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On the real number line, the only path between two points a and b is the interval whose ends they form.
However, f is defined over a continuous interval whose samples are infinite dimensional vector.
Let (B_{1},ldots,B_{s}) be Borel subsets of the unit interval, whose boundaries have zero Lebesgue measure.
A set of articulatory targets is searched for each segmental interval, whose boundaries are manually defined before optimization.
HFLTS is described using envelope method within linguistic interval whose upper and lower bounds are shown as ((H_{S^ )) and ((H_{S^ )), respectively.
Let (B_{1}, B_{2}, ldots, B_{s}) be Borel subsets of the unit interval whose boundaries have zero Lebesgue measures.
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Specifically, the set of all rational numbers can be surrounded by a collection of intervals whose total length is as small as is wanted.
"You have to be sensible," he said in a telephone interview, "and remember that most of your singers won't have perfect pitch, so you don't give them intervals whose purpose they might not understand or get right.
We have the following results concerning local existence theory on bounded intervals whose existence can be found in [11, 17 19].
First, it introduces extra-attenuation around the so-called folding bands, i.e., frequency intervals whose spurious signals are folded down to baseband during the decimation process.
Thanks to the property (9), these sets form a family of nested closed non-empty intervals whose diameter tend to 0 as (nto +infty).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com