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Exact(33)
He provided elegant results for the summation of series of squares and cubes.
A key to trading cycles is to look for the summation of cyclical swings in the same direction.
For the summation range from 230 to 300 km, the horizontal distance between the tangential points is about 330 km.
The restriction on m d,F is because of m d,F − 1, as an upper limit for the summation in (21).
Since ε is a scalar multiplication constant for the summation in the second term on the RHS of Equation 20, the term remains the same.
The denominator on the right-hand side accounts for the summation of the average noise power in all subcarriers, when the length of the equalizers is one.
Similar(27)
Some notes: In our theorems, the range of the summation for m is from 0 to h.
If a time point of either the SC or LGN signals had a negative value, that time point was excluded from the summation for both structures.
The time range for the summations in Equation 1 is the same as that for the child time windows, and tpre and tsig represent the sample time periods preceding and succeeding the arrival time (t = 0), respectively.
The i and j are dummy variables for the summations, we have added clarification for this in the text.
where the kernel is a nonnegative measurable function defined for and the summation is over all ordered -tuples.
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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