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Here we present data on the Portuguese validation of the Functioning Assessment Short Test (FAST), which was explicitly designed to gauge functioning dimensions empirically linked to bipolar disorder.
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The loading and unloading process was repeated a few times and this procedure also helped to check whether the dial gauges functioned properly.
Such functions are called gauge functions or Minkowski functionals, and are well studied in convex analysis and functional analysis.
We note that a b-Bianchini-Grandolfi gauge function also satisfies the following functional equation: σ ( t ) = q σ ( φ ( t ) ) + t. (2.5).
where is a Bianchini-Grandolfi gauge function.
This function φ is called a gauge function.
We have shown that is a Bianchini-Grandolfi gauge function.
Consider the Bianchini-Grandolfi gauge function φ given by.
One of such gauge functions was introduced by Fang [16].
It is easy to see that every b-Bianchini-Grandolfi gauge function is also a Bianchini-Grandolfi [16] gauge function but the converse may not hold.
A gauge function φ : J → J is said to be a Bianchini-Grandolfi gauge function if ∑ n = 0 ∞ φ n ( t ) < ∞ for all t ∈ J [16].
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