indices n and n′.
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It is convenient to discard any set (C_{k}) which does not intersect any of the lines (L_{1}, L_{2}, ldots, L_{r}).
It is convenient to neglect any set (C_{k}) that does not intersect any of the lines (L_{1}, L_{2}, ldots, L_{r}).
Since (T_{1}(0,delta ') = delta '), the unstable invariant curve through ((0, delta ')) intersects any vertical line (x = x_{0}) with (0 < x_{0} le delta ').
This picture will make it clear: Make another line intersecting any of the four lines of the given plane and use the same technique as above to create a plane,just make sure that the parallel line for this intersecting line intersects the opposite parallel line for the first plane.
If (B=(c,d]times r,delta]) intersects any of the lines, suppose these are (L_{s},L_{s+1},ldots,L_{t}) ((1leq sleq tleq r)).
If (B=(c,d]times r,delta]) intersects any of the lines, suppose that these are (L_{s},L_{s+1},ldots,L_{t}) ((1leq s< tleq r)).
Each TH-positive cell with its nucleus included in the probe or intersecting any of the acceptance lines was counted.
Let all this horizontal lines intersect the vertical line.
Let all these horizontal lines intersect the vertical line by their middle.
If the horizontal line does not intersect the vertical line, the test is significantly different from the overall mean LOR.
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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