Sentence examples for elementary properties for the from inspiring English sources

In this section, we state some elementary properties for the (weighted) variable exponent Lebesgue-Sobolev spaces which will be used in the next sections.

In this section, we state some elementary properties for the variable exponent Lebesgue-Sobolev spaces which will be used in the next sections.

Next, we collect some elementary properties for Riemann-Liouville fractional integral and derivative.

Now, we state the following result summarizing the elementary properties of the mean-map (mlongmapsto m^{ q)}) for (qin 0,1)).

Based on elementary properties of the discrete Fourier transform, simple rules for the change of the coefficients c k under translation, scale, and rotation immediately follow.

Using the Alzer integral inequality and the elementary properties of the gamma function, a double inequality for gamma function is established, which is an improvement of Merkle's inequality.

A study investigating the elementary properties of the resultant mean-map has been stated in [1].

The following lemma states elementary properties of the function Φ, see Definition 2.3.

The elementary properties of the mean-transformation m ⟶ m π t are summarized in the next result.

We can find the definition and some elementary properties of the fractional Laplacian operator in Yosida [2].

We end this section by stating the following result, which summarizes some elementary properties of the index.