Sentence examples for pap functions from inspiring English sources

The next section is on preliminaries including the definition and properties of pap functions, boundness of the output of (1) and the generalized Halanay inequality.

We also found that PAP functions in nociceptive circuits as an ectonucleotidase by dephosphorylating adenosine monophosphate (AMP) to adenosine [3].

When taken together, our findings suggest PAP functions as an ecto-5'-nucleotidase (with relative selectivity for AMP) at neutral pH and as a generic ectonucleotidase (with selectivity for AMP, ADP and ATP) at acidic pH.

The solution of (1) is not necessarily pap for a general pap function (a_{ij}(cdot)).

Moreover, we found that PAP functioned as an ectonucleotidase with relative specificity adenosine 5'-monophosphate [17], [18].

Let us start with the construction of μ-paa (μ-pap) functions through convolution.

Meanwhile, it known that two spaces of μ-paa (μ-pap) functions are the same if the measures of the spaces are equivalent.

We notice that many applications of μ-pseudo almost automorphic (periodic) functions (abbr. μ-paa (μ-pap) functions) are based on the uniqueness of their decompositions, and this relies on the translation invariance of this kind of functions.

Furthermore, by Theorem 3.2 and similar arguments of the proofs of the corresponding results in [19, 20], we can obtain the following properties of μ-paa (μ-pap) functions.

Especially, a pseudo almost automorphic (pseudo almost periodic) function is a μ-paa (μ-pap) function with μ the Lebesgue measure.

Especially, a pseudo almost automorphic (pseudo almost periodic) function is a μ-paa (μ-pap) function with μ the Lebesgue measure.  .