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The techniques for doing this can be found in the papers [20 24] and the details are left to interested readers.
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Here, #(·, str) means the number of occurrences of the string str in the interested CEM, right(·, n) and left(·, n) denote the substring with the length of n right or left to the interested CEM, and offset(·, start) and offset(·, left) indicate the start or end offset of the interested CEM.
More examples are left to the interested readers.
Future works are left to the interested readers.
However, the details are left to the interested reader.
The statement and the formulation of the results are left to the interested reader.
The details of the application of (2.23) will be left to the interested reader.
Similar results may be stated for the convex function with However the details are left to the interested reader.
In [9], Radha and Thangavelu gave the following theorem, but the proof is left to the interested reader.
for any u ∈ R. Similar results may be stated for the finite Fourier-Stieltjes cosine transform, however the details are left to the interested reader.
Using similar techniques to the proof of the previous theorem, one can express the degenerate poly-Cauchy polynomials in terms of other families, for instance, Frobenius-Euler polynomials (the proof is left to the interested reader).
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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