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We define note boundaries using both pitch and harmonicity functions by setting selection criteria.
Let be given and define Note that According to the assumptions, there exist neighborhoods of and of such that (25).
In these cases it is then natural to define, and, on recasting, we see that it is also natural for us to define (note that this is not consistent with our definition of above).
Since is separable and is -measurable, there exists a -measurable function satisfying that for every where means the Borel subsets of Now define Note that is an identically distributed sequence of -mixing random sets, and this leads to that is also of mixing dependence, since the definitions of mixing dependence rely on -fields.
Similar(56)
The orderer, generally, wishes to begin and end on a high, defining note; to mix weak with strong, shorter with longer, formal with free; and to lead the ideal reader along a certain contour of implied argument.
Fig. 8B shows an IRBC containing a ring-stage parasite; here, the parasite-related cluster (ii) is less defined (note the different scale) because of the small region occupied by the ring relative to the RBC cytoplasm (i).
The disclosure of diagnosis (DD), adherence and desire of a family are defining notes describing these patients.
Now, define and note that for.
Namely, let us define, and Note that the parameters satisfy condition Then, the best possible constant from Theorem 2.4 becomes from Theorem 1.1 (see also [4]).
The procedure to define the note patterns and the preprocessing stage required at the input of our PIC detector are described in the next subsections.
It has shaped our lives in many ways up to this point, and it will be a defining (note I said "a" and not "the") factor in the rest of our lives.
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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